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Article  |   November 2014
Complementary effects of gaze direction and early saliency in guiding fixations during free viewing
Author Affiliations
  • Ali Borji
    Computer Science Department, University of Wisconsin, Milwaukee, WI, USA
    borji@usc.eduhttp://pantherfile.uwm.edu/borji/www/index.html
  • Daniel Parks
    Neuroscience Graduate Program, University of Southern California, Los Angeles, CA, USA
    danielfp@usc.edu
  • Laurent Itti
    Neuroscience Graduate Program, University of Southern California, Los Angeles, CA, USA
    Department of Computer Science, University of Southern California, Los Angeles, CA, USA
    Department of Psychology, University of Southern California, Los Angeles, CA, USA
    itti@usc.eduhttp://ilab.usc.edu/itti/
Journal of Vision November 2014, Vol.14, 3. doi:10.1167/14.13.3
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      Ali Borji, Daniel Parks, Laurent Itti; Complementary effects of gaze direction and early saliency in guiding fixations during free viewing. Journal of Vision 2014;14(13):3. doi: 10.1167/14.13.3.

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Abstract

Gaze direction provides an important and ubiquitous communication channel in daily behavior and social interaction of humans and some animals. While several studies have addressed gaze direction in synthesized simple scenes, few have examined how it can bias observer attention and how it might interact with early saliency during free viewing of natural and realistic scenes. Experiment 1 used a controlled, staged setting in which an actor was asked to look at two different objects in turn, yielding two images that differed only by the actor's gaze direction, to causally assess the effects of actor gaze direction. Over all scenes, the median probability of following an actor's gaze direction was higher than the median probability of looking toward the single most salient location, and higher than chance. Experiment 2 confirmed these findings over a larger set of unconstrained scenes collected from the Web and containing people looking at objects and/or other people. To further compare the strength of saliency versus gaze direction cues, we computed gaze maps by drawing a cone in the direction of gaze of the actors present in the images. Gaze maps predicted observers' fixation locations significantly above chance, although below saliency. Finally, to gauge the relative importance of actor face and eye directions in guiding observer's fixations, in Experiment 3, observers were asked to guess the gaze direction from only an actor's face region (with the rest of the scene masked), in two conditions: actor eyes visible or masked. Median probability of guessing the true gaze direction within ±9° was significantly higher when eyes were visible, suggesting that the eyes contribute significantly to gaze estimation, in addition to face region. Our results highlight that gaze direction is a strong attentional cue in guiding eye movements, complementing low-level saliency cues, and derived from both face and eyes of actors in the scene. Thus gaze direction should be considered in constructing more predictive visual attention models in the future.

Introduction
A tremendous amount of research has been undertaken to discover and understand cues that influence eyes movements in daily life attentional behavior for tasks such as reading, scene perception, and visual search (see, e.g., Borji & Itti, 2013; Carrasco, 2011; Henderson, 2003; Land & Hayhoe, 2001; Posner, 1980; Schütz, Braun, & Gegenfurtner, 2011; Tatler, Hayhoe, Land, & Ballard, 2011). Two categories of cues have been identified: bottom-up (BU) cues such as discontinuities in contrast, color, intensity, brightness, motion, and spatial frequency in the visual stimulus (a.k.a. saliency; Borji, 2012; Borji & Itti, 2012a; Itti & Koch, 2001; Itti, Koch, & Niebur, 1998; Koch & Ullman, 1985; Krieger, Rentschler, Hauske, Schill, & Zetzsche, 2000; Mannan, Ruddock, & Wooding, 1996; Milanese, Wechsler, Gill, Bost, & Pun, 1994; Parkhurst, Law, & Niebur, 2002; Peters, Iyer, Itti, & Koch, 2005; Reinagel & Zador, 1999; Treisman & Gelade, 1980); and top-down (TD) cues mediated by factors such as task demands (Ballard, Hayhoe, & Pelz, 1995; Borji & Itti, 2014; Borji, Sihite, & Itti, 2014; Einhäuser, Rutishauser, & Koch, 2008; Land & Hayhoe, 2001; Land & Lee, 1994; Triesch, Ballard, Hayhoe, & Sullivan, 2003; Yarbus, 1967), context effects and scene gist (Torralba, Oliva, Castelhano, & Henderson, 2006), expertise with similar scenes (Underwood, Foulsham, & Humphrey, 2009), object appearance and spatial priors in visual search (Ehinger, Hidalgo-Sotelo, Torralba, & Oliva, 2009; Kanan, Tong, Zhang, & Cottrell, 2009; Wolfe, 1998; Wolfe & Horowitz, 2004), tendency of observers to look near the center of displays (also known as image center-bias; Tatler, 2007), tendency of observers to look near the center of objects (also known as object center-bias; Nuthmann & Henderson, 2010), memory (Carmi & Itti, 2006; Droll, Hayhoe, Triesch, & Sullivan, 2005), emotion (Ramanathan, Divya, Nicu, & David, 2014), gender (Shen & Itti, 2012), and culture (Chua, Boland, & Nisbett, 2005). 
One additional attentional cue is gaze direction, which so far has been overlooked since it is hard to quantitatively measure in unconstrained natural scenes. A number of electrophysiology and imaging studies (E. A. Hoffman & Haxby, 2000; Pelphrey, Viola, & McCarthy, 2004) have shown that several brain areas (e.g., the superior temporal sulcus) are highly sensitive to gaze direction. Further, gaze direction has been shown to be important in social interaction and in conditions such as autism (Fletcher-Watson, Leekam, Benson, Frank, & Findlay, 2009; Klin, Lin, Gorrindo, Ramsay, & Jones, 2009). Thus, we believe it is important to assess what role this cue plays in predicting eye fixations in natural scenes. Finally, gaze behavior is a function of both BU and TD components. For example, in driving, depending on the situation temporal task demand magnitude of attention may change from freely wandering around when driving a straight, less crowded road to highly focused when negotiating a curvy road which is a dangerous. 
Gaze direction (Bock, Dicke, & Thier, 2008; Cline, 1967; Schweinberger, Kloth, & Jenkins, 2007; Symons, Lee, Cedrone, & Nishimura, 2004; Todorović, 2006) and pointing (Louwerse & Bangerter, 2005) are two well-known cues thought to guide behaviors in human and nonhuman species. Gaze following is a rapid and effortless sociocognitive behavior that serves several functions including social interactions, social learning, collaboration, coordination, threat assessment, understanding the intentions of others, signaling what is important in the shared visual field to direct the attention of others, and communicating thoughts, judgments, emotions, desires, and needs (Emery, 2000). Some studies have postulated that gaze cueing might be influenced by facial cues signaling status, gender, dominance, leadership, familiarity, and group membership. For example, monkeys selectively attend more to gaze direction of individuals rated as high in social status (Shepherd, Deaner, & Platt, 2006). Gaze following is also a core aspect of joint attention (when two or more people are paying attention to the same entity) and allows coupling of visual appearances to verbal descriptions (Bakeman & Adamson, 1984; Kobayashi & Kohshima, 1997). 
Yu, Ballard, and Aslin (2005) compared lexical acquisition in adults with and without eye gaze cues to show that gaze information significantly improved word learning. Yu's lab has also shown how gaze-following behavior can be driven by other humans or agents in a joint attention task where they had to instruct the other agent what pseudoword is given to a random object in the joint field of view (Yu, Schermerhorn, & Scheutz, 2012). They found that humans were sensitive to changes in head pose of their agent or human partner, substantially increasing the probability of looking at their face 800–900 ms after the change of head pose. 
In laboratory experiments, perceived gaze has been shown to facilitate covert attention in the direction of gaze, even when the gaze cue is not informative of the task (Driver et al., 1999; Friesen & Kingstone, 1998). Perceived gaze has also been shown to facilitate overt attention if the gaze is congruent with the task direction, and to hamper it if the gaze is not congruent (Ricciardelli, Bricolo, Aglioti, & Chelazzi, 2002). In a set of experiments, the subject had to saccade to either the left or the right target based on a color cue at a central fixation. Placing a face with a gaze directly out of the screen or congruent with the color direction had about the same error. However, the incongruent direction had higher error, which did not happen when the faces were replaced with arrows. These studies suggest that these attentional cues happen automatically, in spite of top-down knowledge of their lack of usefulness, and beyond the explicit control of the subject. Thus, it seems that to have a complete model of bottom-up attention, simple features (orientations, color, intensity) along with face detection are not enough (Cerf, Frady, & Koch, 2009), as gaze cueing is also required. 
Gaze following helps us understand and interpret intentions and mental states of others. Humans have the ability to model other people's current knowledge of the world as well as their goals, which is frequently referred to as theory of mind (Premack & Woodruff, 1978). An observer has to infer body pose, head pose, and eye postures of other people and from this information extract the effective gaze direction (line of sight), which then in turn allows the viewer to perceive the world from the perspective of others. People with autism have deficits in using gaze to facilitate theory of mind. For example, children with autism have been shown to be able to assess whether a cartoon was looking at them as accurately as children without autism (Baron-Cohen, Campbell, Karmiloff-Smith, Grant, & Walker, 1995). This indicates that they are able to see and process eye gaze to a certain extent. However, they failed to use that knowledge to infer internal states about the viewed cartoon. In another experiment, four candies were placed around a cartoon face, which gazed at one of the candies. Children were asked which candy the cartoon face wanted. Children with autism were unable to infer that the cartoon face desired the candy that it was gazing towards (see Baron-Cohen et al., 1995, figure 3, p. 386). Instead, when asked to pick the candy that the cartoon face liked, they consistently chose the candy that they themselves wanted. This seems to imply that they ignored cues from the other person and instead modeled that person with the same goal states they themselves had. 
From a developmental perspective, it has been shown that nonverbal communication cues such as gaze imitation play a central role in social and cognitive development, language acquisition, and cognitive learning during early infancy (Baldwin, 1995; M. W. Hoffman, Grimes, Shon, & Rao, 2006; Okumura, Kanakogi, Kanda, Ishiguro, & Itakura, 2013; Tomasello, 2009). This is also known as the cooperative eye hypothesis (Kobayashi & Kohshima, 1997). Infants are capable of following the gaze direction of humans (Flom, Lee, & Muir, 2007; Gredebäck, Theuring, Hauf, & Kenward, 2008; Theuring, Gredebäck, & Hauf, 2007) and nonhuman agents or robots (Csibra & Gergely, 2006; Meltzoff, Brooks, Shon, & Rao, 2010; Okumura et al., 2013). In humans, gaze direction estimation has been shown to be at least crudely present (capable of discriminating left, right, or straight) as early as 3 months of age (D'Entremont, Hains, & Muir, 1997; Scaife & Bruner, 1975). Infants as young as 6 months are capable of following the direction of gaze. At 12 months, an infant can accurately follow a perceived gaze across an intervening stimulus and to the correct target. Prior to this age, objects that occur between the initial fixation and the true target seem either to override the search task or to be presumed to be the target (Butterworth & Jarrett, 1991). Infants at 1 year old are able to follow the gaze direction of an adult/caregiver and determine which object he or she is currently focused on (Butterworth, 1991). It is not until 14 months of age, however, that both eye position and head pose are reliably taken into account when estimating gaze (Caron, Butler, & Brooks 2002). By 18 months, an infant can even estimate perceived gaze that is outside its field of view (Butterworth & Jarrett, 1991; Moll & Tomasello, 2004). But it is at the age of 3 years when toddlers are able to explicitly discriminate the gaze direction (Doherty, Anderson, & Howieson, 2009). 
Previous literature has investigated the role of subcomponents of gaze following (body, head, face, and eye) in directing attention in natural scenes. It is known that people in scenes capture eye fixations (potency of people; Humphrey & Underwood, 2010; Zwickel & Võ, 2010). Within the human body, faces provide a wealth of information regarding a person's identity, gender, direction of attention (Cerf et al., 2009), needs, desires, interpersonal relations, and emotion as well as internal mental states (see, e.g., Baron-Cohen, Wheelwright, & Jolliffe, 1997). Observers also derive complex trait judgments, such as competence (see, e.g., Ballew & Todorov, 2007) and trustworthiness (Todorov, Baron, & Oosterhof, 2008; Winston, Strange, O'Doherty, & Dolan, 2002), from facial appearance, and such judgments are made rapidly and accurately and can help guide decision making during social interactions (compare Skarratt, Cole, & Kuhn, 2012). A large number of studies have shown that observers preferentially attend to faces in free viewing of scenes (e.g., Bindemann, Burton, Hooge, Jenkins, & de Haan, 2005; Cerf et al., 2009; Ro, Russell, & Lavie, 2001; Vuilleumier, 2000). Within faces, it is believed that the eyes convey the most information, and it has been shown that people have a strong preferential bias to attend to the eyes of other people (Baron-Cohen et al., 1997; Birmingham, Bischof, & Kingstone, 2008; Foulsham, Cheng, Tracy, Henrich, & Kingstone, 2010; Henderson, Williams, & Falk, 2005; Pelphrey et al., 2002; Yarbus, 1967). The importance of facial features and gaze following is further emphasized by the finding that some dedicated brain regions exist for representing faces (see, e.g., Kanwisher, McDermott, & Chun, 1997; Kanwisher & Yovel, 2006; Moeller, Freiwald, & Tsao, 2008; Tsao, Freiwald, Tootell, & Livingstone, 2006) and gaze directions (e.g., superior temporal sulcus; E. A. Hoffman & Haxby, 2000; Pelphrey et al., 2004). 
While influence of gaze direction in perception and the judgment of gaze direction has been given extensive treatment using simple synthetic scenes (see, e.g., Driver et al., 1999; Friesen & Kingstone, 1998, 2003; Jones et al., 2010; Mansfield, Farroni, & Johnson, 2003; von Grünau & Anston, 1995; some under the name of gaze cueing by employing the standard gaze cueing paradigm of Posner, 1980), less work has inspected the influence of gaze direction in the viewing of natural scenes. Birmingham et al. (2009) showed that saliency does not account for fixations to eyes within social scenes. Instead, it appears that observers' fixations are driven largely by their default interest in social information. Some studies predict that observers are more likely to attend toward regions (and for longer times) that are being looked at by the central figure in the display (e.g., Fletcher-Watson, Findlay, Leekam, & Benson, 2008). Some other studies have investigated gaze direction in the context of magic tricks (Kuhn & Tatler, 2005; Macknik et al., 2008), where a technique called misdirection is frequently used to distract the attention of the observer (often through gazing at something irrelevant). While the effect of gaze direction is well established, less work has addressed its interaction with other factors such as properties of the gazed-at objects in the scene—e.g., saliency (Itti et al., 1998) or importance (Spain & Perona, 2010). In other words, gaze-following behavior depends not only depend on the gaze direction of an actor but also on the entity being looked at. Sometimes, in interpreting a scene, gaze direction can override or modulate bottom-up saliency, allowing attention to be directed to less salient objects or locations. 
To the best of our knowledge, Castelhano, Wieth, and Henderson (2007) were the first to study the effect of gaze direction of actors in natural scenes in guiding the eye movements of observers of those scenes. They conducted a study in which subjects viewed a sequence of scenes presented as a slide show that portrayed the story of a janitor (the actor) cleaning an office. They found that (a) the actor's face was highly likely to be fixated (as also later suggested and modeled by Cerf et al., 2009) and (b) the observers' next saccade was more likely to be toward the object that was the focus of the actor's gaze than in any other direction. This study is interesting as it provides the seed to look deeper into the role of gaze direction in free viewing and fixation prediction. Eventually, gaze direction of actors in a scene could provide an additional source of information for visual attention models, similar to the manner in which human faces and written text have recently been added to saliency models (Cerf et al., 2009; Judd, Ehinger, Durand, & Torralba, 2009; H.-C. Wang & Pomplun, 2012). But before gaze direction can be included in saliency models, several central questions need to be answered which have not yet been fully addressed by previous studies. For example, if saliency can already explain all saccades that leave the head in the direction of the gaze, then there is no need to model gaze direction explicitly. These questions are: 
  • (a)   
    Does gaze direction causally guide observer attention and eye movements?
  • (b)   
    How might gaze direction cues complement low-level, feature-based saliency cues in predicting fixation locations?
  • (c)   
    Are gaze direction cues modulated by the presence of other faces in the scene, as such presence could be a confounding factor in attracting attention?
  • (d)   
    Does gaze-following strength change over viewing time?
  • (e)   
    What is the contribution of eyes beyond what the face already offers in estimation of gaze direction?
In Experiments 1 and 2, we test whether viewers, in interpreting real-world scenes, prioritize looking at less salient objects or locations if they happen to be in the direction of the gaze. We also investigate the power of a simple gaze map in predicting fixations. In Experiment 3, we quantify the informativeness of head and eye regions in determining gaze direction. Further, we discuss how models can be built that effectively incorporate gaze direction, and what the important problems are to address. 
Experiment 1
Here we attempt to test the hypothesis that free-viewing observers follow the gaze direction of people in the scene above chance on a set of controlled stimuli. Since gaze following might be due to saliency of the object at the gaze endpoint, we also account for this confounding factor. In what follows, we will use the term “actors” to refer to persons depicted in images, whose gaze direction might influence the attention and eye movements of external observers inspecting those images. Throughout the article, we concentrate on observer saccades that start from actor head regions (unless stated otherwise). 
Methods
Stimuli
We collected two sets of controlled stimuli. Several actors were instructed to look, in turn, at one of two objects in a scene. Figure 1 shows six example image pairs along with blurred1 saccade heat maps (made only from fixations leaving the actor's head area) and saliency maps. We collected 30 pairs of images (60 images in total). See Appendix A for complete set of image pairs used in this experiment. The camera position remained fixed across the two shots from the same scene. We then collected another 60 images at random from the Web to be used as fillers so that observers would be less likely to realize that the study was about gaze direction following. There was no gaze direction in some of these images, while in some others people looked at something or faced the camera. Filler images had much more variety (multiple objects, different locations, etc.) than our controlled set. We then created two sets of stimuli by putting together one image from each image pair (30 images) and 30 images chosen from the random set. Thus each set had 60 images. No observer viewed both images in a pair. Images were resized to 1920 × 1080 pixels by adding gray margins while preserving the aspect ratio (see Figure 1). 
Figure 1
 
