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Article  |   November 2018
The contribution of local and global motion adaptation in the repulsive direction aftereffect
Author Affiliations
  • Alan L. F. Lee
    Department of Applied Psychology, Lingnan University, Hong Kong
Journal of Vision November 2018, Vol.18, 2. doi:10.1167/18.12.2
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      Alan L. F. Lee; The contribution of local and global motion adaptation in the repulsive direction aftereffect. Journal of Vision 2018;18(12):2. doi: 10.1167/18.12.2.

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Abstract

After adapting to a certain motion direction, our perception of a similar direction will be repelled away from the adapting direction, a phenomenon known as the direction aftereffect (DAE). As the motion system consists of local and global processing stages, it remains unclear how the adaptation of the two stages contributes in producing the DAE. The present study addresses this question by independently inducing adaptation at local and global motion-processing levels. Local adaptation was manipulated by presenting test stimuli at either adapted or nonadapted locations. Global adaptation was manipulated by embedding one or five global motion directions in the adapting motion. Repulsive DAE, when measured using a multiple-element test pattern, was stronger when it was produced by global adaptation than when produced by local adaptation. Specifically, the DAE resulting from local adaptation (a) decreased when test orientations differed from adapting orientation, (b) decreased when local directions were disambiguated using plaid stimuli, (c) remained the same even when attention was focused at specific test locations during adaptation, and (d) increased when tested with a single element. Overall, these findings suggest that the strength of repulsive DAE depends on both the motion-processing level at which adaptation occurs and the level at which the DAE was tested. Furthermore, the repulsive DAE arising from local adaptation alone can be explained by the propagation of local speed repulsion instead of local direction repulsion. Findings are discussed in the context of how motion aftereffects arise from the adaptation of a hierarchical motion system.

Introduction
Our perception can be altered by changes in recent stimulus history. Specifically, after adapting to a certain sensory stimulus (e.g., adaptor = upward motion direction), the subjective percept of a subsequently presented test stimulus (e.g., test = 45° clockwise from upward) is repelled away from the adapting stimulus (e.g., percept = 60° clockwise from upward). Such adaptation-induced perceptual repulsion (Clifford et al., 2007) has been widely observed in many perceptual domains, including orientation (Gibson & Radner, 1937), motion (Levinson & Sekuler, 1976; Schrater & Simoncelli, 1998; Stocker & Simoncelli, 2009), face (Webster, Kaping, Mizokami, & Duhamel, 2004), and biological motion (Troje, Sadr, Geyer, & Nakayama, 2006). In particular, the direction aftereffect (DAE) is an important measure to quantify the strength of the adaptation-induced repulsive effect. It is measured as the angular difference between the direction of the true testing stimulus and perceived direction. 
However, given that the visual system is a hierarchical system, adaptation can induce changes at different levels of visual processing. In particular, motion processing can be generally divided into two stages: Local motion signals are extracted across multiple locations in the visual field and then integrated to produce a global motion percept in a later processing stage. When this hierarchical, multilevel, motion-processing system adapts, how do different levels of adaptation contribute to the generation of DAE? 
It has been proposed that DAE is mainly driven by adaptation of local motion detectors. Curran, Clifford, and Benton (2006) measured DAE strengths across different adapting speeds and found that DAE was speed-tuned: DAE was the strongest when the test speed was the same as the adaptor speed. They then constructed two models that focus on different stages of motion processing, namely local and global. They found that the local-motion model was better in predicting variation in DAE strength than the global-motion model was, suggesting that the DAE is mainly driven by the adaptation of detectors at the local-processing stage in the motion system. 
On the other hand, perceptual repulsion can be generated from the adaptation of the global level of motion processing. Direction-selective units in area MT were found to shift their tuning peaks toward the adaptor direction (Kohn & Movshon, 2004), which could be driving the repulsive DAE. Although V1 neurons generally shift their tuning peaks away from the adaptor direction, such “repulsive peak shift” alone should actually produce perceptual attraction (Jin, Dragoi, Sur, & Seung, 2005). Such apparent discrepancy raises two questions regarding hierarchical adaptation in the generation of DAE. First, how do the adaptations of the local and global motion-processing levels contribute in generating the repulsive DAE? If one could independently induce adaptation at the local and global levels of motion processing, it would be possible to measure the DAE generated from the adaptation of a specific level of motion processing. From such results, it would be possible to compare the contribution of the adaptation of different processing levels in generating DAE. Second, Curran et al.'s (2006) findings may be more precisely interpreted as that the speed-tuning property of DAE is based on local speed instead of global speed. If it is the speed component in the local motion signals that is driving DAE, does the direction component of the local motion signals also contribute in generating DAE? 
One challenge in addressing these questions is to design an appropriate stimulus that induces adaptation independently to low- and high-level motion detectors. In a number of studies on motion processing, researchers have used various psychophysical techniques to induce or suppress adaptation at a specific level of processing. 
For low-level detectors, drifting gratings have been widely used as an inducer for adaptation (Anstis, Verstraten, & Mather, 1998; Kohn & Movshon, 2003, 2004; Nishida & Ashida, 2001). Gratings allow researchers to specifically probe low-level, local motion detectors because they allow researchers to independently manipulate various aspects of motion, including stimulus location, orientation, spatial frequency, and temporal frequency, for which low-level motion detectors are known to be selectively tuned (Adelson & Bergen, 1985; Ibbotson & Price, 2001; van Santen & Sperling, 1985). 
To suppress low-level adaptation, some researchers have probed perceptual aftereffect at locations or regions at which adaptation stimulus has not been presented (Kohn & Movshon, 2003; Scarfe & Johnston, 2011; Snowden & Milne, 1997; Weisstein, Maguire, & Berbaum, 1977). Because low-level detectors are believed to have small and localized receptive fields, one could minimize local adaptation by adapting the motion system in certain parts of the visual field and then test it at the nonadapted regions or locations. Because high-level global-motion units usually integrate motion signals across relatively large receptive fields (Morrone, Burr, & Vaina, 1995), the aftereffect observed at these nonadapted regions is generally assumed to be caused by the adaptation of these global detectors. Indeed, using this technique, researchers have found what has been known as the “phantom” aftereffect (Lee & Lu, 2012, 2014; Price, Greenwood, & Ibbotson, 2004; Snowden & Milne, 1997; Weisstein et al., 1977). However, it should be emphasized that “local level” in the present study refers to location-specific motion-processing mechanisms. Therefore, “local adaptation” or “adaptation of the local level” refers to the changes in these location-specific mechanisms resulting from prolonged stimulus exposure at their corresponding receptive field locations. 
For the global motion-processing level, one way to suppress the adaptation of direction-selective units is to embed multiple motion directions within one motion pattern. Population response of direction-selective MT neurons depends on the underlying composition of motion directions in a stimulus pattern (Treue, Hol, & Rauber, 2000). When two widely separated directions (e.g., 0° and 180°) are presented, population response is bimodal, which gives rise to the percept of transparent motion (Qian, Andersen, & Adelson, 1994; Treue et al., 2000). However, because there is a limit of bandwidth in their direction tuning (Bair & Movshon, 2004), if more directions were embedded within the same spatial region in the visual field, the population response of direction-selective units would become too flat to encode any specific directions. This is further supported by the psychophysical finding that humans are unable to perceive, for example, five evenly separated directions embedded within a single motion pattern (Greenwood & Edwards, 2006a, 2006b, 2009). Therefore, it is possible to “overload” the direction-selective global-motion units with a multidirectional pattern. If such a multidirectional pattern is used as an adaptor, it is possible to suppress direction-specific adaptation at the global level of motion processing. By suppressing the contribution from the global level of motion processing, one could separate adaptation-induced effects that are generated from the adaptation of local motion processing. 
Along this direction, “global level” in the present study refers to the direction-selective units with large receptive fields that integrate local motion signals across locations, and “adaptation of the global level” in this study refers to the changes in such high-level mechanisms resulting from prolonged exposure to a motion with a specific global direction. 
The present study combined the above techniques to investigate the contribution of level-specific adaptation in generating the repulsive DAE. Strength of the repulsive DAE induced by adaptation at local and global levels of motion processing was measured. Specifically, I combined the multiple-aperture stimulus (Amano, Edwards, Badcock, & Nishida, 2009), which allows independent manipulation of local and global motion signals, with the “direction-overloading” technique (Lee & Lu, 2014) to induce adaptation at specific processing levels in the motion-processing hierarchy. 
In Experiment 1, I independently induced adaptation at the local and global levels of motion processing and separately measured the DAE generated from such level-specific adaptation. As a shorthand, in the remaining sections of this paper, I refer to (a) the DAE generated solely based on the adaptation of the global level of motion processing as DAE-GLOBAL and (b) the DAE generated solely based on the adaptation of the local level of motion processing as DAE-LOCAL
In Experiments 2 and 3, I focused on mechanisms underlying the generation of DAE-LOCAL by manipulating the difference between adapting and test orientations (Experiment 2) and stimulus type by replacing Gabor elements with plaid elements (Experiment 3). In Experiment 4, I manipulated observer's attention during adaptation, changing it from focusing on central fixation to focusing on specific local elements, and measured the resulting DAEs. In Experiment 5, I quantified the strength of local adaptation by measuring location-specific DAE using a single Gabor element as test stimulus. 
General methods
Participants
Participants were undergraduate students at the University of California, Los Angeles (UCLA) for Experiments 13 and at Lingnan University, Hong Kong (Lingnan), for Experiments 4 and 5. They participated either for course credit or for monetary reward. All participants had normal or corrected-to-normal vision and were naïve to the purpose of the experiments. The experiments were approved by UCLA's Office for Protection of Research Subjects (for Experiments 13) and Lingnan's Research Ethics Committee (for Experiments 4 and 5). 
Design
The general design was similar to my previous study (Lee & Lu, 2014), which aimed to separately evaluate the contribution of adaptation at the local and the global levels of motion processing in producing motion aftereffect (MAE). Two key stimulus features were manipulated. First, test locations were manipulated to control local-level adaptation. Aftereffect was either tested at locations at which motion stimulus was presented during adaptation (Adapted) or at locations at which motion stimulus was absent during adaptation (Nonadapted). Second, the number of global adapting directions was manipulated to control direction-specific, global-level adaptation. When all elements exhibited one global motion direction during adaptation (1Dir), global adaptation should be strong. When five global directions were introduced to the adapting stimulus (5Dir), there should be minimal direction-specific activation and, thus, adaptation at the global level. Crossing these two independent variables resulted in a two-by-two factorial design, which consisted of four conditions, named by the level(s) at which adaptation was introduced: BOTH (1Dir-Adapted), GLOBAL (1Dir-Nonadapted), LOCAL (5Dir-Adapted), and NEITHER (5Dir-Nonadapted). 
Stimulus and apparatus
The stimulus (illustrated in the left panel of Figure 1) consisted of 264 Gabor elements. Each element was a sine wave grating, windowed by a stationary Gaussian function with a standard deviation of 0.21°. Spatial frequency was 2 c/° for all elements. Contrast was fixed at a low level for all experiments (Michelson contrast: 0.05 for Experiments 13, 0.10 for Experiment 4, and 0.15 for Experiment 5) in order to enhance the perception of global motion based on spatial integration of local motion signals in the multiple-Gabor stimulus (Takeuchi, 1998). The diameter of each element spanned a visual angle of 1°. Positions of elements were fixed within a 20-by-20 grid and arranged in an annulus spanning 4°–10° of visual angle. Central elements were removed to minimize eye movements caused by tracking motion of elements near fixation. Elements were tightly packed, so that separation between any two adjacent cells was zero. The whole pattern was centered within a circular aperture, with radius spanning 13° of visual angle. The background luminance value within this large aperture was at the mean (i.e., gray), and pixels outside this aperture were set to black. This circular aperture was to minimize possible directional bias in responses caused by the rectangular frame of the monitor. 
Figure 1
 