Sample image pairs in Experiment 1 along with their corresponding heat maps and saliency maps from the AWS model (Garcia-Diaz et al., 2012). Heat maps are constructed from those fixations of all observers that start from the head region and end somewhere in the image. In each image, an actor was explicitly instructed to look at one of the two objects. Head and two object regions, as well as gaze directions, were annotated. The looked-at object is marked with a red polygon (ignored = green). Blue dots represent fixations.
Figure 1
 
Sample image pairs in Experiment 1 along with their corresponding heat maps and saliency maps from the AWS model (Garcia-Diaz et al., 2012). Heat maps are constructed from those fixations of all observers that start from the head region and end somewhere in the image. In each image, an actor was explicitly instructed to look at one of the two objects. Head and two object regions, as well as gaze directions, were annotated. The looked-at object is marked with a red polygon (ignored = green). Blue dots represent fixations.
Observers
Two groups of observers, comprising 15 subjects each, participated in this experiment. Observers in Group 1 (six male, nine female; mean age = 19.73, SD = 1.03) viewed images in Set 1. Observers in Group 2 (three male, 12 female; mean age = 19.8, SD = 1.26) viewed images in Set 2. Observers were undergraduate students at the University of Southern California (USC) from majors including neuroscience, psychology, biology, sociology, business, communication, music, biomedical engineering, and religion. The experimental methods were approved by USC's Institutional Review Board. Observers had normal or corrected-to-normal vision and received course credit for participation. They were naïve to the purpose of the experiment and had not previously seen the stimuli. They were instructed to simply watch and enjoy the pictures (free viewing). 
Apparatus and procedure
Observers sat 106 cm away from a 42-in. LCD monitor screen so that scenes subtended approximately 45.5° × 31° visual angle. A chin rest was used to stabilize head movements. Stimuli were presented at 60 Hz at a resolution of 1920 × 1080 pixels. Eye movements were recorded via a noninvasive infrared Eyelink (SR Research, Osgoode, ON, Canada) eye-tracking device at a sample rate of 1000 Hz (spatial resolution less than 0.5°). Each image was shown for 30 s followed by a 5-s delay (gray screen). The eye tracker was calibrated using five-point calibration at the beginning of each recording session. Observers viewed images in random order. Saccades were classified as events where eye velocity was greater than 35°/s and eye acceleration exceeded 9500°/s2 as recommended by the manufacturer of the Eyelink-1000 device. Faces took up, on average, 0.99% of the image, while they accounted for 9.22% of all fixations. The controlled pairs of objects took up 1.12% of the image each, but the gazed-at object received 7.75% of all fixations, while the ignored object received only 5.20% of all fixations. The average head size was 143 × 180 pixels (approximately 3.6° × 5.2° visual angle). The average object size was 167 × 174 pixels (approximately 4.2° × 5.1° visual angle). The average ground-truth2 gaze length was 724 pixels (approximately 18° visual angle). 
For saliency computation, we used the Adaptive Whitening Saliency model (AWS) by Garcia-Diaz, Leboran, Fdez-Vidal, and Pardo (2012), which has been shown to outperform other saliency models in recent benchmarks3 in predicting eye movements of observers in free viewing of natural scenes (Borji et al., 2012a). 
Analysis and results
We annotated (manually traced) head regions4 and the two looked-at objects in all image pairs (object boundaries). Note that the ground-truth gaze direction is known here, since actors in images were explicitly instructed to look at one of the two objects. 
Actor gaze direction influences observer saccade endpoints irrespective of saliency
To evaluate the effect of gaze direction on free-viewing behavior, we quantify the extent to which fixations are drawn to the gazed-at object versus the ignored object. We have two objects in each image: gazed-at and ignored. We compute the fraction of all saccades that start from the head and end inside each of these two objects (overall, 3,331 such saccades). This gives us two fractions, one for the gazed-at and one for the ignored object. For all 60 images, we thus obtain two arrays/vectors of size 60 of these fractions (one for the gazed-at and one for the ignored object). We then compare the medians of these two vectors. The median of the gazed-at vector is 0.069, which is significantly higher than the median 0.022 of the ignored vector (sign test, p = 6.132 × 10−9). Medians of the normalized saliency map activation for both cases are not significantly different from each other (0.019 vs. 0.020; p = 0.901). For 78.3% of cases, the gazed-at object attracted a higher fraction of fixations compared to the ignored object. These results clearly show that low-level saliency does not account for the influence of gaze direction on fixations. 
Actor gaze direction predicts observer saccade direction
Beyond analyzing observer saccade endpoints, we here also consider more broadly observer saccade directions, as this yields an analysis that can be extended to Experiment 2, which uses an uncontrolled data set where it is unknown exactly which objects the actors may be looking at. 
For each image, we measured probability distributions of angular directions for all saccades initiating somewhere from the head region to some part of the image but not on the same head. We used all fixations starting from the face, whether they ended up inside one of the two objects or not, because we were interested in the gaze-following effect. We first measured the histogram of angular saccade directions in 20 bins of 18° each5, and then converted it to a probability density function (pdf) by dividing this histogram to its sum. A higher pdf value at the ground-truth gaze direction hence means stronger gaze following irrespective of the exact endpoint. Figure 2 shows nine image pairs along with their distributions of saccade directions for data of all observers. As this figure shows, there is a peak in the direction of the looked-at object in the majority of images. 
Figure 2
 