Stimulus and design of the experiments. Left: Illustration of the adapting stimulus. Dashed circles (not shown in actual stimuli) highlight the locations without Gabor elements (i.e., the nonadapted locations). Number of elements has been reduced for illustration purposes. The actual stimulus contained about four times more elements. Right (adopted from Lee & Lu, 2014): The illustrations of the conditions resulting from the 2 × 2 design based on the example pattern on the right panel. Under “Adapting pattern,” each circle represents a Gabor element. Colors represent different sets that were assigned different global adapting directions (indicated by the arrow within each empty circle). Elements with the same color were assigned the same global adapting direction. In this example, red represents the reference set (see description of stimulus in Stimulus and apparatus for details). Under “Test locations,” solid circles represent locations at which elements were presented during the test phase. Red and black colors correspond to the reference-set locations and the nonadapted locations (i.e., the dashed circles on the left panel), respectively.
Figure 1
 
Stimulus and design of the experiments. Left: Illustration of the adapting stimulus. Dashed circles (not shown in actual stimuli) highlight the locations without Gabor elements (i.e., the nonadapted locations). Number of elements has been reduced for illustration purposes. The actual stimulus contained about four times more elements. Right (adopted from Lee & Lu, 2014): The illustrations of the conditions resulting from the 2 × 2 design based on the example pattern on the right panel. Under “Adapting pattern,” each circle represents a Gabor element. Colors represent different sets that were assigned different global adapting directions (indicated by the arrow within each empty circle). Elements with the same color were assigned the same global adapting direction. In this example, red represents the reference set (see description of stimulus in Stimulus and apparatus for details). Under “Test locations,” solid circles represent locations at which elements were presented during the test phase. Red and black colors correspond to the reference-set locations and the nonadapted locations (i.e., the dashed circles on the left panel), respectively.
The grating of each element was set to drifting motion, and its position remained constant. Orientation of each element Display Formula\(\def\upalpha{\unicode[Times]{x3B1}}\)\(\def\upbeta{\unicode[Times]{x3B2}}\)\(\def\upgamma{\unicode[Times]{x3B3}}\)\(\def\updelta{\unicode[Times]{x3B4}}\)\(\def\upvarepsilon{\unicode[Times]{x3B5}}\)\(\def\upzeta{\unicode[Times]{x3B6}}\)\(\def\upeta{\unicode[Times]{x3B7}}\)\(\def\uptheta{\unicode[Times]{x3B8}}\)\(\def\upiota{\unicode[Times]{x3B9}}\)\(\def\upkappa{\unicode[Times]{x3BA}}\)\(\def\uplambda{\unicode[Times]{x3BB}}\)\(\def\upmu{\unicode[Times]{x3BC}}\)\(\def\upnu{\unicode[Times]{x3BD}}\)\(\def\upxi{\unicode[Times]{x3BE}}\)\(\def\upomicron{\unicode[Times]{x3BF}}\)\(\def\uppi{\unicode[Times]{x3C0}}\)\(\def\uprho{\unicode[Times]{x3C1}}\)\(\def\upsigma{\unicode[Times]{x3C3}}\)\(\def\uptau{\unicode[Times]{x3C4}}\)\(\def\upupsilon{\unicode[Times]{x3C5}}\)\(\def\upphi{\unicode[Times]{x3C6}}\)\(\def\upchi{\unicode[Times]{x3C7}}\)\(\def\uppsy{\unicode[Times]{x3C8}}\)\(\def\upomega{\unicode[Times]{x3C9}}\)\(\def\bialpha{\boldsymbol{\alpha}}\)\(\def\bibeta{\boldsymbol{\beta}}\)\(\def\bigamma{\boldsymbol{\gamma}}\)\(\def\bidelta{\boldsymbol{\delta}}\)\(\def\bivarepsilon{\boldsymbol{\varepsilon}}\)\(\def\bizeta{\boldsymbol{\zeta}}\)\(\def\bieta{\boldsymbol{\eta}}\)\(\def\bitheta{\boldsymbol{\theta}}\)\(\def\biiota{\boldsymbol{\iota}}\)\(\def\bikappa{\boldsymbol{\kappa}}\)\(\def\bilambda{\boldsymbol{\lambda}}\)\(\def\bimu{\boldsymbol{\mu}}\)\(\def\binu{\boldsymbol{\nu}}\)\(\def\bixi{\boldsymbol{\xi}}\)\(\def\biomicron{\boldsymbol{\micron}}\)\(\def\bipi{\boldsymbol{\pi}}\)\(\def\birho{\boldsymbol{\rho}}\)\(\def\bisigma{\boldsymbol{\sigma}}\)\(\def\bitau{\boldsymbol{\tau}}\)\(\def\biupsilon{\boldsymbol{\upsilon}}\)\(\def\biphi{\boldsymbol{\phi}}\)\(\def\bichi{\boldsymbol{\chi}}\)\(\def\bipsy{\boldsymbol{\psy}}\)\(\def\biomega{\boldsymbol{\omega}}\)\(\def\bupalpha{\unicode[Times]{x1D6C2}}\)\(\def\bupbeta{\unicode[Times]{x1D6C3}}\)\(\def\bupgamma{\unicode[Times]{x1D6C4}}\)\(\def\bupdelta{\unicode[Times]{x1D6C5}}\)\(\def\bupepsilon{\unicode[Times]{x1D6C6}}\)\(\def\bupvarepsilon{\unicode[Times]{x1D6DC}}\)\(\def\bupzeta{\unicode[Times]{x1D6C7}}\)\(\def\bupeta{\unicode[Times]{x1D6C8}}\)\(\def\buptheta{\unicode[Times]{x1D6C9}}\)\(\def\bupiota{\unicode[Times]{x1D6CA}}\)\(\def\bupkappa{\unicode[Times]{x1D6CB}}\)\(\def\buplambda{\unicode[Times]{x1D6CC}}\)\(\def\bupmu{\unicode[Times]{x1D6CD}}\)\(\def\bupnu{\unicode[Times]{x1D6CE}}\)\(\def\bupxi{\unicode[Times]{x1D6CF}}\)\(\def\bupomicron{\unicode[Times]{x1D6D0}}\)\(\def\buppi{\unicode[Times]{x1D6D1}}\)\(\def\buprho{\unicode[Times]{x1D6D2}}\)\(\def\bupsigma{\unicode[Times]{x1D6D4}}\)\(\def\buptau{\unicode[Times]{x1D6D5}}\)\(\def\bupupsilon{\unicode[Times]{x1D6D6}}\)\(\def\bupphi{\unicode[Times]{x1D6D7}}\)\(\def\bupchi{\unicode[Times]{x1D6D8}}\)\(\def\buppsy{\unicode[Times]{x1D6D9}}\)\(\def\bupomega{\unicode[Times]{x1D6DA}}\)\(\def\bupvartheta{\unicode[Times]{x1D6DD}}\)\(\def\bGamma{\bf{\Gamma}}\)\(\def\bDelta{\bf{\Delta}}\)\(\def\bTheta{\bf{\Theta}}\)\(\def\bLambda{\bf{\Lambda}}\)\(\def\bXi{\bf{\Xi}}\)\(\def\bPi{\bf{\Pi}}\)\(\def\bSigma{\bf{\Sigma}}\)\(\def\bUpsilon{\bf{\Upsilon}}\)\(\def\bPhi{\bf{\Phi}}\)\(\def\bPsi{\bf{\Psi}}\)\(\def\bOmega{\bf{\Omega}}\)\(\def\iGamma{\unicode[Times]{x1D6E4}}\)\(\def\iDelta{\unicode[Times]{x1D6E5}}\)\(\def\iTheta{\unicode[Times]{x1D6E9}}\)\(\def\iLambda{\unicode[Times]{x1D6EC}}\)\(\def\iXi{\unicode[Times]{x1D6EF}}\)\(\def\iPi{\unicode[Times]{x1D6F1}}\)\(\def\iSigma{\unicode[Times]{x1D6F4}}\)\(\def\iUpsilon{\unicode[Times]{x1D6F6}}\)\(\def\iPhi{\unicode[Times]{x1D6F7}}\)\(\def\iPsi{\unicode[Times]{x1D6F9}}\)\(\def\iOmega{\unicode[Times]{x1D6FA}}\)\(\def\biGamma{\unicode[Times]{x1D71E}}\)\(\def\biDelta{\unicode[Times]{x1D71F}}\)\(\def\biTheta{\unicode[Times]{x1D723}}\)\(\def\biLambda{\unicode[Times]{x1D726}}\)\(\def\biXi{\unicode[Times]{x1D729}}\)\(\def\biPi{\unicode[Times]{x1D72B}}\)\(\def\biSigma{\unicode[Times]{x1D72E}}\)\(\def\biUpsilon{\unicode[Times]{x1D730}}\)\(\def\biPhi{\unicode[Times]{x1D731}}\)\(\def\biPsi{\unicode[Times]{x1D733}}\)\(\def\biOmega{\unicode[Times]{x1D734}}\)\(\theta \) was independently and uniformly sampled in the range of 0°–180°. A global motion vector with speed Display Formula\(v\) and direction Display Formula\(\alpha \), was assigned to each element. The local drifting speed Display Formula\(u\) for each element was then computed based on the following equation:  
\begin{equation}u = v\sin \left( {\alpha - \theta } \right){\rm {,}}\end{equation}
where Display Formula\(v\) was set to be 2°/s for all experiments and Display Formula\(\alpha \) depended on the number of adapting directions (see descriptions below).  
To manipulate level-specific adaptation, all 264 elements were randomly split into six sets, so that the number of global adapting directions and test locations could be independently manipulated. One of the six sets was randomly chosen to be the reference set (e.g., the red locations in the right panel in Figure 1) and another one the nonadapted set (e.g., the black locations in the right panel in Figure 1). During the adaptation phase of all conditions, elements in the nonadapted set would not be presented so that there would not be any adapting motion signals at those locations. The number of global adapting directions was manipulated by assigning global motion directions to the five sets (i.e., reference and the other four). In the 1Dir conditions (BOTH and GLOBAL), the same global motion direction Display Formula\(r\) was assigned to all elements, i.e., Display Formula\(\alpha = r\). In the 5Dir conditions (LOCAL and NEITHER), five global motion vectors, all with the same speed but different directions (evenly spaced around 360°) were assigned to the five sets. Formally, the global direction Display Formula\({a_i}\) for each set Display Formula\(i\) (for Display Formula\(i = 1,2,3,4,\rm and\ 5\)) was  
\begin{equation}{\alpha _i} = r + \left( {i - 1} \right)\left( {72^\circ } \right){\rm {,}}\end{equation}
with Display Formula\({\alpha _1}\) being the global direction for the reference set, so that Display Formula\({\alpha _1} = r\). In Experiment 1A, observers performed a direction-judgment task (see General procedure), and the reference direction Display Formula\(r\) was randomly varied across blocks of trials in order to avoid any direction-specific effects on the responses. In other experiments in which observers performed a direction-discrimination task (see General procedure), Display Formula\(r\) was always 45° away either to the left or right from the upward direction.  
In the test stimulus, all elements were assigned the same global-motion vector. The speed of this vector was the same as the adapting speed (i.e., 2°/s). The direction of this vector depended on the task (see General procedure). Test locations were manipulated by choosing which set of elements was to be displayed as a test stimulus. In the Adapted conditions (BOTH and LOCAL), only elements in the reference set were displayed during the test so that, at these test locations, adapting motion signals had all been consistent with one single global adapting direction, i.e., Display Formula\(r\). In the Nonadapted conditions (GLOBAL and NEITHER), only elements in the nonadapted set were presented for the test so that the aftereffect probed at these locations should have minimal (if any) contribution from the adaptation of low-level, location-specific motion detectors. Four demo movies that illustrate the four conditions can be found in the Supplementary Materials (Supplementary Movies S1S4). 
For all experiments, MATLAB (MathWorks, Natick, MA) and PsychToolbox (Brainard, 1997; Pelli, 1997) were used to generate the stimuli. For Experiments 13, stimuli were presented in a dim room on a Viewsonic CRT monitor (refresh rate = 75 Hz, resolution = 1,024 × 768 pixels). Viewing distance was kept constant at 57 cm using a chinrest and forehead rest, resulting in a visual angle of 2.01 arcmin for each pixel on the monitor. A Minolta CS-100 photometer was used to calibrate the monitor and converted a luminance range of 0–146.5 cd/m2 into a linear lookup table for 256 intensity levels. For Experiments 4 and 5, stimuli were presented in a dim room on a BenQ XL2411Z LCD monitor (refresh rate = 120 Hz, resolution = 1,440 × 900 pixels). The luminance range of around 0–100 cd/m2 was calibrated into a linear lookup table for 256 intensity levels using a psychophysical procedure (To, Woods, Goldstein, & Peli, 2013). 
General procedure
In all experiments, observers were instructed to maintain fixation at the fixation cross located at the center of the display. Each trial consisted of three phases: adaptation, test, and response. In order to inform observers of the different phases in each trial, the fixation cross was green, red, and white during the adaptation, test, and response phases, respectively. During adaptation, observers viewed the adapting stimulus for a relative long duration (initial adaptation: 40–60 s; top-up adaptation: 5–10 s; exact duration differed across experiments). After adaptation, a blank screen was presented for 500 ms, followed by the test phase, which lasted for 720 ms and during which the test stimulus was presented. In the response phase, none of the stimulus elements were presented on the screen, and the observer made a response, normally within 3 s. These durations were chosen to match with those used in Schrater and Simoncelli's (1998) study. 
Observers performed one of the two tasks described below, depending on the specific experiment setup. In Experiment 1A, the observer performed a direction-judgment task, in which a simulated dial was displayed during the response phase with a white circular frame (radius = 11° of visual angle) and a short (1.5°) red indicator line extending outward from the circular frame to the edge of the large aperture. Observers were instructed to turn this dial (i.e., move the red indicator line around the white circle) by pressing the left or the right arrow key to indicate their perceived global direction of motion during the test phase. When the red indicator was pointing at the desired direction, the observer pressed the space bar to submit this direction as the response for the trial. To minimize any systematic bias caused by the default position, the initial direction to which the red indicator line pointed was uniformly sampled around the 360° range in every trial. In all other experiments, observers performed a direction-discrimination task. Nothing except the fixation cross was displayed on the monitor during the response phase. The task was to determine whether the global motion direction of the test stimulus was to the left (i.e., counterclockwise) or to the right (i.e., clockwise) relative to the upward direction. 
Trials were grouped into blocks of 10–16 trials with the first trial in the block having the longest initial adaptation duration. Top-up adapting motion patterns within the same block were random excerpts of the adapting stimulus of the first trial so that the adapting stimulus of each trial within the same block showed exactly the same element configuration (e.g., orientations, assignment of sets, assignment of global adapting directions, etc.). 
Experiment 1: To compare the DAEs generated from adaptation of different levels of motion processing
In Experiment 1, I investigated whether adaptation at the local and the global levels of motion processing would lead to different DAE strengths. I employed the two-by-two factorial design described in General methods and instructed observers to perform the direction-judgment task. The BOTH and NEITHER conditions would, respectively, provide the benchmarks for the maximum and minimum DAE strengths. In the data analysis, I focus on comparing the DAE strengths between the GLOBAL and LOCAL conditions: If DAE depended on the level at which adaptation occurs, perceptual biases in the GLOBAL and LOCAL conditions would differ. 
Experiment 1A: Assessing DAE across the full range of test directions
Methods
Stimulus was as described in the General methods. The two-by-two factorial design was employed, resulting in the four conditions: BOTH, GLOBAL, LOCAL, and NEITHER. For each condition, 16 directions Display Formula\({t_i}\), for Display Formula\(i = 1,2, \ldots ,16\), relative to the reference adapting direction Display Formula\(r\) were tested. The 16 directions were evenly spaced within the range [−168.75°, 168.75°] with an interval of Display Formula\(22.5^\circ \),  
\begin{equation}{t_i} = r + \left( { - 168.75^\circ + 22.5^\circ \left( {i - 1} \right)} \right){\rm {.}}\end{equation}
 
Thirty-six observers participated in this experiment with nine in each of the four conditions. Observers performed the direction-judgment task. In order to assess whether there were any preexisting biases in direction judgment, observers first completed a Test-only session: the adaptation phase was removed, and observers viewed the test stimulus only and judged its motion direction. There were five blocks of 16 trials. The 16 test directions Display Formula\({t_i}\) were randomly assigned to the 16 trials within a block so that each direction was tested five times (once in each block) for each observer in each session. Afterward, observers completed the Adapt-Test session, which was identical to the previous Test-only session except that the adaptation phase preceded the test phase in each block. In this Adapt-Test session, each block was assigned the reference adapting direction Display Formula\(r\), which was randomly sampled from a uniform distribution with the constraint that the five Display Formula\(r\) values were at least 60° apart in order to avoid massing all Display Formula\(r\) values within a limit range for a particular observer. A 60-s rest period was given between every two blocks to allow time for the previous block's adaptation effects to dissipate. Initial and top-up adaptation durations were 60 s and 10 s, respectively. Observers completed two short practice blocks at the beginning of each session to familiarize themselves with the experiment. 
Results
In each trial, perceptual bias was computed by subtracting the actual test direction from the reported direction. A 0° bias represents a reported direction that coincided with the actual test direction. Trials with absolute perceptual bias greater than 90° were removed (234 out of 2,880 trials, around 8%) from the analysis for each observer because they appeared to be outlier responses relative to the other trials. The averaged perceptual bias for each observer in each session was then computed. 
Figure 2A shows the perceptual biases for all four conditions in both the Test-only and Adapt-Test sessions averaged across observers. Perceptual bias was around zero in the Test-only session across all conditions, suggesting that there was not systematic bias in direction judgment without motion adaptation. For the Adapt-Test session (thick, colored lines with open symbols), perceptual bias appears to differ across conditions. The characteristic “S” shape of a repulsive bias curve was found in the BOTH condition but was absent in the NEITHER condition. A similar trend of DAE was found in the GLOBAL condition, but the bias curve for the LOCAL condition does not show much DAE. 
Figure 2
 