Sample images in Experiment 1. In each panel, the two images of the image pair are shown on the left, with their corresponding saccade probability distributions (for saccades starting somewhere in the annotated head; see Figure 1) shown on the right (polar plot). Red lines in polar plots indicate the ground-truth gaze direction. Gaze following is strong for some images (e.g., the person looking at the CRT monitor and the trash can), while it is weaker for some others (e.g., the person looking at the yellow food box and the tissue—perhaps due to the complexity of the background and saliency of one of the objects).
Figure 2
 
Sample images in Experiment 1. In each panel, the two images of the image pair are shown on the left, with their corresponding saccade probability distributions (for saccades starting somewhere in the annotated head; see Figure 1) shown on the right (polar plot). Red lines in polar plots indicate the ground-truth gaze direction. Gaze following is strong for some images (e.g., the person looking at the CRT monitor and the trash can), while it is weaker for some others (e.g., the person looking at the yellow food box and the tissue—perhaps due to the complexity of the background and saliency of one of the objects).
Here, we show that the value of the saccade distribution (pdf) in the direction of the ground-truth gaze is significantly higher than in a random direction chosen uniformly (i.e., chance level). For 60 images, we have a vector of size 60 of pdf values. Similarly, we have another vector of the same size with pdf values read out from random directions. As shown in Figure 3A, the median of the saccade direction vector is 0.220, which is significantly higher than the median 0.023 of the saccade vector at uniform random directions using a sign test6 (i.e., vs. uniform chance level; p = 6.750 × 10−17). The median of the saccade direction vector is also significantly higher than a smart chance level in which directions are sampled randomly from the average ground-truth gaze direction pdf shown in Figure 3B (i.e., naïve Bayes chance level of 0.061; sign test, p = 6.171 × 10−10). Hence, observers tended to look significantly more (overall) in the direction of actor gaze than in any other direction. 
Figure 3
 
Results of Experiment 1. (A) Histogram of saccade direction pdf values (gaze-following strength) in the ground-truth gaze direction and the most salient location direction (saliency maps are normalized to be pdfs). (B) Distribution of ground-truth gaze directions over all 60 images in Experiment 1 (i.e., prior gaze direction distribution). Prior distribution is used to compute the naïve Bayes chance level. (C) Average annotation map (average of all object polygons over all images) for faces and objects, as well the mean eye position map over all images for saccades that start from somewhere inside the head region. As can be seen, there is a high fixation density around faces even for saccades that leave the head region. This can be partly due to uncertainty of observers in landing saccades or eye-tracker error.
Figure 3
 
Results of Experiment 1. (A) Histogram of saccade direction pdf values (gaze-following strength) in the ground-truth gaze direction and the most salient location direction (saliency maps are normalized to be pdfs). (B) Distribution of ground-truth gaze directions over all 60 images in Experiment 1 (i.e., prior gaze direction distribution). Prior distribution is used to compute the naïve Bayes chance level. (C) Average annotation map (average of all object polygons over all images) for faces and objects, as well the mean eye position map over all images for saccades that start from somewhere inside the head region. As can be seen, there is a high fixation density around faces even for saccades that leave the head region. This can be partly due to uncertainty of observers in landing saccades or eye-tracker error.
In another analysis, we assessed the relative strength of the saccade direction pdf values when the actor looked at an object and when he or she did not (i.e., looked at the other object). Let P+ be the pdf value in the direction of an object when it was looked at by the actor, and P when it was not (because the actor looked at the other object). We define the relative gaze strength denoted by z to be P+/(P+ + P). A z value of 1 means that observers always looked at the object that the actor was looking at, i.e., observers always followed the actor's gaze direction; and a z value of 0 means they never followed the actor's gaze direction. Averaged over all image pairs, we reached the value of μz = 0.647 (σz = 0.142) for z, which is higher than the 50% chance level (t test,7 p = 5.03 × 10−11). This implicitly means that if we were to guess the ground-truth gaze direction on each image based on the relative saccade direction pdf value (i.e., the decision criterion being the direction of the gazed-at object with higher pdf value), then we would have reached an accuracy of 65%. This result shows that actor gaze direction has a significant causal effect onto the directions of observer eye movements. 
Gaze direction versus most salient location direction
To complement the analysis of saliency at saccade endpoints, we here also evaluate saliency in particular gaze directions. One might argue that it was saliency that attracted observers to look in a particular direction and not gaze following (i.e., the effect could be partly due to low-level saliency). To account for this confounding factor, we measured the saccade pdf value in the direction of maximum saliency (not necessarily inside annotated objects) and compared it with the saccade pdf value in the ground-truth gaze direction. Median saccade pdf value for the maximum saliency direction is 0.10, which is significantly lower than the median pdf value 0.22 for the ground-truth gaze direction (sign test, p = 3.223 × 10−6). Saccade pdf value for the direction of maximum salient location is significantly higher that the uniform chance level (p = 6.022 × 10−9) and naïve Bayes chance (p = 0.01788). Thus, while saliency is an important factor in predicting observer gaze direction, it can not fully explain our data. This means that gaze direction and saliency are two complementary sources of information in guiding eye movements. 
Experiment 2
Our aim in this experiment was to explore the generality of gaze-following behavior on a wider range of uncontrolled natural scenes, including scenes with more cluttered backgrounds and with multiple people interacting with each other as well as multiple other objects. Having several persons in a scene raises the additional challenge that gaze-following behavior might not be due to a person looking toward someone, but might instead be because the looked-at person is salient and captures attention by him- or herself. Indeed, recent evidence suggests that human faces strongly attract eye movements, often capturing the first fixation on a new scene (Borji, 2012; Cerf et al., 2009; Judd et al., 2009). Here we investigate this challenge by breaking down the analysis into cases where the entity at the gaze endpoint is another person or an object. 
Methods
Stimuli
Stimuli consisted of a set of 200 color photographs collected mostly from the ImageNet data set (Deng et al., 2009).8 Photographs span a variety of topics and locations such as indoors, outdoors, social interactions, object manipulations, instrument playing, athletics, reading, and dancing. As in Experiment 1, images were resized to 1920 × 1080 pixels (see Figures 4 and 5 for sample images) while keeping the aspect ratio. We chose images in which at least one of the faces was large enough, visible, and gazing at something visible in the scene (another person or an object). In several of the images, some people are looking into the camera or out of the scene, but these heads were discarded in the gaze-following analysis. Images were shown to observers in two sessions with 100 images each. Observers had a 5-min break in between two sessions. The eye tracker was recalibrated before the second session. We annotated heads, faces, eyes, and gaze directions for all 200 images. We annotated the gaze direction from the entire image content, including the head area and candidate gazed-at objects. When multiple objects are spatially close to each other, the gaze can be ambiguous. In this case, even if we can infer general head direction, it is quite hard to know which object the person is gazing at. Thus, spatial accuracy of gaze following requires a very precise computation of gaze data with a high-resolution eye image, which is not available in all our images. 
Figure 4
 
Sample images in Experiment 2 with heads, faces, eyes, and gaze directions annotated. Blue lines indicate ground-truth gaze direction. We use the head region for calculating saccade pdfs. We annotated the gaze directions of the people that looked at something or a person in the scene (and not to the camera or out of the image plane). All faces were annotated.
Figure 4
 
Sample images in Experiment 2 with heads, faces, eyes, and gaze directions annotated. Blue lines indicate ground-truth gaze direction. We use the head region for calculating saccade pdfs. We annotated the gaze directions of the people that looked at something or a person in the scene (and not to the camera or out of the image plane). All faces were annotated.
Figure 5
 
Twelve sample images in Experiment 2 along with their corresponding eye movement map (second row), fixation map composed from all saccades (third row), fixation map composed from all saccades that start from one face (fourth row), and AWS saliency map (fifth row). Eye movement data is over all observers. Note that the AWS saliency model does not have an explicit face channel. Try to guess to which face the third row belongs to!
Figure 5
 
Twelve sample images in Experiment 2 along with their corresponding eye movement map (second row), fixation map composed from all saccades (third row), fixation map composed from all saccades that start from one face (fourth row), and AWS saliency map (fifth row). Eye movement data is over all observers. Note that the AWS saliency model does not have an explicit face channel. Try to guess to which face the third row belongs to!
The average number of heads (with faces visible or not) in scenes was 2.65 (SD = 2.02, median = 2). Fifty-one images had only one head in them, 78 had two, and 71 images had three or more. Overall, there were 530 heads, of which only 305 were looking at something in the scene (had their gaze annotated). From these 305 heads, 138 were looking at another head and 167 were looking elsewhere. In every image there was at least one person whose face was visible and who was looking at someone or something visible within the image, which could be used for analysis of gaze following. Although a face occupies 2.68% of the image on average, it contained 15.3% of all fixations. The average head size was 220 × 270 pixels (approximately 5.5° × 7.9° visual angle). The average gaze length was 459 pixels (approximately 11.5°). 
Observers
A total of 30 students (four male, 26 female) from USC took part in the study (mean age = 19.46, SD = 0.97). Observers had normal or corrected-to-normal eyesight and were compensated with course credits. 
Apparatus and procedure
Procedure and apparatus were the same as in Experiment 1, except that here images were shown for 10 s with 5 s of gray screen in between two consecutive images. 
Analysis and results
Figure 4 shows sample images from the stimulus set in Experiment 2 and their annotations. Figure 5 shows sample images along with their corresponding fixation maps (from all observers), blurred fixation maps, blurred maps for fixations starting from head, and AWS saliency maps. Figure 6 shows angular saccade probability distributions for sample images in Experiment 2 (over all observers). Note how there is a bias toward the upper regions of fixation maps, where faces are more likely to occur in our scenes (Figures 3C and 7B). This bias is away from the classical center bias (Borji et al., 2011; Tatler, 2007) but is close to the hot spot present in the head annotation map. 
Figure 6
 
Sample images and their corresponding saccade direction pdfs in Experiment 2 (Case 1). In each panel, the face under investigation in the image (left) is marked with a polygon. The polar plot (right) shows the saccade direction pdf for all saccades (Case 1; see text). Data are for saccades that start from inside the polygon and land somewhere else in the image.
Figure 6
 
Sample images and their corresponding saccade direction pdfs in Experiment 2 (Case 1). In each panel, the face under investigation in the image (left) is marked with a polygon. The polar plot (right) shows the saccade direction pdf for all saccades (Case 1; see text). Data are for saccades that start from inside the polygon and land somewhere else in the image.
Figure 7
 
Results of Experiment 2. (A) Distribution of gaze-following and saliency strengths over all data (Case 1). Inset shows the average distribution of saccades over all data (for saccades starting from a head region). The horizontal bias could be largely caused by locations of people and their heads in scenes. This prior is used for calculating the naïve Bayes chance level in all three cases. (B) Average head annotation (Case 3) and average fixation map over all data (for saccades starting from a face). Top horizontal biases can be because faces happen around the top of scenes. (C–D) Distribution of gaze-following and saliency strengths for Cases 2 and 3. Gaze-following strength is significantly higher than both chance levels and maximum saliency direction in all three cases.
Figure 7
 