Results of Experiment 1A (n = 36, n = 9 in each condition). (A) Bias curves across all 16 test directions relative to the adapting direction. Each column represents one of the four conditions. Top row shows the biases in the Test-only session. Bottom panel shows the biases in the Adapt-Test sessions. Thin lines show biases of individual observers. Thick lines represent the means across observers in each session. (B) Fitting of bias curves for the Adapt-Test session for four example observers, one from each condition. (C) Bias indices for the four conditions in the Adapt-Test session. Error bars are ±1 between-subjects SEM.
Figure 2
 
Results of Experiment 1A (n = 36, n = 9 in each condition). (A) Bias curves across all 16 test directions relative to the adapting direction. Each column represents one of the four conditions. Top row shows the biases in the Test-only session. Bottom panel shows the biases in the Adapt-Test sessions. Thin lines show biases of individual observers. Thick lines represent the means across observers in each session. (B) Fitting of bias curves for the Adapt-Test session for four example observers, one from each condition. (C) Bias indices for the four conditions in the Adapt-Test session. Error bars are ±1 between-subjects SEM.
In order to quantify the strength of DAE, I fitted the average perceptual bias Display Formula\({b_i}\) for each observer using the following function:  
\begin{equation}{\hat b_i} = a\sin {t_i}\exp \left( {\cos {t_i}} \right){\rm {,}}\end{equation}
where Display Formula\(a\) serves as a bias index for each observer. Sample fitting results are shown in Figure 2B. The sign of Display Formula\(a\) indicates the direction of bias; positive means repulsive bias, and negative means attractive bias. The magnitude of Display Formula\(a\) represents the strength of bias, particularly around a test direction of Display Formula\( \pm \)45° from the adapting direction.  
For the Test-only session, average bias indices for BOTH, GLOBAL, LOCAL, and NEITHER were, respectively, 1.98 (95% confidence inverval [CI] = [−1.86, 5.83]), −0.31 (95% CI = [−1.49, 0.86]), −0.04 (95% CI = [−2.27, 2.18]), and 0.45 (95% CI = [−1.31, 2.21]). Overall, observers did not show significant bias in the Test-only session (i.e., before adaptation) as the CIs of all bias indices included zero. 
Next, I analyzed the bias indices in the Adapt-Test session using a two-way ANOVA with two factors, test location (adapted vs. nonadapted) and global adaptation directions (one vs. five). These two factors correspond to the presence and absence of adaptation at two levels of motion processing, i.e., global adaptation and local adaptation. Figure 2C shows the average bias index in the Adapt-Test session for the four conditions. There was no significant two-way interaction, F(1, 32) = 0.164, p = 0.689. The main effects of both factors were found to be significant: global adaptation, F(1,,32) = 110.724, p < 10−11; local adaptation: F(1, 32) = 11.472, p = 0.002, suggesting that adaptation at both levels contributed to the generation of DAE. In particular, the magnitude of perceptual bias was found to be much stronger in the GLOBAL condition (M = 9.83, SD = 2.42) than in the LOCAL condition (M = 3.78, SD = 3.06), F(1, 32) = 25.458, p < 10−4, which was significantly stronger than the NEITHER condition (M = 0.57, SD = 1.71, 95% CI = [−1.16, 2.30]), F(1, 32) = 7.188, p = 0.012. 
Perceptual bias in the BOTH condition (M = 12.36, SD = 2.77) was significantly stronger than that in the GLOBAL condition, F(1, 32) = 28.742, p = 0.043. Finally, as expected, the bias index in the NEITHER condition was close to zero (M = 0.57, SD = 1.71, 95% CI = [−1.16, 2.30]). 
Results in Experiment 1A suggest that DAE depends on the processing level at which adaptation occurs. In particular, DAE-GLOBAL was found to be significantly stronger than DAE-LOCAL when the DAE was tested using a multiple-element pattern. 
In order to obtain a more precise and reliable measure of the strengths of the DAEs in the four conditions, I conducted Experiment 1B, which employed the same two-by-two design but different psychophysical paradigms and a different task. The goal of Experiment 1B was to narrow down the measurement of the strength of DAE at Display Formula\( \pm 45^\circ \) away from the adapting direction. I used these directions based on the results of Experiment 1A in which the strongest DAEs were revealed with these directions. This approach has been used in previous psychophysical studies in measuring the strength of DAE (Curran et al., 2006; Wenderoth & Wiese, 2008). 
Experiment 1B: To measure the strength of DAE caused by level-specific adaptation
Methods
Experiment 1B aimed to measure the point of subjective equality (PSE) of the upward direction after adapting to the oblique 45° (up-left or up-right) direction. 
General stimulus parameters were identical to those used in Experiment 1A unless otherwise specified. General procedure was similar to that in Experiment 1A except that observers performed the direction-discrimination task during the response phase. They pressed the left or right arrow key to, respectively, indicate whether the overall motion direction of the test stimulus was counterclockwise or clockwise relative to the upward direction. 
Two psychophysical procedures, namely constant-stimuli and adaptive-staircase, were used to measure the PSE in each condition. For the constant-stimuli procedure, five observers participated for monetary reward. Nine test directions were chosen based on pilot experiments. They spanned a range of 60° and were evenly spaced around the upward direction. The reference adapting direction Display Formula\(r\) was either counterclockwise 45° or clockwise 45° relative to the upward direction. Adaptation durations were the same as those used in Experiment 1A (initial: 60 s; top-up: 10 s). Observers completed the four conditions of the experiments in separate sessions with one condition assigned to each session. Order of conditions was counterbalanced across observers. In each condition, observers made 144 direction-discrimination responses (nine test directions × 16 trials). These 144 trials were blocked into eight blocks of 18 trials. Two repetitions of the nine test directions were randomly interleaved within a block. The counterclockwise and clockwise 45° adapting directions of Display Formula\(r\) were alternated across the blocks, and there were eight trials for each adapting direction in each condition. There was a 60-s rest period between every two blocks of trials. Observers completed two short practice blocks at the beginning of the first session for familiarization of the task. 
For the adaptive-staircase procedure, 12 observers participated for course credits. In this procedure, I used the adaptive Psi staircase method (Kontsevich & Tyler, 1999) implemented in the Palamedes Toolbox (Prins & Kingdom, 2009). Test directions were determined adaptively using the adaptive Psi method. Initial and top-up adaptation durations were 45 and 6 s, respectively. Each observer completed 12 blocks of 16 trials, resulting in a total of 196 trials (48 trials for each of the four conditions). The number of global adapting directions (one or five) was alternated across blocks with the reference adapting direction (counterclockwise 45° or clockwise 45°) randomized across blocks with the constraint that no three consecutive blocks had the same reference adapting direction. Within each block, trials with different test locations (adapted or nonadapted) were randomly interleaved. Specifically, trials of the BOTH and the GLOBAL conditions were interleaved within the same block, and trials of the LOCAL and NEITHER conditions were interleaved within the same block. The PSEs of the upward direction for the four conditions were estimated on independent tracks of adaptive staircases. There was a 45-s rest period between every two blocks of trials. Observers completed two short practice blocks to familiarize themselves with the task and procedure before running the experimental blocks. The cumulative normal distribution was chosen as the underlying psychometric function for the adaptive algorithm of the Psi method, which provided the 50% threshold (i.e., the mean Display Formula\(\mu \) parameter) estimate as the PSE for each condition. 
Results
For the constant-stimuli procedure for the clockwise 45° adapting direction, the PSE of the upward direction was found to shift toward the clockwise direction and vice versa for the counterclockwise 45°. Because there was no systematic difference between the two adapting directions, trials of these two adapting directions were combined in the analyses. Test directions and PSEs are labeled as positive if they were toward the adapting direction and negative if they were opposite to the adapting direction. 
Psychometric curves were fitted based on a cumulative normal distribution function. Figure 3A shows the fitted psychometric curves of one observer (RH) for all four conditions. Fitting was good for all observers in all conditions, R2 range = (0.955, 0.9994). For each observer in each condition, the estimated parameter Display Formula\(\mu \) was taken to be the PSE estimate. A positive PSE represents a DAE in the repulsive direction. The overall trend was similar to that found in Experiment 1A. DAE was the strongest in the BOTH condition (M = 19.78°, SD = 5.26°, 95% CI = [13.25, 26.31]), less strong in the GLOBAL condition (M = 13.19°, SD = 2.33°, 95% CI = [8.29, 18.10]), further reduced in the LOCAL condition (M = 9.81°, SD = 3.87°, 95% CI = [5.00, 14.62]), and close to zero in the NEITHER condition (M = −1.06°, SD = 3.95°, 95% CI = [−5.96, 3.84]). 
Figure 3
 
Results of Experiment 1B. (A) Psychometric curves of one example observer (RH) from the constant-stimuli procedure (n = 5). For each observer, responses were fitted independently for each of the four conditions (BOTH: magenta, solid symbols, thick line; GLOBAL: red, open symbols; LOCAL: blue, solid symbols; NEITHER: black, open symbols, dashed line). (B) Independent tracks of PSE estimates for the four conditions (BOTH: top left magenta; GLOBAL: bottom left red; LOCAL: top right blue; NEITHER: bottom right black) of one example observer (TM) from the adaptive-staircase procedure (n = 12). The thick line in each small panel traces through the estimated PSE across trials. Test stimulus directions presented at each trial are marked by open symbols and connected by thin lines. (C) Averaged PSEs for all participants (n = 17). Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 3
 
Results of Experiment 1B. (A) Psychometric curves of one example observer (RH) from the constant-stimuli procedure (n = 5). For each observer, responses were fitted independently for each of the four conditions (BOTH: magenta, solid symbols, thick line; GLOBAL: red, open symbols; LOCAL: blue, solid symbols; NEITHER: black, open symbols, dashed line). (B) Independent tracks of PSE estimates for the four conditions (BOTH: top left magenta; GLOBAL: bottom left red; LOCAL: top right blue; NEITHER: bottom right black) of one example observer (TM) from the adaptive-staircase procedure (n = 12). The thick line in each small panel traces through the estimated PSE across trials. Test stimulus directions presented at each trial are marked by open symbols and connected by thin lines. (C) Averaged PSEs for all participants (n = 17). Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
For the adaptive-staircase procedure, Figure 3B shows the results of one observer (TM). The four panels show the four independent tracks of adaptive staircases, one for each condition. Estimates of PSEs (thick lines) tended to stabilize early on. The fluctuation in the test directions (thin lines, open symbols) was for better estimates of the slope of the psychometric curve, representing sensitivity, which was not the main concern for this experiment. The strongest DAE was observed in the BOTH condition (M = 13.43°, SD = 7.68°, 95% CI = [8.55°, 18.31°]), followed by the GLOBAL condition (M = 11.02°, SD = 6.30°, 95% CI = [7.02°, 15.02°]). DAE was found to be much weaker in the LOCAL condition (M = 4.44°, SD = 6.81°, 95% CI = [0.11°, 8.77°]), and was close to null in the NEITHER condition (M = 2.08°, SD = 6.26°, 95% CI = [−1.90°, 6.06°]). 
Figure 3C shows the aggregated results (n = 17). A mixed-design, 2 × 2 × 2 ANOVA with two within-subject factors (Global adaptation: presence, absence; Local adaptation: presence, absence) and one between-subjects factor (Procedure: constant stimuli, n = 5; Adaptive staircase, n = 12) was conducted. None of the effects related to the procedure was significant: three-way interaction, F(1, 15) = 1.98, p = 0.18; Global × Procedure interaction, F(1, 15) = 0.95, p = 0.35; Local × Procedure interaction, F(1, 15) = 3.29, p = 0.09; and main effect, F(1, 15) = 1.60, p = 0.23). This was expected because the measurement procedure should not affect DAE strengths. 
For the two level-of-adaptation factors, results were consistent with those found in Experiment 1A. The Global × Local two-way interaction was not significant, F(1, 15) = 1.89, p = 0.19, but the main effects of Global adaptation, F(1, 15) = 42.57, p < 10−5, partial Display Formula\({\eta ^2}\) = 0.74, and Local adaptation, F(1, 15) = 10.07, p = 0.006, partial Display Formula\({\eta ^2}\) = 0.40, were significant, suggesting that adaptation at specific levels of motion processing significantly and independently affected DAE. In particular, DAE for the BOTH condition (M = 16.61°, SD = 1.89°, 95% CI = [12.57, 20.64]) was significantly stronger than that for the GLOBAL condition (M = 12.11°, SD = 1.47°, 95% CI = [8.97, 15.25]), F(1, 15) = 7.00, p = 0.02, partial Display Formula\({\eta ^2}\) = 0.32, which was significantly stronger than that for the LOCAL condition (M = 7.12°, SD = 1.64°, 95% CI = [3.62, 10.62]), F(1, 15) = 5.53, p = 0.03, partial Display Formula\({\eta ^2}\) = 0.27, which was significantly stronger than that for the NEITHER condition (M = 0.51°, SD = 1.52°, 95% CI = [−2.75, 3.77]), F(1, 15) = 9.88, p = 0.007, partial Display Formula\({\eta ^2}\) = 0.40, which was close to null. 
Taken together, results from Experiments 1A and 1B suggest that DAE, tested using a multiple-element pattern, is stronger when adaptation is specifically induced at the global level of motion processing than when induced only at the local level. Because the test pattern involved integrating multiple motion signals across locations, this difference can be explained by the adaptation of the direction-selective units at the global-integration level of motion processing. It has been shown that the specific adaptation-induced changes in direction tuning found in neurons in MT (Kohn & Movshon, 2004) can lead to stronger perceptual repulsion (Seung & Sompolinsky, 1993). 
The small DAE found in the LOCAL condition was possibly caused by propagation of location-specific effects of adaptation arising from low-level processing (Xu, Dayan, Lipkin, & Qian, 2008). Although adapting to grating stimulus produces repulsive aftereffects on both direction (Schrater & Simoncelli, 1998) and speed (Stocker & Simoncelli, 2009), it is unclear which of these effects or both of them were propagated to produce the percept of DAE in the LOCAL condition. 
In Experiments 1A and 1B, adapting orientation and test orientation remained the same at each location. The local motion signal at each location was confined to the single dimension that was perpendicular to the grating orientation (i.e., the 1-D motion in Amano et al., 2009). As a result, from adaptation to test, local 1-D motion only varied in speed but not in direction. This local manipulation resembles that used by Stocker and Simoncelli (2009) to obtain repulsive speed aftereffect. Given that local test directions did not differ from local adapting directions, the DAE-LOCAL may actually be driven by the integrations of repulsive speed aftereffects across locations instead of by the integrations of repulsive direction aftereffects across locations. 
Experiments 2 and 3 were conducted to pin down which kind of local repulsive effect, speed or direction, was propagated downstream to produce DAE-LOCAL. Both experiments aimed at reducing local speed repulsion and enhancing local direction repulsion. If the resulting DAE-LOCAL was stronger, it would suggest local direction repulsion contributes more to the generation of the DAE-LOCAL. On the contrary, if the resulting DAE-LOCAL was weaker, it would suggest that local speed repulsion has greater contribution toward the generation of DAE-LOCAL than local direction repulsion does. 
Experiment 2: To measure local orientation specificity of the DAE
Experiment 2 aimed at remeasuring DAE-LOCAL when local orientations were varied between adapting and test stimuli. This could potentially change the strength of the resulting DAE-LOCAL. Such technique of manipulating orientation difference between adaptation and test to manipulate local adaptation has been used in a previous neuroimaging study (Amano et al., 2012). 
Methods
The stimulus and the procedure were identical to those in the LOCAL condition of Experiment 1B except for the details described below. For all elements in the test stimulus, orientations were either 45° tilted or orthogonal to the adapting orientation. The 45° condition was designed so that, at each test location, the test speed was similar to the adapting speed. As explained in General methods, for each local element Display Formula\(j\), the adapting speed Display Formula\({u_j}\) is given by  
\begin{equation}\tag{1}{u_j} = v\sin \left( {r - {\theta _j}} \right),\end{equation}
where Display Formula\(r\) is the global reference adapting direction, Display Formula\(v\) is the global speed (same for both adaptation and test), and Display Formula\({\theta _j}\) is the orientation of element Display Formula\(j\). The local test speed Display Formula\(u_j^t\) of element Display Formula\(j\) is given by  
\begin{equation}\tag{2}u_j^t = v\sin \left( {{t_i} - \theta _j^t} \right),\end{equation}
where Display Formula\({t_i}\) is the global test direction for trial Display Formula\(i\), and Display Formula\(\theta _j^t\) is the orientation of element Display Formula\(j\) during the test. Because DAE was the strongest at around 45° away from the adapting direction across all conditions, the global test direction Display Formula\({t_i}\) was always about 45° away from the adapting direction Display Formula\(r\) (i.e., Display Formula\({t_i} - r \approx \pm 45^\circ \)). In the LOCAL condition in Experiment 1, adapting and test orientations were identical at each location (i.e., Display Formula\({\theta _j} = \theta _j^t\)). Therefore, the difference between the adapting Display Formula\(r\) and the test directions Display Formula\({t_i}\) caused the adapting speed Display Formula\({u_j}\) and the test speeds Display Formula\(u_j^t\) to be different. In the 45° condition of Experiment 2, I attempted to cancel out this speed difference by introducing a difference in orientation between adaptation Display Formula\({\theta _j}\) and test Display Formula\(\theta _j^t\). Every test element was turned 45° away from its adapting orientation so that Display Formula\(\theta _j^t - {\theta _j} = \pm 45^\circ \). The direction of tilt (clockwise or counterclockwise) was determined based on the relative difference between the test direction Display Formula\({t_i}\) and the global adapting direction Display Formula\(r\) for each trial. Formally,  
\begin{equation}\tag{3}\theta _j^t = {\theta _j} + sign\left( {{t_i} - r} \right) \times 45^\circ .\end{equation}
 
When Display Formula\({t_i}\) was counterclockwise to Display Formula\(r\), test orientations Display Formula\(\theta _j^t\) were tilted counterclockwise; when Display Formula\({t_i}\) was clockwise to Display Formula\(r\), test orientations Display Formula\(\theta _j^t\)were tilted clockwise. As a result,  
\begin{equation}\theta _j^t - {\theta _j} = 45^\circ \approx {t_i} - r\end{equation}
 
\begin{equation} \Rightarrow r - {\theta _j} \approx {t_i} - \theta _j^t\end{equation}
 
\begin{equation} \Rightarrow {u_j} = v\sin \left( {r - {\theta _j}} \right) \approx v\sin \left( {{t_i} - \theta _j^t} \right) = u_j^t{\rm {.}}\end{equation}
 