Results of Experiment 2. (A) Distribution of gaze-following and saliency strengths over all data (Case 1). Inset shows the average distribution of saccades over all data (for saccades starting from a head region). The horizontal bias could be largely caused by locations of people and their heads in scenes. This prior is used for calculating the naïve Bayes chance level in all three cases. (B) Average head annotation (Case 3) and average fixation map over all data (for saccades starting from a face). Top horizontal biases can be because faces happen around the top of scenes. (C–D) Distribution of gaze-following and saliency strengths for Cases 2 and 3. Gaze-following strength is significantly higher than both chance levels and maximum saliency direction in all three cases.
Analysis of gaze following
We repeat the same analysis as in Experiment 1 by reading out and comparing saccade pdf values in the ground-truth gaze direction, in the direction of the maximum saliency location (anywhere in the scene), and in random directions. Results are shown in Figure 7. We break down the analysis (stimulus set) into three cases: (1) all data; (2) single-head, where there is only one person in the scene looking at something; and (3) face saliency control, where a person is gazing at something other than a face and there are multiple persons in the scene. Case 1 addresses whether our results in Experiment 1 generalize to uncontrolled complex natural scenes. Case 2 verifies the generality of our results in natural scenes with only one person. Case 3 controls gaze following due to the gaze direction and not face saliency. In other words, it checks whether the gaze-following effect is still present when the direction of other faces is incongruent with the actor's gaze direction. For example, consider the image in Figure 6A, in which there are two men, one looking at a newspaper and the other looking at the first man. The question is whether an observer starting from the left man's head will saccade to the newspaper or to the right man's head. This partitioning of the data set results in 51 samples for Case 2 and 116 samples for Case 3. Note that some images in Case 3 may contain several faces looking at something, resulting in several data points (e.g., Figure 6B). The overall number of gaze-following data points (Case 1) is 305. 
The total number of saccades over all observers and images (Case 1) that start from annotated heads is 21,737. From this, 4,411 saccades belong to Case 2 and 7,776 saccades belong to Case 3. The median saccade pdf value for the ground-truth gaze direction (Case 1) is 0.326, which is significantly above the uniform chance level of 0.029 (sign test, p = 4.051 × 10−62; over a vector of 305 probability values, one for each head, across all observers). The median saccade pdf value for the gaze direction in Case 2 is 0.378, which is again significantly above the uniform chance level of 0.046 (sign test, p = 1.586 × 10−12). This is in alignment with our results in Experiment 1. The median saccade direction pdf value for the gaze direction in Case 3 is 0.241, which is above the uniform chance level of 0.035 (sign test, p = 1.167 × 10−18). Median gaze-following strengths in all three cases are significantly above naïve Bayes chance levels using the sign test (respectively, p = 3.975 × 10−39, p = 1.767 × 10−9, and p = 8.656 × 10−10). Comparing gaze-following strengths for Cases 2 and 3 shows a significant difference (sign test, p = 1.220 × 10 −5). This indicates that observers follow the gaze direction less on images with multiple faces, suggesting that they were sometimes distracted by face saliency. 
The median saccade pdf value for the direction of maximum saliency over all data (Case 1) is 0.132, which is significantly above the uniform chance level of 0.037 (sign test, p = 1.102 × 10−19). This means that observers gazed toward something salient in the scene from the actor's face significantly more than would be expected by chance. These values for Case 2 and Case 3 are, respectively, 0.149 (significantly different vs. uniform chance using sign test, p = 4.436 × 10−5) and 0.138 (significant vs. uniform chance, p = 1.428 × 10−7). Saccade pdf values for the direction of the maximum salient location are significantly above naïve Bayes chance levels in all three cases (p = 0.001955, p = 0.02324, and p = 0.03438). 
Median saccade pdf values for ground-truth gaze directions are significantly higher than those for the maximum saliency direction in all three cases (p = 9.696 × 10−30, p = 1.220 × 10−5, and p = 1.380 × 10−4). This, in accordance with Experiment 1, confirms that gaze direction drives saccade direction more than the direction of the most salient location in free viewing of natural scenes. 
Addressing memory confound
In our analysis so far, we have considered all saccades that start from the head region. One confounding factor here is the memory of previously visited locations, which may attract or repel subsequent fixations. Observers might want to look back at the objects because they may find them somehow interesting or important, or they may want preferentially discover new items in the scene. As a consequence, one might for example first explore the scene in many directions, then look at a face, and from there follow the actor's gaze direction accidentally because it points toward an as yet unexplored portion of the scene.9 Here, to make sure the gaze-following effect is not because of memory, we limited our analysis to the first saccades in the scene which also happened to be on the face. The difference between median gaze-following strength and median saliency strength (in the direction of the maximum location) in Experiment 2 for just the first fixations (n = 151) is statistically significant (0.428 vs. 0.000; sign test, p = 1.142 × 10−8). Median values for both uniform and naïve Bayes chance levels are 0. Hence, even discounting any possible effect of memory, we still see a significant gaze-following effect. Please see Appendix B for a histogram of gaze-following strength in this analysis. 
Temporal analysis of gaze-following strength
To investigate gaze following over viewing time, we analyzed the effect of saccade order in gaze-following strength in Experiments 1 and 2. Figure 8 illustrates the results for the first 30 saccades partitioned in bins of 10 saccades (culled from the first 30 saccades over all data, but only ones that initiated somewhere in the head region were selected). We find that gaze following is a stronger cue during early saccades and drops over time in both experiments (it stays above maximum saliency strength over all 30 saccades). For Experiment 1, the first bin of 10 saccades had a significantly higher median strength of 0.42, while the second and third bins had medians of 0.28 and 0.25, respectively (Bonferroni corrected [Bland & Altman, 1995] significance value of 0.5/3 = 0.017; p values for bin comparisons: 1 vs. 2, 2.20 × 10−5; 1 vs. 3, 2.20 × 10−5; 2 vs. 3, 0.596). This was also true for the second experiment, where the medians were 0.33, 0.26, and 0.27, respectively (p values for bin comparisons: 1 vs. 2, 2.60 × 10−4; 1 vs. 3, 1.52 × 10−4; 2 vs. 3, 0.970). 
Figure 8
 
Temporal analysis of gaze-following strength for the first 30 saccades. The average is taken for all saccades that start from a face and land somewhere else in the image. For example, an order of second means all saccades that started from a face and were the second overall saccade for a subject on an image. In both panels, the top part shows the gaze-following strength and the bottom part shows the number of samples in each order. The data were binned into three groups when comparing strength over time: Bins 1 (saccades 1–10), 2 (saccades 11–20), and 3 (saccades 21–30), which are colored yellow, blue, and pink, respectively. (A) Experiment 1. (B) Experiment 2.
Figure 8
 
Temporal analysis of gaze-following strength for the first 30 saccades. The average is taken for all saccades that start from a face and land somewhere else in the image. For example, an order of second means all saccades that started from a face and were the second overall saccade for a subject on an image. In both panels, the top part shows the gaze-following strength and the bottom part shows the number of samples in each order. The data were binned into three groups when comparing strength over time: Bins 1 (saccades 1–10), 2 (saccades 11–20), and 3 (saccades 21–30), which are colored yellow, blue, and pink, respectively. (A) Experiment 1. (B) Experiment 2.
Predicting fixation locations with a simple gaze map
Having shown that gaze direction influences eye movements in free viewing, here we explore how gaze direction can be utilized to explain fixation locations. We construct the simplest map, referred to here as the gaze map, which has 1s inside a cone (±9° starting from a head and centered along the gaze vector) and 0s anywhere else. This cone corresponds to a single bin in the polar histograms shown in Figures 3 and 7. Gaze maps present the advantage of being directly comparable to saliency maps, so that we can here run a direct quantitative assessment of the relative strengths of gaze following versus saliency in driving observer eye movements. Gaze and saliency maps are converted to a pdf by dividing each of their values by the total sum of their values. 
Figure 9 shows the histogram of gaze and saliency map values at fixation locations over both experiments. As can be seen, the histogram for gaze map values is bimodal, with a large leftmost peak near 0 and another peak at higher values. The peak around 0 is because many fixations do not fall inside the cone. Note that this a relative effect: Although a large portion of fixations fall off the cone, the gaze cone still contains the largest fraction of fixations relative to any other cone of the same size in the image. Saliency map values, on the other hand, show only a left peak near 0. This observation hints toward efficient ways to integrate saliency and gaze maps (see Discussion). Although the gaze map has higher frequencies at larger values, its median is dominated by 0s, which makes its median lower than the saliency median (dashed vertical lines in Figure 9). 
Figure 9
 
Fixation prediction results for our simple gaze map and the AWS saliency model over both experiments. Both maps are normalized to be pdfs. Histograms are of saliency and gaze map values at fixation locations (saccades starting from head regions) for (A) controlled pairs in Experiment 1, (B) all data in Experiment 2 (Case 1), (C) images that have only one person in the scene looking at something (Experiment 2, Case 2), and (D) images that have a person gazing at something other than a face when there are multiple people in the scene (Experiment 2, Case 3). Note that, as expected, in all cases there is a peak at the left around 0 for the gaze map because many saccades fell off the gaze map (i.e., misses), mainly because observers did not follow the gaze (although overall they followed gaze direction higher than any other direction). Dashed lines represent medians. Insets show the ROC curves. ROC is measured by thresholding all gaze maps and then calculating the ratio of ground-truth and random fixations that fall above the threshold (corresponding to true positive rate/hit rate and false positive rate/false alarm).
Figure 9
 
Fixation prediction results for our simple gaze map and the AWS saliency model over both experiments. Both maps are normalized to be pdfs. Histograms are of saliency and gaze map values at fixation locations (saccades starting from head regions) for (A) controlled pairs in Experiment 1, (B) all data in Experiment 2 (Case 1), (C) images that have only one person in the scene looking at something (Experiment 2, Case 2), and (D) images that have a person gazing at something other than a face when there are multiple people in the scene (Experiment 2, Case 3). Note that, as expected, in all cases there is a peak at the left around 0 for the gaze map because many saccades fell off the gaze map (i.e., misses), mainly because observers did not follow the gaze (although overall they followed gaze direction higher than any other direction). Dashed lines represent medians. Insets show the ROC curves. ROC is measured by thresholding all gaze maps and then calculating the ratio of ground-truth and random fixations that fall above the threshold (corresponding to true positive rate/hit rate and false positive rate/false alarm).
As a complementary analysis, we also calculated the receiver operating characteristic (ROC) curves by thresholding maps and measuring the true positive rate (fraction of fixations above threshold) and false positive rate (fraction of uniformly random chosen points above threshold). Results are shown in Figure 9 insets. The area under the ROC curve (AUC) values in both experiments are significantly above chance, which is AUC = 0.5 (t test over gaze-direction cases; 60 in Experiment 1, p = 3.855 × 10−18; 305 in Experiment 2, Case 1, p = 4.79 × 10−61), but significantly below the AUC values of the saliency map (t test; Experiment 1, p = 1.18 × 10−21; Experiment 2, Case 1, p = 2.27 × 10−56). Thus we conclude that both gaze direction and saliency strongly influence observer eye movements, with saliency here being a stronger predictor of saccade endpoint but gaze direction still providing significant prediction performance. 
Is there any benefit from gaze direction in prediction of fixation locations on top of early saliency? To answer this question, in Figure 10 we illustrate scatter plots of gaze and saliency map predictions on all images in both experiments. The gaze map results in above-chance accuracy (AUC > 0.5) for 56/60 (93.33%) images in Experiment 1 and for 236/305 (77.38%) images in Experiment 2 (case 1). The corresponding numbers for the saliency map are 60/60 (100%) and 299/305 (98.03%). The gaze map outperforms the saliency map for 2/60 (3.33%) images in Experiment 1 and for 25/305 (8.20%) images in Experiment 2. Some success and failure cases for both maps are shown on the right side of Figure 10. Images for which the gaze map has high prediction power (image 3 in Figure 10A and image 2 in Figure 10B) usually contain low background clutter and few salient objects at the gaze direction. Several factors may lead to low performance of the gaze map, including high scene clutter, ambiguous gaze angle, and large gaze map area when the cone starts near one image corner and points to the opposite corner (see image 1 in Figure 10A and images 1 and 7 in Figure 10B). 
Figure 10
 