Therefore, by tilting the test orientations by 45°, local adapting speed Display Formula\({u_j}\) and local test speed Display Formula\(u_j^t\) for every element Display Formula\(j\) were set to be similar in the 45° condition. 
In the Orthogonal condition, each test orientation was turned 90° relative to its adapting orientation. Because local motion detectors are known to be orientation-selective, probing the aftereffect with an orthogonal condition should result in minimal, if any, local motion aftereffects. This condition was designed to serve two purposes: (a) to assess how much the DAE found in the LOCAL condition depends on orientation-specific adaptation and (b) to provide a benchmark in comparison with the effect found in the 45° condition. The same five observers who were tested in the constant-stimuli version of Experiment 1B participated in Experiment 2
Results
Results are shown in Figure 4 (left panel), together with the results from the LOCAL condition obtained in Experiment 1B (labeled as “Same” to denote the same local orientations between adaptation and test) for comparison. A repeated-measures ANOVA (three levels: Same, 45°, Orthogonal) revealed that the shift of PSE was significantly modulated by test orientation, F(2, 8) = 23.709, p = 0.0004, partial Display Formula\({\eta ^2}\) = 0.856. In particular, DAE in the 45° condition (M = 3.44°, SD = 2.84°, 95% CI = [−0.086, 6.97]) was significantly weaker than that in the Same condition (M = 9.81°, SD = 3.87°, 95% CI = [5.00, 14.62]), F(1, 4) = 15.792, p = 0.016. This trend was consistently observed across all five observers. DAE was weak and almost nonexistent in the Orthogonal condition (M = 1.81°, SD = 2.58°, 95% CI = [−1.40°, 5.01°]). DAE was slightly stronger in the 45° condition than in the Orthogonal condition, F(1, 4) = 10.20, p = 0.033. 
Figure 4
 
Results of Experiment 2 and simulation. Left: Results of the LOCAL condition (labeled as “Same”) in Experiment 1B were replotted in the figure for easy comparison. Results from the constant-stimuli experiment for the three conditions. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Each bar shows the PSE estimate for each condition, averaged across observers. Error bars represent ±1 SEM. Right: Results from the simulation of local speed repulsion. Open bars show the simulated DAE for each condition averaged over 5,000 runs of simulation.
Figure 4
 
Results of Experiment 2 and simulation. Left: Results of the LOCAL condition (labeled as “Same”) in Experiment 1B were replotted in the figure for easy comparison. Results from the constant-stimuli experiment for the three conditions. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Each bar shows the PSE estimate for each condition, averaged across observers. Error bars represent ±1 SEM. Right: Results from the simulation of local speed repulsion. Open bars show the simulated DAE for each condition averaged over 5,000 runs of simulation.
Simulation: Integrating local speed repulsion across locations to produce DAE-LOCAL
In Experiment 2, the adapting and test speeds at each local remained unchanged in the 45° and Orthogonal conditions. This would minimize the resulting local speed repulsion. Because DAE-LOCAL was weaker in these conditions, local speed repulsion may play an important role in the generation of DAE-LOCAL. To test whether the propagation of local speed repulsion alone is sufficient for generating the results observed in Experiment 2, I ran a toy simulation using Stocker and Simoncelli's (2009) speed-repulsion model (see Supplementary Material for details). 
At each test location, I computed the predicted speed by feeding the adapting speed into their model. The predicted local direction was determined based on the orientation manipulation in Experiment 2. In other words, assuming zero direction repulsion at each location, local test direction was simulated to be the same, 45° away from, and orthogonal to its corresponding adapting direction for the Same, 45°, and Orthogonal conditions, respectively. This would produce a predicted local motion vector for each test location. The predicted direction-judgment response was obtained by averaging local motion vectors across test locations. 
Parameters were fitted to match the average DAE strengths from the five observers in the LOCAL condition. I then fixed these parameters and used them to predict the DAE strengths for the 45° and Orthogonal conditions. As shown in the right panel of Figure 4, the simulation results closely follow those from the human experiment. This suggests that the propagation of speed repulsion alone is sufficient in explaining the repulsive DAE observed in the LOCAL condition. 
Overall, results from Experiment 2 and the simulation show that DAE-LOCAL is orientation-specific and can be explained solely based on local speed repulsion. These results seem to suggest that local direction repulsive effects did not contribute to the generation of DAE-LOCAL for a multiple-element test pattern. One possible reason is that each Gabor element is ambiguous in signaling the true 2-D motion signal, which could hinder the propagation of local direction repulsive effects. 
To address the above issue, in Experiment 3, I disambiguated the 2-D motion direction at each element location using a plaid element at each location. By superimposing two orthogonal Gabor elements to produce a plaid element, speed and direction at each local would unambiguously signal global speed and global direction, respectively. Because speed would remain unchanged between adaptation and test, local speed repulsion should be minimal. However, same as Experiments 1 and 2, test direction would be around 45° away from the adapting direction. Because adaptation to a plaid stimulus has been found to produce significant repulsive DAE (Schrater & Simoncelli, 1998), the design of Experiment 3 aimed at generalizing this to a multiple-plaid pattern. If repulsive DAE could be generated at each plaid location, this would allow more room for local direction repulsion (if any) after adaptation. If such illusory local direction repulsions could be later integrated to produce a DAE percept, DAE in the Plaid condition should be stronger than in the Gabor condition. However, if similar or even weaker DAE were observed for the plaid stimulus, it would suggest that integration of local direction repulsions does not contribute to the percept of DAE. 
Experiment 3: To enhance local direction repulsion by disambiguating local motion directions
Methods
The stimulus and the procedure were the same as those in Experiment 2, except for the details below. In Experiment 3, a Plaid condition was introduced based on the original LOCAL condition in Experiment 1: During both adaptation and test phases of a trial, at every location, the Gabor element was replaced by a plaid element, which was created by superimposing two identical Gabor elements with a 90° difference in orientation. Similar to the LOCAL condition in Experiment 1, the two orientations of each plaid element remained the same during both adaptation and test phases. Overall contrast of each plaid element was maintained at the same level as Experiments 1 and 2 by halving the contrast of each of the two underlying Gabor elements. 
Like Experiment 1B, both constant-stimuli and adaptive-staircase procedures were used in Experiment 3. The same five observers in Experiments 1B and 2 participated in Experiment 3 by going through the constant-stimuli procedure for the Plaid condition. For the adaptive-staircase procedure, 18 observers participated for course credits under the Psi adaptive-staircase method (Kontsevich & Tyler, 1999) implemented in the Palamedes Toolbox (Prins & Kingdom, 2009). Each observer ran both the Gabor and the Plaid conditions with the order of the conditions interleaved across six blocks of 16 trials (a total of 96 trials with 48 trials for each condition). The condition for the first block (Gabor or Plaid) was counterbalanced across observers. 
Results
Figure 5 shows the results of Experiment 3. A mixed-design, 2 × 2 ANOVA with one within-subject factor of stimulus type (Gabor vs. Plaid) and one between-subjects factor of procedure (constant-stimuli, n = 5 vs. adaptive-staircase, n = 18) was conducted. Same as the previous experiments, DAE strength was measured by the magnitude of the PSE shift: positive shift refers to a PSE shift toward the adapted direction, representing a repulsive DAE. Overall, DAE was significantly stronger for Gabor (M = 9.06°, SD = 4.66°) than for Plaid stimuli (M = 5.35°, SD = 3.56°), main effect of stimulus type: F(1, 21) = 26.60, p < 0.0001, partial Display Formula\({\eta ^2}\) = 0.56, and the DAE for Plaid stimuli was significantly above zero (95% CI = [3.81, 6.89]), t(22) = 7.21, p < 0.0001. The difference in DAE strength between the constant-stimuli procedure (M = 6.18°, SD = 6.55°) and the adaptive-staircase procedure (M = 7.49°, SD = 3.84°) was insignificant, main effect of procedure: F(1, 21) = 0.64, p = 0.433, partial Display Formula\({\eta ^2}\) = 0.03. There was a significant interaction between stimulus type and procedure, F(1, 21) = 10.13, p = 0.004, partial Display Formula\({\eta ^2}\) = 0.33. To further explore such interaction, the simple effect of stimulus type for each procedure was examined. For the constant-stimuli procedure, DAE was significantly stronger for Gabor (M = 10.78°, SD = 5.53°) than for Plaid (M = 1.57°, SD = 3.59°), simple effect of stimulus type for constant-stimuli: F(1, 21) = 22.22, p < 0.0005, and the effect was strong (partial Display Formula\({\eta ^2}\) = 0.514). For the adaptive-staircase procedure, DAE was also significantly stronger for Gabor (M = 8.58°, SD = 4.45°) than for Plaid (M = 6.40°, SD = 2.83°), simple effect of stimulus type for adaptive-staircase: F(1, 21) = 4.485, p = 0.046, but the effect was weaker (partial Display Formula\({\eta ^2}\) = 0.176). This suggests both procedures revealed that repulsive DAE generated by the adaptation of location-specific mechanisms was stronger for Gabor than for Plaid. 
Figure 5
 
Results of Experiment 3. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 5
 
Results of Experiment 3. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
In the attempt to strengthen the DAE generated by LOCAL adaptation, I tried changing test orientations to allow for more local direction repulsion to be integrated (Experiment 2) and by changing each element to a plaid for less local-motion ambiguity (Experiment 3). However, DAE-LOCAL was found to decrease when these stimulus factors were manipulated. It might be that some nonstimulus factors could enhance the DAE generated from local adaptation. One such factor could be attention: participants might not have paid enough attention to local elements during adaptation, causing DAE-LOCAL to be weaker than DAE-GLOBAL. Indeed, it has been found that attention can modulate motion aftereffects (e.g., Boynton, Ciaramitaro, & Arman, 2006; Chaudhuri, 1990; Culham, Verstraten, Ashida, & Cavanagh, 2000). 
Experiment 4 was conducted to measure the effect of attention on DAE-LOCAL. Participants were instructed to pay attention to either (a) specific local elements that would be tested later or (b) the fixation cross during adaptation. If attending to specific locations could boost the resulting DAE-LOCAL, we should observe a stronger DAE-LOCAL in the former than in the latter condition. 
Experiment 4: The effect of attention on DAE-LOCAL
Methods
Procedure was identical to the LOCAL condition administered using the adaptive-staircase procedures in Experiment 1B except that, during adaptation, observers were instructed to perform a change-detection task. Sixteen observers, who were naïve to the purpose of the experiment and with normal or correct-to-normal vision, participated in Experiment 4 for monetary reward. 
During adaptation (45 s initial, 6 s top-up), the presentation of the adapting motion pattern was identical to that in the LOCAL condition in Experiment 1B. In addition, two independent changes in the stimulus were introduced in order to capture the observer's attention: (a) The color of the central fixation cross would change from green to yellow and then back to green; (b) one of the Gabor elements located at a test location (i.e., a location at which an element would be presented in the following test phase) would increase its contrast by 10 times (i.e., to 1.0) and then return to its original contrast (i.e., 0.1). The contrast increase in a Gabor element was designed to direct the observer's attention to specific test locations, and the color change in the fixation cross served as a control. Both changes were randomly and independently triggered every frame at a probability of 0.01. Once triggered, the change (i.e., yellow color or high contrast) would last for 750 ms, and the changed item (i.e., fixation cross or the Gabor element) would return to its original state. Immediately following the offset of a change, there was a 1-s period during which the same type (fixation color change or element contrast increase) would not be triggered again in order to separate changes in time for easier detection. 
There were eight blocks of 12 trials (96 trials in total). At the beginning of each block, observers were instructed to pay attention to either the color change of the fixation cross or the contrast increase of a randomly located element during adaptation. They were instructed to perform the change-detection task: Report the targeted change and ignore the other “distractor” change. They pressed the space bar on the keyboard once whenever the targeted change happened. The order of the target (fixation color change or element contrast increase) was randomized across blocks but remained the same within each block. As a result, all stimulus parameters were held constant throughout the experiment, but attention during adaptation varied across blocks. The test and response phases were identical to those described in previous adaptive-staircase experiments. PSEs were measured under two different attention conditions during adaptation, using the Psi adaptive-staircase method (Kontsevich & Tyler, 1999) implemented in the Palamedes Toolbox (Prins & Kingdom, 2009). 
Results
Performance in the change-detection task during adaptation was analyzed based on signal-detection theory. A target-present trial was defined to be the duration from the onset of the targeted change (e.g., Gabor contrast change) to the disappearance of it, which was 750 ms. A target-absent trial was defined to be the duration from the onset of the distractor change (e.g., fixation color change) to the disappearance of it. Because the targeted and the distractor changes were triggered independently, the onset of a targeted change could happen during the presentation of a distractor change. To avoid double counting, such trials were discounted from the target-absent trials. This resulted in 132.9 target-present trials and 54.2 target-absent trials, averaged across the two conditions and across all observers. Based on such definition, a hit was defined as a space bar key press recorded during the target-present trial, and a false alarm was defined as a space bar key press recorded during the target-absent trial. 
Sensitivity was computed as Display Formula\(d^{\prime} = \phi \left( {p\left( H \right)} \right) - \phi \left( {p\left( {FA} \right)} \right)\), where Display Formula\(\phi \left( p \right)\) is the inverse of the standard normal distribution for probability Display Formula\(p\), Display Formula\(p\left( H \right)\) is the proportion of hit trials, and Display Formula\(p\left( {FA} \right)\) is the proportion of false-alarm trials. 
Sensitivity values for both change-detection tasks were high and significantly above a Display Formula\(d^{\prime} \) of two (fixation color change: M = 4.01°, SD = 0.66°, 95% CI = [3.66°, 4.37°]; element contrast increase: M = 2.64°, SD = 0.37°, 95% CI = [2.44°, 2.83°]), suggesting that observers performed both attention tasks as instructed. The lower sensitivity in detecting contrast increase in Gabor elements might be due to the higher demand of the attention task itself: Attention might have been more diffused across a larger, peripheral region as observers were to detect a target appearing at an uncertain location. 
Figure 6 shows the PSEs for both attention conditions (fixation color change: M = 6.93°, SD = 8.19°, 95% CI = [2.57°, 11.30°]; element contrast increase: M = 7.11°, SD = 9.11°, 95% CI = [2.25°, 11.96°]). Both PSEs were significantly different from zero: fixation color change, t(15) = 3.38, p = 0.0041; element contrast increase, t(15) = 3.12, p = 0.007, suggesting that the adaptation of location-specific mechanisms could produce significant DAE when observers were performing certain attention tasks during adaptation. DAEs between these two conditions were not significantly different, t(15) = 0.056, p = 0.96. In order to evaluate the null hypothesis (Display Formula\({H_0}\)) that the PSE was the same between the two attention conditions, the Bayes factor, Display Formula\({B_{01}} = p\left( {{H_0}|D} \right)/p\left( {{H_1}|D} \right)\), was computed based on the JZS Bayes factor with the scale r = 1 for the Cauchy distribution of effect size (Rouder, Speckman, Sun, Morey, & Iverson, 2009). The result was in favor of the null hypothesis, Display Formula\({B_{01}}\) = 5.29, Display Formula\(p\left( {{H_0}|D} \right) = \) 0.84, suggesting that DAE strength generated from location-specific adaptation remains the same even when observers pay attention to specific locations during adaptation. 
Figure 6
 
Results of Experiment 4. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 6
 
Results of Experiment 4. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Another possible explanation for the “GLOBAL > LOCAL effect” is that location-specific adaptation was inadequate in the LOCAL conditions. This could be due to many possible reasons, e.g., the specific structure of the multiaperture stimulus, which could cause local interactions among motion elements or the lack of attention to specific locations (in Experiments 13). Regardless of the reason, inadequate local adaptation would result in weak DAEs across locations, which, when integrated, would produce a weaker DAE in the LOCAL condition than in the GLOBAL condition as observed in Experiment 1
In order to assess this possibility, Experiment 5 was conducted to measure DAE using a single-element test stimulus. If location-specific adaptation was inadequate, DAE produced by a single test element should also be weak. If such single-element DAE was weaker in the LOCAL adaptation condition than in the GLOBAL adaptation condition, the weak LOCAL-DAE reported in the above experiments (measured with multiple elements) could then be explained by inadequate local adaptation, which resulted in weak DAE at individual locations and, when integrated, a weak overall DAE. However, if the single-element DAE in the LOCAL adaptation condition was similar to or stronger than in the GLOBAL adaptation condition, it would further support the idea that global adaptation contributes more to the repulsive DAE than local adaptation does. 
Furthermore, the test pattern in Experiments 14 was always a multiple-element pattern, which required global motion integration. Testing DAE with a single element would also be probing DAE specifically at the local-motion processing level, which could potentially produce a stronger DAE-LOCAL than DAE-GLOBAL. The results would demonstrate how DAE might change when the level at which adaptation occurs matches with (or is different from) the level at which the aftereffect is tested. 
Experiment 5: Comparing DAE tested with a single element versus with a multielement pattern
Methods
Experiment 5 employed a 2 × 2 within-subject factorial design. One factor was adaptation level, with the two levels being GLOBAL and LOCAL. The other factor was number of test elements, with the two levels being Single and Multiple. This factorial design resulted in four conditions: GLOBAL-Multiple (same as GLOBAL in Experiment 1), LOCAL-Multiple (same as 45° in Experiment 2), GLOBAL-Single, and LOCAL-Single. Twenty-five (including the author) observers with normal or correct-to-normal vision participated in Experiment 5. All observers, except for the author, were naïve to the purpose of the experiment and participated for monetary reward. 
For the two Single conditions, four to-be-tested elements were randomly chosen from predetermined test locations. As described in the General methods, for the LOCAL-adaptation condition, the predetermined test locations were the reference set (whose underlying global adapting direction was either 45° or 135°, alternated across blocks, as described in General methods). For the GLOBAL-adaptation condition, they were the nonadapted locations. These four to-be-tested elements were randomly selected at the beginning of each block of trials and remained the same throughout the block. In each trial of a Single-condition block, one element was randomly chosen from these four elements to be presented as the test stimulus. 
Because a single Gabor element can only drift in the direction that is orthogonal to its orientation, adapting and test orientations would have to be different to allow for DAE to be observed for a single element. If orientation remained unchanged between adaptation and test, the element's drifting direction would also remain unchanged, and there would not be any single-element DAE. Therefore, the orientations of these four elements were always orthogonal to their assigned global motion directions. This was done during both adaptation and test in the LOCAL-Single condition and during test only in the GLOBAL-Single condition (because the four elements were at nonadapted locations). As a result, these four elements had a drifting speed that was always the same as the assigned global motion and had orientations that were tilted for about 45° from adaptation to test (because adapting and test directions were about 45° apart, similar to the 45° condition in Experiment 2). For consistency, this manipulation of adapting and test orientations for the four chosen elements was also done for the LOCAL-Multiple condition, in which all four elements were always visible during both adaptation and test. 
Contrast was increased to 0.15 to minimize the chance that, when a single test element was presented, participants might miss it due to low contrast. All other details about the stimulus and apparatus were as described in Experiment 4 (except for the stimulus manipulation related to the attention task). 
The procedure was the same as those described in the above adaptive-staircase experiments except for the following. Each observer ran four sessions. In each session, there were four blocks of 10 trials (40 in total) of the same condition. In each block, initial and top-up adaptation durations were 40 s and 5 s, respectively. Order of the four conditions was counterbalanced across participants using a balanced Latin square. Participants completed two practice sessions (two blocks of four trials) in order to familiarize themselves with all the possible adapting (one coherent adapting direction for GLOBAL vs. five adapting directions for LOCAL) and test (Single-element vs. Multiple-element) configurations. 
Results
Figure 7 shows the results of Experiment 5. A repeated-measures, factorial ANOVA revealed a significant two-way interaction between adaptation level and number of test elements, F(1, 23) = 27.29, p < 10−4, partial Display Formula\({\eta ^2}\) = 0.53. When tested with multiple elements, DAE was stronger when the GLOBAL level was adapted (M = 6.84, SD = 1.49, 95% CI = [3.76, 9.91]) than when the LOCAL level was adapted (M = 2.12, SD = 1.31, 95% CI = [−0.58, 4.81]), F(1, 23) = 6.33, p = 0.02, partial Display Formula\({\eta ^2}\) = 0.210, replicating the key findings from Experiment 1. Critically, when tested with a single element, the opposite was observed: DAE was stronger when the LOCAL level was adapted (M = 5.73, SD = 0.98, 95% CI = [3.72, 7.75]) than when the GLOBAL level was adapted (M = 1.04, SD = 0.82, 95% CI = [−0.64, 2.73]), F(1, 23) = 24.57, p < 10−4, partial Display Formula\({\eta ^2}\) = 0.51, suggesting that the local DAE resulting from this adaptation paradigm was actually not weak, and local adaptation was adequate in the LOCAL conditions in the above experiments. It should be noted that the DAE strength for the LOCAL-Single condition was comparable to that for the GLOBAL-Multiple condition. This suggests that, when tested with a single element, DAE-LOCAL could be as strong as DAE-GLOBAL. 
Figure 7
 