Gaze maps predict fixations in free viewing. (A) Area under ROC curve for gaze and saliency map predictions of fixated locations pooled over all observers in each image. Each data point corresponds to one head gaze (thresholding each map separately). Histograms of AUCs are depicted as marginals (same axes as scatter plot). For points below the diagonal, the gaze map's accuracy is better than the saliency map's (two images). The opposite is the case above the diagonal (58 images). The gaze map has above-chance accuracy for 56 images (60 for the saliency map). (B) The same as (A), but for Experiment 2. Here, 25 images are below the diagonal. The gaze map performs better than chance over 236 images (296 for the saliency map). Example images where either one or both maps perform well are shown on the right, along with their gaze maps, saliency maps, and ROC curves. Overlaid points represent eye movements. Interestingly, in some cases the gaze map predicts fixations much better than the saliency model (e.g., the pregnant woman and the woman watching TV).
Figure 10
 
Gaze maps predict fixations in free viewing. (A) Area under ROC curve for gaze and saliency map predictions of fixated locations pooled over all observers in each image. Each data point corresponds to one head gaze (thresholding each map separately). Histograms of AUCs are depicted as marginals (same axes as scatter plot). For points below the diagonal, the gaze map's accuracy is better than the saliency map's (two images). The opposite is the case above the diagonal (58 images). The gaze map has above-chance accuracy for 56 images (60 for the saliency map). (B) The same as (A), but for Experiment 2. Here, 25 images are below the diagonal. The gaze map performs better than chance over 236 images (296 for the saliency map). Example images where either one or both maps perform well are shown on the right, along with their gaze maps, saliency maps, and ROC curves. Overlaid points represent eye movements. Interestingly, in some cases the gaze map predicts fixations much better than the saliency model (e.g., the pregnant woman and the woman watching TV).
We learn that uniform distribution of activation in the cone is not efficient, as this simple cone has no sense of features or objects. In some instances, however, the gaze map was able to account for observer fixations that were almost completely missed by saliency, pointing toward the possibility of future synergies (e.g., the belly of the pregnant woman or the woman watching TV in Figure 10B). Perhaps the best method to combine saliency and gaze maps is to multiply them first and add the result to the saliency map (see Discussion). 
Table 1 summarizes results of the first two experiments. 
Table 1
 
Summary results of Experiments 1 and 2 for prediction of gaze direction and fixation locations (for fixations that start from the head region). For saccade direction prediction: Both gaze and most salient directions are significant predictors of observers' saccade direction (p < 0.05 using sign test vs. both uniform and naïve chance levels) in both experiments and in all cases. In both experiments, gaze direction performs significantly higher than maximum saliency direction in predicting observers' saccade directions. For saccade endpoint prediction: Both gaze and saliency maps outperform chance significantly above chance (AUC for chance is 0.5, corresponding to a white-noise map). AUCs here are calculated by thresholding all maps at a certain threshold level and measuring true positive and false positive rates across all maps. Overall, our simple gaze map explains fixations significantly below the best existing purely bottom-up saliency model, but there are some cases where our gaze map wins over the saliency map.
Table 1
 
Summary results of Experiments 1 and 2 for prediction of gaze direction and fixation locations (for fixations that start from the head region). For saccade direction prediction: Both gaze and most salient directions are significant predictors of observers' saccade direction (p < 0.05 using sign test vs. both uniform and naïve chance levels) in both experiments and in all cases. In both experiments, gaze direction performs significantly higher than maximum saliency direction in predicting observers' saccade directions. For saccade endpoint prediction: Both gaze and saliency maps outperform chance significantly above chance (AUC for chance is 0.5, corresponding to a white-noise map). AUCs here are calculated by thresholding all maps at a certain threshold level and measuring true positive and false positive rates across all maps. Overall, our simple gaze map explains fixations significantly below the best existing purely bottom-up saliency model, but there are some cases where our gaze map wins over the saliency map.
Experiment 1 Experiment 2, Case 1 Experiment 2, Case 2 Experiment 2, Case 3
Predicting saccade direction (medians)
 Gaze direction 0.220 0.326 0.378 0.241
 Most salient direction 0.101 0.132 0.149 0.138
 Uniform chance 0.023 0.029 0.046 0.035
 Naïve Bayes chance 0.061 0.081 0.098 0.080
Predicting fixation locations (AUC values)
 Gaze map 0.612 0.625 0.646 0.568
 Saliency map 0.797 0.789 0.795 0.794
 Chance 0.5 0.5 0.5 0.5
Experiment 3
Our data set provides rich opportunities to measure characteristics of gaze following, including the acuity of the gaze angle estimate, that may provide important constraints for future modeling efforts. Thus, here we explore interobserver variability in estimating gaze direction and gaze distance, as well as the relative importance of head pose (inferred from the face region) versus eye orientation in a person's ability to estimate final gaze direction, as these may guide the development of computational models. 
Several studies have carefully explored the accuracy of human observers in estimating eye gaze and head pose under various conditions (e.g., in controlled and virtual environments). Langton, Honeyman, and Tessler (2004) studied the effect of head contour and nose angle on head pose estimation. Kluttz, Mayes, West, and Kerby (2009) inspected the effect of head turn on gaze perception. Todorovic (2009) found a face eccentricity effect on gaze perception. Gibson and Pick (1963) showed that proper gaze estimation relies on the relative position of the iris within the eye socket as well as the head pose. For instance, when the eyes are looking right while the head is facing left, they combine to form a straight-ahead gaze. Or when the eyes are looking straight ahead along with a left-facing head, they combine to produce a left-facing gaze (see Gibson & Pick, 1963, figure 2, p. 389). Wilson, Wilkinson, Lin, and Castillo (2000) studied head pose estimation accuracy for a limited horizontal range (−30° to 30°). They found a 2° discrimination threshold for 0°–15° head poses and a threshold of 4.9° for 30° head poses. 
Humans' ability of gaze estimation in uncontrolled and unconstrained scenes has so far been overlooked. In this experiment, we aimed to study the accuracy and the degree to which observers can explicitly determine the gaze direction of people in natural scenes. Further, we wanted to know which item is more informative in determination of final gaze direction: faces or eyes. Note that gaze direction depends on both. Results of this experiment will be particularly important to enhance the gaze map suggested in the previous section and build general saliency models that utilize both face and eyes. The reason for choosing faces was that they are easier to detect and incorporate in a gaze-augmented saliency model. The same experimental setting, however, can be used to study head regions. 
Methods
Stimuli
Stimuli were the same as in Experiment 2 (i.e., 200 color photographs; see Figure 11). Ground-truthing was done by using the entire image, while observers only viewed the head region. Thus, the ground truth is only approximate, because it was created post hoc from a collection of pictures that were captured beyond the authors' control in a wide range of settings. While this is a limitation, we believe it is outweighed by the strength of using a diverse uncontrolled data set. 
Figure 11
 
Sample images in Experiment 3. Each panel shows the image, the ground-truth gaze direction (shown by a red line, and annotated in the unmasked original scene), and observers' estimations of gaze directions when eyes are visible (top left) and when eyes are masked (bottom left). The top right and bottom right show corresponding polar distributions. The initial point where observers start their vector has been annotated by the experimenter. For some images, eyes are critical for correctly estimating the gaze direction (A). For some cases, observers were equally good with eyes visible and with eyes masked (B), although it seems that in general observers had more variance in their decisions in the eyes-masked condition.
Figure 11
 
Sample images in Experiment 3. Each panel shows the image, the ground-truth gaze direction (shown by a red line, and annotated in the unmasked original scene), and observers' estimations of gaze directions when eyes are visible (top left) and when eyes are masked (bottom left). The top right and bottom right show corresponding polar distributions. The initial point where observers start their vector has been annotated by the experimenter. For some images, eyes are critical for correctly estimating the gaze direction (A). For some cases, observers were equally good with eyes visible and with eyes masked (B), although it seems that in general observers had more variance in their decisions in the eyes-masked condition.
Observers
We had two groups of observers. Fifteen observers (four male, 11 female) were in Group 1, with a mean age of 19.53 (SD = 1.50). Thirteen observers (two male, 11 female) were in Group 2, with a mean age of 19.46 (SD = 1.26). Observers were undergraduate students from USC and had normal or corrected-to-normal vision. Informed consent was obtained from observers prior to their beginning the experiments. 
Procedure
Observers were asked to draw a line starting from a point on the face (premarked by the experimenter and falling somewhere between the two eyes) to the point where they thought the person in the image was looking. Observers were required to guess both gaze direction and gaze endpoint. Observers in Group 1 were shown faces with eyes visible, while observers in Group 2 were shown faces with eyes masked. The experiment was self-paced and observers had to press any key to proceed to the next trial. Figure 11 shows distribution of gaze estimations for 12 sample images in the eyes-visible and eyes-masked conditions. 
Analysis and results
Analysis of observer gaze estimation accuracy
The analysis was carried out in the same fashion as in Experiments 1 and 2, except here we replaced the saccade direction pdf with the pdf of observers' estimated gaze direction (see Figure 12). We read out the estimated pdf values in the ground-truth gaze direction and in a uniformly random direction. This way, we generated two real-valued vectors of size 279 (each value in [0 1]). The medians of these vectors are significantly different from each other for the eyes-visible (0.2 vs. 0; sign test, p = 3.60 × 10−129) and eyes-masked conditions (0.13 vs. 0; sign test, p = 2.05 × 10−107). We also calibrated a smart (naïve Bayes) chance by sampling from the prior distribution over the ground-truth gaze directions (see Figure 7A inset). The median gaze estimation using this chance level for the eyes-visible condition is 0 (mean = 0.035, SD = 0.087), which is still significantly lower than observers' annotations (p = 3.75 × 10−110). The naïve Bayes median chance level for the eyes-masked condition is also 0 (mean = 0.040, SD = 0.089), which is again significantly below the observers' annotations (sign test, p = 3.00 × 10−76). 
Figure 12
 
Results of Experiment 3. (A) Histogram of gaze estimation strength by observers for eyes-visible and eyes-masked conditions. (B) Median gaze strengths for ground truth and two chance levels for the two conditions, as well as statistical test using the sign test. The median value for chance in the eyes-visible condition is 0 (mean = 0.022, SD = 0.065); for the eyes-masked condition it is also 0 (mean = 0.021, SD = 0.058). See Figure 7A inset for naïve Bayes prior.
Figure 12
 
Results of Experiment 3. (A) Histogram of gaze estimation strength by observers for eyes-visible and eyes-masked conditions. (B) Median gaze strengths for ground truth and two chance levels for the two conditions, as well as statistical test using the sign test. The median value for chance in the eyes-visible condition is 0 (mean = 0.022, SD = 0.065); for the eyes-masked condition it is also 0 (mean = 0.021, SD = 0.058). See Figure 7A inset for naïve Bayes prior.
We compared the eyes-visible and eyes-masked conditions and observed that the difference is statistically significant (sign test, p = 5.76 × 10−15). This indicates that eye regions convey information regarding estimation of gaze direction, as observers are better at determining gaze direction when eyes are visible (equal to eyes-masked condition; pdf value of 0.13). This result is important from a modeling perspective in that, when constructing a saliency model that incorporates gaze direction, one might want to weigh pose detection more than eye gaze detection. 
Figure 13 shows the normalized gaze length for ground-truth annotations (gaze direction vectors) and estimated gaze vectors (by the observers) in Experiment 3 for both conditions. Normalization is performed by dividing the length of the drawn vector by the length of a vector in the same direction extending to the image border. Histograms of ground truth and estimated gaze lengths look similar, as both have a central peak around 0.4–0.5. It seems that observers slightly underestimated the gaze length and leaned toward closer distances to the person in the image. This result means that observers are to some extent able to locate the object a person is looking at (by using relative size cues, scene depth, etc.). It is also important in the sense that it can be used for spatially biasing a gaze map (e.g., emphasizing more at a distance halfway along the cone to the image edge instead of uniformly distributing activations across the entire map). 
Figure 13
 
Histogram of normalized saccade length for (A) ground-truth gaze annotations (by the experimenter and when the entire scene is visible), (B) observers' guesses with eyes of people in the scene visible, and (C) observers' guesses with eyes of people in the scene masked. All three histograms show a central peak around 0.4–0.5.
Figure 13
 
Histogram of normalized saccade length for (A) ground-truth gaze annotations (by the experimenter and when the entire scene is visible), (B) observers' guesses with eyes of people in the scene visible, and (C) observers' guesses with eyes of people in the scene masked. All three histograms show a central peak around 0.4–0.5.
Analysis of observer gaze estimation uncertainty
We also analyzed uncertainty of observers in estimating gaze angle in both conditions. For each ground-truth gaze-annotated face, we measured the standard deviation of estimated gaze angles (in degrees). Histograms of values are shown in Figure 14A. The median standard deviation for the eyes-visible condition is significantly lower than for the eyes-masked condition (11.77 vs. 18.73; sign test, p = 4.092 × 10−17), indicating that observers were more consistent when people's eyes were visible in the scenes. This analysis helps understand how to spread angular uncertainty in a gaze map. 
Figure 14
 
(A) Histogram of gaze estimation variance in Experiment 3 (in degrees). (B) Histogram of range of estimated gaze angles (cone width).
Figure 14
 
(A) Histogram of gaze estimation variance in Experiment 3 (in degrees). (B) Histogram of range of estimated gaze angles (cone width).
Finally, to obtain a sense of the cone width that a gaze map should use, we measured the range of observers' estimated angles. Figure 14B shows the histogram of absolute differences between maximum and minimum angles over all annotated faces. As it shows, the median range is significantly smaller when eyes were visible in images versus when they were masked (41.09 vs. 68.29; sign test, p = 2.475 × 10−16). This result suggests that a cone width of about 41° might be a good choice for building a gaze map. Here we attempted to study the ability of observers to explicitly report the gaze direction, to constrain the parameters of a gaze map. Another alternative would be learning parameters directly from eye movements for fixation prediction. 
Discussion
Our quantitative results in Experiments 1 and 2 indicate that free-viewing observers strongly follow the gaze direction of human actors in natural scenes. In Experiment 1, we found that the fraction of fixations that start from a head region and land on an object was significantly higher for the attended object compared to the ignored object. While actor gaze was a stronger predictor of saccade direction than saliency or chance in both experiments, it performed worse than saliency in predicting saccade endpoint, although above chance. We also noted that observers follow the gaze direction less on images with multiple faces, suggesting that they were sometimes distracted by face saliency (results of Experiment 2: higher gaze-following strength and AUC values for Case 2 vs. Case 3 in Figures 7 and 9, respectively). However, it remains to be investigated which cue (face, saliency, or gaze direction) observers prioritize in viewing natural scenes. In addition to our quantitative results, we also noted a few qualitative observations. Our observers sometimes followed the gaze direction of inanimate objects (statues, robots, dolls, masks, etc.). We saw a cyclical behavior in fixation patterns—in alignment with Borji and Itti, 2014; DeAngelus and Pelz, 2009; and Yarbus, 1967—such that observers look back and forth between the actor and the gazed-at object. Contrary to our expectation, we did not find a correlation between low-level saliency and gaze-following strength. 
We suggest that four main components are involved in gaze-following behavior: (a) stimulus (scene content, actors, and objects at gaze endpoints), (b) observer top-down knowledge and internal states, (c) task, and (d) context or environment in which gaze following happens. Here, we looked at the first component, which is the effect of actor gaze direction on observer viewing behavior. Some studies have investigated how mood and emotional states of actors modulate the gaze-following effect. For example, it has been shown that gaze following in monkeys is modulated by observed facial expressions (Goossens, Dekleva, Reader, Sterck, and Bolhuis, 2008). Also, it has been suggested that fearful emotions result in stronger gaze-cueing effects than happy faces (Kuhn & Tipples, 2011). The complexity of the scene or scene clutter (i.e., images with a large field of view which may contain many faces, objects, background clutter, etc.) might also influence the magnitude of the gaze following. If the scene is very complex, observers may not follow actor gaze as much, particularly when the presentation time is short (see, e.g., Figure 6D). Instead, they may use their time to scan the entire scene (i.e., gaze direction as a function of scene complexity). 
The second component is observer top-down inferential mechanisms, which may also interact with the first component. For example, observers may not follow the gaze of an actor who is looking outside the scene (e.g., when a person in the scene is near the right side of the image and is looking toward the right), looking at an open space (a mountain, beach, or horizon), or looking at an object which is close to the actor's body (in such case, observers may perceive the actor and object both at the same time). Another example is a person looking in a book, newspaper, or monitor which is facing toward the actor but has its back toward the observer (see, e.g., Figure 6C). 
Task, the third component, also can play a major role in gaze-following strength. For example, when asked to guess what people in the scene are doing, make a story of the scene, or guess relationships among people and objects, observers might be more influenced by the gaze direction. Conversely, when observers are asked to perform tasks such as searching for a particular object or remembering positions of objects, one might expect a lesser role for gaze direction. This is similar in spirit to the finding by Cerf et al. (2009) that salience of faces and text is task dependent. 
Finally, the fourth component is context, where the current saccade decision is influenced by a more global understanding of the image (e.g., that it is a scene of a beach, and particular regions are more likely to be interesting). Less work has addressed the second and fourth components of gaze-following behavior, which warrant more attention in the future. For example, the emotional and physical state of the observer, or his or her mental state (e.g., alertness, sleepiness, or confusion), may influence gaze-following strength. This relates to findings that normal human beings from different categories and/or under different conditions might have different viewing behaviors—e.g., depending on gender (Shen & Itti, 2012) or culture (Chua et al., 2005). Regarding context, viewers may follow the gaze direction more strongly in a risky environment than a safe environment. 
In Experiment 1 we introduced a novel causality-testing stimulus set. The same paradigm can be used to study other effects in viewing behavior of observers and reduce complexity of the stimuli. In Experiment 2, we showed that gaze following happens in arbitrary natural scenes containing humans and objects. It still remains to be discovered what properties of a face modulate gaze following more. For example, do observers look more at the face in the direction of gaze than a control face somewhere in the image (i.e., dyadic and triadic gaze interactions with objects and humans)? More controlled stimuli and tasks are needed to measure gaze-following strength for the following example conditions: (a) three faces, two of them looking at each other and the third one facing the camera; (b) three faces, two of them looking at an object and the third one facing the camera; (c) three faces, two of them looking at an object and the third one looking at another object; and (d) four faces, three of them looking at the fourth face, which is looking at an object. 
Note that we found that gaze direction, while providing a strong directional cue, is overall a weaker predictor than saliency in predicting the saccade endpoint, and it is important to qualify this statement. First, here we employed the best existing bottom-up saliency model according to a recent comparative benchmark of 35 saliency models (Borji et al., 2012a). This is particularly important, since using weaker models can sometimes reverse the conclusions of a study (see, e.g., Borji et al., 2013a). Yet like all models, this saliency model is only a coarse approximation of human saliency. Second, most saliency models analyze the image along a number of feature dimensions, some of which can be fairly complex (e.g., face detection, text detection). Because saliency modeling is a mature field and these models are complex, it would have been quite surprising if gaze direction alone (in the form of our simple gaze map) had surpassed complex and sophisticated saliency models, which integrate many known cues that attract attention. However, our results point toward a possible future synergy between gaze direction models and saliency models. Our analysis shows an important concept, which is that predicting fixations is different from predicting directions. Gaze can be viewed as something like a face or text channel, which alone cannot explain a large number of fixations but when combined with bottom-up saliency (assuming that gaze directions is a reliable cue and makes rare mistakes) can enhance the prediction power of the model (i.e., biasing saliency in one direction). 
Here, we discuss how a saliency model that takes advantage of gaze direction could be built. Such a model should include three components. First, it should be able to detect heads, faces, and eyes. Second, it should be able to detect gaze direction of people in the scene (head and gaze directions, i.e., the effective gaze direction). Third, it should have a mechanism to bias the saliency map in the direction of the gaze. The first component is considered almost solved (at least for faces), as nowadays reliable face detectors exist (e.g., Viola & Jones, 2001), though their performance is mainly limited to frontal-view faces. The second component has recently been addressed (see, e.g., Asteriadis, Karpouzis, & Kollias, 2013; Marin-Jimenez, Zisserman, Eichner, & Ferrari, 2014; Park, Jain, & Sheikh, 2012; Zhu & Ramanan, 2012), in works that estimate body pose (e.g., Ferrari, Marin-Jimenez, & Zisserman, 2008), eye gaze (e.g., J. Wang, Sung, & Venkateswarlu, 2003), head orientation (e.g., Murphy-Chutorian, Doshi, & Trivedi, 2007), or a combination of all (e.g., Valenti, Sebe, & Gevers, 2012; Weidenbacher, Layher, Bayerl, & Neumann, 2006; Yücel et al., 2013). However, reliable gaze direction estimation models for arbitrary 2-D angles still do not exist, especially from only pixel data (also in user-independent calibration-free conditions). Another challenge here is the projection from the 3-D world to 2-D images, which may cause confusion about what object a person in the scene is looking at. Further, eye detection and tracking remains challenging due to the individuality of eyes, occlusion, variability in scale, location, and lighting conditions. Not much effort has been devoted to the third component, mainly because the second is still unsolved. 
In Experiment 2, we addressed this third component. We studied the prediction power of a very simple gaze map and offered insights toward building more predictive gaze-augmented saliency models. We discovered that four challenges need to be addressed before making a general model: (a) How to adjust the parameters of the cone? Some parameters that constrain a gaze map include width of the cone, angular uncertainty, and effective length from the center to focus energy (attentional span). Ideally, one would want to only bias the object(s) that the actor is looking at in the scene. If one modulates everything along the cone, then background unattended objects falling on the cone will be modulated as well (which is not efficient). In Experiment 2, we employed a uniform map. The results of Experiment 3 can be used to calibrate this simple map. For example, a better than uniformly distributing activation would emphasize more at the center line (bisector angle) of the cone and decay it using a Gaussian distribution (e.g., similar to Schauerte, Richarz, & Fink, 2010, who used cone maps to emphasize pointing direction). It might be also better to emphasize more at the center of the cone map (i.e., somewhere between the origin of the cone and the image border). In the end, it should be studied whether a cone is the best shape to use to modulate a saliency map according to actor gaze direction. (b) How to combine a low-level saliency map S and a gaze map G? Some possibilities include addition, multiplication, and a combination of both (i.e., αS + βG + γSG, learning free parameters α, β, and γ from eye movement data). (c) How to detect and handle cases where observers do not follow the gaze direction? Some examples include images where people look out of plane or look at something outside the image. (d) How to combine multiple gaze direction cues present in a single image? For example, when multiple people are jointly looking at an object, how should gaze direction cues be integrated in constructing a cone map? 
We believe the result of Experiment 3 is important for two reasons: First, it helps constrain parameters of saliency models that bias predictions in the direction of gaze. For example, what would be a good cone width to use in a model given the variability in lines drawn by our observers? This information is not dependent on the accuracy of our ground-truth gaze directions. Second, currently we are far away from models that can accurately detect gaze direction in digital images. Some moderately accurate models for head pose detection exist (Murphy-Chutorian & Trivedi, 2009), but almost no model yet addresses final gaze direction, since eyes are often small in images and are poorly visible. It is very important to know to what extent each element carries information regarding the final gaze direction. Gaze estimation in natural scenes can be inherently ambiguous (e.g., when multiple objects overlap with the gaze direction). In some scenarios in daily life, however, it is possible to reliably estimate gaze, for example when talking to people at a short distance in a bus. In such scenarios, both eye and head directions are important. Our results from Experiment 3 show that eye direction contributes significantly to final gaze direction. 
Gaze direction is a function of both head pose and eye direction. With eyes masked in an image, observers are still able to report the gaze direction to some extent (we assume that subjects would rely on head pose to estimate the gaze line when eyes are masked). The standard deviation of subject responses in the eyes-masked condition was 18.73°, versus 11.77° in the eyes-visible condition, suggesting that subjects were not drawing their lines at random. Further, randomly drawn lines would lead to much smaller gaze estimation strengths than those reported in Figure 12 for the eyes-masked condition. We believe this is an ecologically-relevant task and happens sometimes in real life, for example when people wear dark sunglasses. In a further study, one might want to annotate the ground-truth head direction and see whether observers' judgments align better with this measure or with the ground-truth gaze direction. 
More accurate gaze direction prediction and saliency models can be useful in a number of scientific and engineering applications: computer vision, e.g., action recognition, scene understanding in videos (Marin-Jimenez et al., 2014), reading intentions of people in scenes (Yun, Peng, Samaras, Zelinsky, & Berg, 2013), and attentive user interfaces; human–computer and human–robot interaction (e.g., Bakeman & Adamson, 1984; Borji et al., 2012b; Breazeal & Scassellati, 2002; Funes Mora & Odobez, 2013; M. W. Hoffman et al., 2006; Lungarella, Metta, Pfeifer, & Sandini, 2003; Nagai, Asada, & Hosoda, 2002); determining the attention levels of a driver (e.g., Murphy-Chutorian et al., 2007); and enriching e-learning systems (e.g., Asteriadis et al., 2013). Also, such models can be useful for psychological research to study psychological disorders and diagnose mental illness—e.g., anxiety and depression (Compton, 2003; Horley, Williams, Gonsalvez, & Gordon, 2004; Kupfer & Foster, 1972), schizophrenia (Franck et al., 2002; Langton, 2000), autism (Fletcher-Watson et al., 2009; Klin et al., 2009; Pelphrey, Morris, & McCarthy, 2005)—and dysfunctions related to joint attention. Specifically, augmented models of low-level saliency and gaze following can be used for constructing signatures for distinguishing people with such disorders from people without. A similar trend has been followed over the years using purely bottom-up saliency models to conduct neuropsychological and clinical research (e.g., Foulsham, Barton, Kingstone, Dewhurst, & Underwood, 2009; Tseng et al., 2012). 
Recent effort has been focused on new means of obtaining users' gaze on portable devices (both handheld and wearable), such as laptops, tablets, smartphones, and glasses. Gaze tracking on such devices can complement the touch modality. Rapid progress in increasing processing power, memory, screen size, and camera resolution of these devices allows running computationally intensive applications under different conditions in real time. Some gaze-aware applications on visual wearable devices include evaluating user experience, monitoring and enhancing reading behavior, and adapting and displaying out-of-reach content on the screen (e.g., Wood & Bulling, 2014). 
Conclusion
Gaze is a critical cue for understanding the meaning of complex natural scenes but has been so far overlooked in the vision community, partly because it is hard to accurately estimate in uncontrolled cluttered natural scenes. In the present study, we investigated the behavior of passive external observers viewing complex real-world scenes involving humans and objects. We showed that actor gaze direction has a profound effect on the allocation of eye movements of an observer during real-world scene exploration, supporting and extending the results of Castelhano et al. (2007). From Experiments 1 and 2, we conclude that gaze direction provides a complementary source of attention guidance in addition to the properties of the gazed-at object (e.g., its salience) and memory of visited locations. In Experiment 2, over a wide data set of natural scenes, we discounted face saliency and showed that even in the presence of faces, observers follow the gaze direction. In Experiment 3 we showed that humans are able to report the gaze direction from the face region and do even better when eyes are visible. This indicates that there is significant additional information provided by the eyes beyond what the head alone provides. 
A promising future research direction is constructing more predictive gaze-augmented saliency models by combining saliency, face detection, and gaze direction. Studying the relationships between gaze direction, attention, language, and scene and object properties is another interesting area. Some related works in this regard have investigated the connection between gaze direction and language (Houston-Price, Plunkett, & Duffy, 2006), attention and language (a notion known as the minimal subscene; Itti & Arbib, 2006), and language and event perception (Macdonald & Tatler, 2013; Papafragou, Hulbert, & Trueswell, 2008). 
Acknowledgments
This work was supported by the National Science Foundation (grant number CCF-1317433), and the Army Research Office (W911NF-11-1-0046 and W911NF-12-1-0433). The authors affirm that the views expressed herein are solely their own and do not represent the views of the United States government or any agency thereof. Thanks to Boris Schauerte for his help collecting the stimulus set for our second experiment. We wish to thank reviewers for their valuable comments. The data and stimuli from of this study are publicly available at http://ilab.usc.edu/borji/Resources.html
Commercial relationships: none. 
Corresponding author: Ali Borji. 
Email: borji@usc.edu. 
Address: University of Southern California, Los Angeles, CA, USA. 
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Footnotes
1  Code for map blurring using Matlab: blurredSacMap=conv2(sacMap,fspecial(‘gaussian',100,20)).
Footnotes
2  Ground-truth gaze direction is the direction that an actor is looking in. It is known in Experiment 1 by construction, but we estimate it for the images of Experiment 2.
Footnotes
3  Note that as we have argued in our other works (Borji et al., 2013a, 2013b), selection of a saliency model is very important and in some cases may alter conclusions of a study. For this reason, here we choose the best performing model in the saliency literature (i.e., the AWS model).
Footnotes
4  We do not distinguish between faces that are in-profile or frontal facing.
Footnotes
5  We chose these parameters to (a) have enough saccade data in each bin and (b) be reasonably precise in labeling each gaze direction.
Footnotes
6  Using the Matlab “ranksum” function.
Footnotes
7  We empirically verified via the Kolmogorov–Smirnov test that variable z is normally distributed.
Footnotes
8  Available online at http://www.image-net.org. Some images were also borrowed from the AFW data set (Zhu & Ramanan, 2012).
Footnotes
9  We perform this analysis for Experiment 2, since we did not have enough of such fixations in Experiment 1 (n = 17).
Footnotes
*  AB and DP contributed equally to this article.
Appendix A
Figure A1
 
The complete set of scenes used in Experiment 1 (30 pairs of images). Some faces have been blurred for privacy reasons.
Figure A1
 
The complete set of scenes used in Experiment 1 (30 pairs of images). Some faces have been blurred for privacy reasons.
Appendix B
Figure A2 depicts histograms of gaze-following strengths over all data in Experiments 1 and 2 for first saccades that start from faces. Such saccades are not contaminated by memory effect. 
Figure A2
 
Gaze-following strength for Experiment 1 and all data (Case 1) in Experiment 2. Data include only the first saccades that also happen to be on the faces.
Figure A2
 
Gaze-following strength for Experiment 1 and all data (Case 1) in Experiment 2. Data include only the first saccades that also happen to be on the faces.
Figure 1
 
Sample image pairs in Experiment 1 along with their corresponding heat maps and saliency maps from the AWS model (Garcia-Diaz et al., 2012). Heat maps are constructed from those fixations of all observers that start from the head region and end somewhere in the image. In each image, an actor was explicitly instructed to look at one of the two objects. Head and two object regions, as well as gaze directions, were annotated. The looked-at object is marked with a red polygon (ignored = green). Blue dots represent fixations.
Figure 1
 
Sample image pairs in Experiment 1 along with their corresponding heat maps and saliency maps from the AWS model (Garcia-Diaz et al., 2012). Heat maps are constructed from those fixations of all observers that start from the head region and end somewhere in the image. In each image, an actor was explicitly instructed to look at one of the two objects. Head and two object regions, as well as gaze directions, were annotated. The looked-at object is marked with a red polygon (ignored = green). Blue dots represent fixations.
Figure 2
 
Sample images in Experiment 1. In each panel, the two images of the image pair are shown on the left, with their corresponding saccade probability distributions (for saccades starting somewhere in the annotated head; see Figure 1) shown on the right (polar plot). Red lines in polar plots indicate the ground-truth gaze direction. Gaze following is strong for some images (e.g., the person looking at the CRT monitor and the trash can), while it is weaker for some others (e.g., the person looking at the yellow food box and the tissue—perhaps due to the complexity of the background and saliency of one of the objects).
Figure 2
 
Sample images in Experiment 1. In each panel, the two images of the image pair are shown on the left, with their corresponding saccade probability distributions (for saccades starting somewhere in the annotated head; see Figure 1) shown on the right (polar plot). Red lines in polar plots indicate the ground-truth gaze direction. Gaze following is strong for some images (e.g., the person looking at the CRT monitor and the trash can), while it is weaker for some others (e.g., the person looking at the yellow food box and the tissue—perhaps due to the complexity of the background and saliency of one of the objects).
Figure 3
 
Results of Experiment 1. (A) Histogram of saccade direction pdf values (gaze-following strength) in the ground-truth gaze direction and the most salient location direction (saliency maps are normalized to be pdfs). (B) Distribution of ground-truth gaze directions over all 60 images in Experiment 1 (i.e., prior gaze direction distribution). Prior distribution is used to compute the naïve Bayes chance level. (C) Average annotation map (average of all object polygons over all images) for faces and objects, as well the mean eye position map over all images for saccades that start from somewhere inside the head region. As can be seen, there is a high fixation density around faces even for saccades that leave the head region. This can be partly due to uncertainty of observers in landing saccades or eye-tracker error.
Figure 3
 
Results of Experiment 1. (A) Histogram of saccade direction pdf values (gaze-following strength) in the ground-truth gaze direction and the most salient location direction (saliency maps are normalized to be pdfs). (B) Distribution of ground-truth gaze directions over all 60 images in Experiment 1 (i.e., prior gaze direction distribution). Prior distribution is used to compute the naïve Bayes chance level. (C) Average annotation map (average of all object polygons over all images) for faces and objects, as well the mean eye position map over all images for saccades that start from somewhere inside the head region. As can be seen, there is a high fixation density around faces even for saccades that leave the head region. This can be partly due to uncertainty of observers in landing saccades or eye-tracker error.
Figure 4
 
Sample images in Experiment 2 with heads, faces, eyes, and gaze directions annotated. Blue lines indicate ground-truth gaze direction. We use the head region for calculating saccade pdfs. We annotated the gaze directions of the people that looked at something or a person in the scene (and not to the camera or out of the image plane). All faces were annotated.
Figure 4
 
Sample images in Experiment 2 with heads, faces, eyes, and gaze directions annotated. Blue lines indicate ground-truth gaze direction. We use the head region for calculating saccade pdfs. We annotated the gaze directions of the people that looked at something or a person in the scene (and not to the camera or out of the image plane). All faces were annotated.
Figure 5
 
Twelve sample images in Experiment 2 along with their corresponding eye movement map (second row), fixation map composed from all saccades (third row), fixation map composed from all saccades that start from one face (fourth row), and AWS saliency map (fifth row). Eye movement data is over all observers. Note that the AWS saliency model does not have an explicit face channel. Try to guess to which face the third row belongs to!
Figure 5
 
Twelve sample images in Experiment 2 along with their corresponding eye movement map (second row), fixation map composed from all saccades (third row), fixation map composed from all saccades that start from one face (fourth row), and AWS saliency map (fifth row). Eye movement data is over all observers. Note that the AWS saliency model does not have an explicit face channel. Try to guess to which face the third row belongs to!
Figure 6
 
Sample images and their corresponding saccade direction pdfs in Experiment 2 (Case 1). In each panel, the face under investigation in the image (left) is marked with a polygon. The polar plot (right) shows the saccade direction pdf for all saccades (Case 1; see text). Data are for saccades that start from inside the polygon and land somewhere else in the image.
Figure 6
 
Sample images and their corresponding saccade direction pdfs in Experiment 2 (Case 1). In each panel, the face under investigation in the image (left) is marked with a polygon. The polar plot (right) shows the saccade direction pdf for all saccades (Case 1; see text). Data are for saccades that start from inside the polygon and land somewhere else in the image.
Figure 7
 
Results of Experiment 2. (A) Distribution of gaze-following and saliency strengths over all data (Case 1). Inset shows the average distribution of saccades over all data (for saccades starting from a head region). The horizontal bias could be largely caused by locations of people and their heads in scenes. This prior is used for calculating the naïve Bayes chance level in all three cases. (B) Average head annotation (Case 3) and average fixation map over all data (for saccades starting from a face). Top horizontal biases can be because faces happen around the top of scenes. (C–D) Distribution of gaze-following and saliency strengths for Cases 2 and 3. Gaze-following strength is significantly higher than both chance levels and maximum saliency direction in all three cases.
Figure 7
 
Results of Experiment 2. (A) Distribution of gaze-following and saliency strengths over all data (Case 1). Inset shows the average distribution of saccades over all data (for saccades starting from a head region). The horizontal bias could be largely caused by locations of people and their heads in scenes. This prior is used for calculating the naïve Bayes chance level in all three cases. (B) Average head annotation (Case 3) and average fixation map over all data (for saccades starting from a face). Top horizontal biases can be because faces happen around the top of scenes. (C–D) Distribution of gaze-following and saliency strengths for Cases 2 and 3. Gaze-following strength is significantly higher than both chance levels and maximum saliency direction in all three cases.
Figure 8
 
Temporal analysis of gaze-following strength for the first 30 saccades. The average is taken for all saccades that start from a face and land somewhere else in the image. For example, an order of second means all saccades that started from a face and were the second overall saccade for a subject on an image. In both panels, the top part shows the gaze-following strength and the bottom part shows the number of samples in each order. The data were binned into three groups when comparing strength over time: Bins 1 (saccades 1–10), 2 (saccades 11–20), and 3 (saccades 21–30), which are colored yellow, blue, and pink, respectively. (A) Experiment 1. (B) Experiment 2.
Figure 8
 
Temporal analysis of gaze-following strength for the first 30 saccades. The average is taken for all saccades that start from a face and land somewhere else in the image. For example, an order of second means all saccades that started from a face and were the second overall saccade for a subject on an image. In both panels, the top part shows the gaze-following strength and the bottom part shows the number of samples in each order. The data were binned into three groups when comparing strength over time: Bins 1 (saccades 1–10), 2 (saccades 11–20), and 3 (saccades 21–30), which are colored yellow, blue, and pink, respectively. (A) Experiment 1. (B) Experiment 2.
Figure 9
 
Fixation prediction results for our simple gaze map and the AWS saliency model over both experiments. Both maps are normalized to be pdfs. Histograms are of saliency and gaze map values at fixation locations (saccades starting from head regions) for (A) controlled pairs in Experiment 1, (B) all data in Experiment 2 (Case 1), (C) images that have only one person in the scene looking at something (Experiment 2, Case 2), and (D) images that have a person gazing at something other than a face when there are multiple people in the scene (Experiment 2, Case 3). Note that, as expected, in all cases there is a peak at the left around 0 for the gaze map because many saccades fell off the gaze map (i.e., misses), mainly because observers did not follow the gaze (although overall they followed gaze direction higher than any other direction). Dashed lines represent medians. Insets show the ROC curves. ROC is measured by thresholding all gaze maps and then calculating the ratio of ground-truth and random fixations that fall above the threshold (corresponding to true positive rate/hit rate and false positive rate/false alarm).
Figure 9
 
Fixation prediction results for our simple gaze map and the AWS saliency model over both experiments. Both maps are normalized to be pdfs. Histograms are of saliency and gaze map values at fixation locations (saccades starting from head regions) for (A) controlled pairs in Experiment 1, (B) all data in Experiment 2 (Case 1), (C) images that have only one person in the scene looking at something (Experiment 2, Case 2), and (D) images that have a person gazing at something other than a face when there are multiple people in the scene (Experiment 2, Case 3). Note that, as expected, in all cases there is a peak at the left around 0 for the gaze map because many saccades fell off the gaze map (i.e., misses), mainly because observers did not follow the gaze (although overall they followed gaze direction higher than any other direction). Dashed lines represent medians. Insets show the ROC curves. ROC is measured by thresholding all gaze maps and then calculating the ratio of ground-truth and random fixations that fall above the threshold (corresponding to true positive rate/hit rate and false positive rate/false alarm).
Figure 10
 
Gaze maps predict fixations in free viewing. (A) Area under ROC curve for gaze and saliency map predictions of fixated locations pooled over all observers in each image. Each data point corresponds to one head gaze (thresholding each map separately). Histograms of AUCs are depicted as marginals (same axes as scatter plot). For points below the diagonal, the gaze map's accuracy is better than the saliency map's (two images). The opposite is the case above the diagonal (58 images). The gaze map has above-chance accuracy for 56 images (60 for the saliency map). (B) The same as (A), but for Experiment 2. Here, 25 images are below the diagonal. The gaze map performs better than chance over 236 images (296 for the saliency map). Example images where either one or both maps perform well are shown on the right, along with their gaze maps, saliency maps, and ROC curves. Overlaid points represent eye movements. Interestingly, in some cases the gaze map predicts fixations much better than the saliency model (e.g., the pregnant woman and the woman watching TV).
Figure 10
 
Gaze maps predict fixations in free viewing. (A) Area under ROC curve for gaze and saliency map predictions of fixated locations pooled over all observers in each image. Each data point corresponds to one head gaze (thresholding each map separately). Histograms of AUCs are depicted as marginals (same axes as scatter plot). For points below the diagonal, the gaze map's accuracy is better than the saliency map's (two images). The opposite is the case above the diagonal (58 images). The gaze map has above-chance accuracy for 56 images (60 for the saliency map). (B) The same as (A), but for Experiment 2. Here, 25 images are below the diagonal. The gaze map performs better than chance over 236 images (296 for the saliency map). Example images where either one or both maps perform well are shown on the right, along with their gaze maps, saliency maps, and ROC curves. Overlaid points represent eye movements. Interestingly, in some cases the gaze map predicts fixations much better than the saliency model (e.g., the pregnant woman and the woman watching TV).
Figure 11
 
Sample images in Experiment 3. Each panel shows the image, the ground-truth gaze direction (shown by a red line, and annotated in the unmasked original scene), and observers' estimations of gaze directions when eyes are visible (top left) and when eyes are masked (bottom left). The top right and bottom right show corresponding polar distributions. The initial point where observers start their vector has been annotated by the experimenter. For some images, eyes are critical for correctly estimating the gaze direction (A). For some cases, observers were equally good with eyes visible and with eyes masked (B), although it seems that in general observers had more variance in their decisions in the eyes-masked condition.
Figure 11
 
Sample images in Experiment 3. Each panel shows the image, the ground-truth gaze direction (shown by a red line, and annotated in the unmasked original scene), and observers' estimations of gaze directions when eyes are visible (top left) and when eyes are masked (bottom left). The top right and bottom right show corresponding polar distributions. The initial point where observers start their vector has been annotated by the experimenter. For some images, eyes are critical for correctly estimating the gaze direction (A). For some cases, observers were equally good with eyes visible and with eyes masked (B), although it seems that in general observers had more variance in their decisions in the eyes-masked condition.
Figure 12
 
Results of Experiment 3. (A) Histogram of gaze estimation strength by observers for eyes-visible and eyes-masked conditions. (B) Median gaze strengths for ground truth and two chance levels for the two conditions, as well as statistical test using the sign test. The median value for chance in the eyes-visible condition is 0 (mean = 0.022, SD = 0.065); for the eyes-masked condition it is also 0 (mean = 0.021, SD = 0.058). See Figure 7A inset for naïve Bayes prior.
Figure 12
 
Results of Experiment 3. (A) Histogram of gaze estimation strength by observers for eyes-visible and eyes-masked conditions. (B) Median gaze strengths for ground truth and two chance levels for the two conditions, as well as statistical test using the sign test. The median value for chance in the eyes-visible condition is 0 (mean = 0.022, SD = 0.065); for the eyes-masked condition it is also 0 (mean = 0.021, SD = 0.058). See Figure 7A inset for naïve Bayes prior.
Figure 13
 
Histogram of normalized saccade length for (A) ground-truth gaze annotations (by the experimenter and when the entire scene is visible), (B) observers' guesses with eyes of people in the scene visible, and (C) observers' guesses with eyes of people in the scene masked. All three histograms show a central peak around 0.4–0.5.
Figure 13
 
Histogram of normalized saccade length for (A) ground-truth gaze annotations (by the experimenter and when the entire scene is visible), (B) observers' guesses with eyes of people in the scene visible, and (C) observers' guesses with eyes of people in the scene masked. All three histograms show a central peak around 0.4–0.5.
Figure 14
 
(A) Histogram of gaze estimation variance in Experiment 3 (in degrees). (B) Histogram of range of estimated gaze angles (cone width).
Figure 14
 
(A) Histogram of gaze estimation variance in Experiment 3 (in degrees). (B) Histogram of range of estimated gaze angles (cone width).
Figure A1
 
The complete set of scenes used in Experiment 1 (30 pairs of images). Some faces have been blurred for privacy reasons.
Figure A1
 
The complete set of scenes used in Experiment 1 (30 pairs of images). Some faces have been blurred for privacy reasons.
Figure A2
 
Gaze-following strength for Experiment 1 and all data (Case 1) in Experiment 2. Data include only the first saccades that also happen to be on the faces.
Figure A2
 
Gaze-following strength for Experiment 1 and all data (Case 1) in Experiment 2. Data include only the first saccades that also happen to be on the faces.
Table 1
 
Summary results of Experiments 1 and 2 for prediction of gaze direction and fixation locations (for fixations that start from the head region). For saccade direction prediction: Both gaze and most salient directions are significant predictors of observers' saccade direction (p < 0.05 using sign test vs. both uniform and naïve chance levels) in both experiments and in all cases. In both experiments, gaze direction performs significantly higher than maximum saliency direction in predicting observers' saccade directions. For saccade endpoint prediction: Both gaze and saliency maps outperform chance significantly above chance (AUC for chance is 0.5, corresponding to a white-noise map). AUCs here are calculated by thresholding all maps at a certain threshold level and measuring true positive and false positive rates across all maps. Overall, our simple gaze map explains fixations significantly below the best existing purely bottom-up saliency model, but there are some cases where our gaze map wins over the saliency map.
Table 1
 
Summary results of Experiments 1 and 2 for prediction of gaze direction and fixation locations (for fixations that start from the head region). For saccade direction prediction: Both gaze and most salient directions are significant predictors of observers' saccade direction (p < 0.05 using sign test vs. both uniform and naïve chance levels) in both experiments and in all cases. In both experiments, gaze direction performs significantly higher than maximum saliency direction in predicting observers' saccade directions. For saccade endpoint prediction: Both gaze and saliency maps outperform chance significantly above chance (AUC for chance is 0.5, corresponding to a white-noise map). AUCs here are calculated by thresholding all maps at a certain threshold level and measuring true positive and false positive rates across all maps. Overall, our simple gaze map explains fixations significantly below the best existing purely bottom-up saliency model, but there are some cases where our gaze map wins over the saliency map.
Experiment 1 Experiment 2, Case 1 Experiment 2, Case 2 Experiment 2, Case 3
Predicting saccade direction (medians)
 Gaze direction 0.220 0.326 0.378 0.241
 Most salient direction 0.101 0.132 0.149 0.138
 Uniform chance 0.023 0.029 0.046 0.035
 Naïve Bayes chance 0.061 0.081 0.098 0.080
Predicting fixation locations (AUC values)
 Gaze map 0.612 0.625 0.646 0.568
 Saliency map 0.797 0.789 0.795 0.794
 Chance 0.5 0.5 0.5 0.5
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