Results of Experiment 5. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 7
 
Results of Experiment 5. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Another way of interpreting the interaction was also meaningful for the purpose of Experiment 5: When the LOCAL level was adapted, DAE was stronger when tested with a single element than with a multiple elements, F(1, 23) = 4.55, p = 0.043, partial Display Formula\({\eta ^2}\) = 0.16. When the GLOBAL level was adapted, DAE was stronger when tested with multiple elements than with a single element, F(1, 23) = 17.06, p = 10−3, partial Display Formula\({\eta ^2}\) = 0.42. 
These results rule out the possibility that the GLOBAL > LOCAL effect observed in Experiment 1 was due to inadequate local adaptation. They further support the idea that the adaptation at the global level of motion processing contributes more to the generation of repulsive DAE than that at the local level does—at least when DAE was tested in a condition that requires global motion integration (e.g., with multiple elements in Experiments 1 and 5, discussed further in General discussion). 
General discussion
By independently inducing adaptation at the global and local levels of motion processing, the present study found that (a) DAE, tested with a multiple-element pattern, was stronger when only the global level was adapted (DAE-GLOBAL) than when only the local level was adapted (DAE-LOCAL); (b) DAE-LOCAL was orientation-specific and can be explained based on integration of repulsive local speed aftereffects across locations; (c) DAE-LOCAL was weaker when local motion signals were disambiguated using plaid stimulus for both adaptation and test; (d) attending to the to-be-tested locations during adaptation had no effect on the strength of DAE-LOCAL; and (e) the weaker DAE-LOCAL observed was not due to inadequate adaptation at individual locations because it was substantially stronger when measured using a single element at a specific location. 
Taken together, these results suggest that the strength of repulsive DAE depends on the level(s) of motion processing at which adaptation occurs. Specifically, when tested with a multiple-element pattern, the adaptation of the global level contributes more to the generation of repulsive DAE when compared with the adaptation of the local level. In the following sections, findings from the present study are interpreted (a) in comparison with findings from Curran et al. (2006); (b) in the context of neural coding; (c) in terms of effects from various factors, including stimulus features, computational rules for global direction, attention, and level-specificity between adaptation and test; and finally and more generally, (d) in the context of the generation of aftereffects from the adaptation of a hierarchical system. 
Present findings versus Curran et al.'s (2006) findings
The finding that DAE-GLOBAL was stronger than DAE-LOCAL (Experiment 1) appears to be inconsistent with the conclusion drawn by Curran et al. (2006). Their findings suggest that DAE is mainly driven by the adaptation of local-motion detectors. Although the stimuli were different between that study (random-dot motion pattern) and the present study (multiple-aperture motion pattern), such difference may not explain the discrepancy in the findings. This is because Schrater and Simoncelli (1998) found that DAE did not depend on spatial pattern (dots or gratings) or even on spatial frequency. Instead, the discrepancy may arise from the difference in defining “local” and “global” levels of motion processing between the two studies. 
In Curran et al.'s (2006) study, they first measured DAE magnitudes across a range of motion speeds. Then, in arbitrating between the contribution of local and global adaptation in producing DAE, they proposed a “local model” and a “global model” for generating DAE. The “local model” first looks up DAE strength for each speed level present in the stimulus (which was taken as “local speed”) and then averages the DAE strengths. The “global model” first evaluates the “global speed” of the whole stimulus by averaging all “local” speed levels and then looks up one DAE strength. In the present study, local and global levels of motion processing were defined by receptive-field size (i.e., local: small, for each element; global: large, for the whole pattern) and the type of computation performed (i.e., local: motion-energy extraction; global: spatial integration). 
The definition employed by Curran et al. (2006) was probably based on previous psychophysical studies on speed perception, and the definition employed in the present study is based more on neurophysiological and computational studies. After all, as the rationales of the two studies are different, it would be difficult to directly compare the apparently contradictory conclusions. It is possible that the motion system produces DAE based on many factors: speed and spatial locations may just be tapping on different parts of the same system. Indeed, if one focuses on local speed representation, the apparent contradiction could be reconciled: both studies support that the percept of DAE depends on local speed representations. In their study, the integration of local speed–dependent DAEs was found to better predict perceived DAE. In the present study, the propagation of local speed repulsion was found to be necessary and sufficient in the generation of perceived DAE. 
From neural coding to perceptual aftereffects
Furthermore, results of Experiment 1 are consistent with those reported in some neurophysiological studies (Jin et al., 2005; Kohn & Movshon, 2004). Specifically, the “DAE-GLOBAL > DAE-LOCAL” trend can be explained by the difference in adaptation-induced tuning changes found in neurons in V1 (Dragoi, Sharma, & Sur, 2000; Müller, Metha, Krauskopf, & Lennie, 1999) and MT (Kohn & Movshon, 2004). After adaptation, the attractive shift of preference in low-level, motion-sensitive neurons weakens the DAE caused by gain reduction, and the repulsive shift of preference in high-level motion neurons strengthens the DAE. 
Nevertheless, one should question whether it is appropriate to label different “repertoires” of adaptation-induced tuning changes based on the levels of processing. In more recent neurophysiological studies (Patterson, Duijnhouwer, Wissig, Krekelberg, & Kohn, 2014; Wissig & Kohn, 2012), V1 neurons have also been found to demonstrate the types of tuning changes, particularly the attractive shift of preference found in neurons in MT. However, the adapting stimulus that triggered the attractive shift of preference in V1 neurons was much larger than the receptive fields of those neurons. These adapting stimuli may have adapted neurons at MT, which could send feedback signals to V1 neurons and cause them to shift their preferences toward the adaptor. 
Effects of computation rules for global motion on DAE
In the GLOBAL condition in Experiment 1, even though both the adapting and test patterns required integration of motion signals in the GLOBAL condition, the underlying computational rules could be different. Specifically, the adapting pattern contained 200+ coherently drifting but randomly oriented Gabor elements, which should elicit a strong global motion based on the rule of intersection-of-constraints (IOC; Adelson & Movshon, 1982). However, with much fewer elements in the test, it is possible that the computation of global direction became more similar to a vector-average rule (VA; Wilson, Ferrera, & Yo, 1992). 
If one takes into consideration the rules for computing global directions between the adapting and test patterns, the GLOBAL condition alone will appear more complex than it has been presented so far. Given that the visual system is flexible in employing IOC and VA for pooling motion signals (Amano et al., 2009), this issue goes beyond a simple distinction between global and local levels of adaptation. Although both IOC and VA should happen at the stage of global motion integration, whether the differences (or similarities) in computational rule between adapting and test could influence the resulting DAE or any aftereffects in general is still an open question. Nonetheless, the paradigm used in the present study could serve as a psychophysical tool for one to address the issue by, for instance, manipulating stimulus features (e.g., density, orientations, location, etc.) between the adapting and test patterns. 
Effects of stimulus features on DAE
Results from Experiments 2 and 3 demonstrate that manipulation of local stimulus features (i.e., orientation and local ambiguity) can lead to changes in the percept of the DAE that is generated from local adaptation. In line with previous findings (Lee & Lu, 2012, 2014; Solomon, Peirce, Dhruv, & Lennie, 2004; Stocker & Simoncelli, 2009; Xu et al., 2008), results from the present study suggest that effects of adaptation at a low level of processing can be propagated downstream to influence aftereffect percepts. 
Although results from Experiment 2 and the simulation support that integration of local speed repulsions alone is sufficient in explaining DAE-LOCAL, the results cannot completely rule out an alternative explanation: that the weaker DAE-LOCAL in the 45° and Orthogonal conditions was due to testing groups of local orientation–specific motion units that had not been fully adapted. However, the integration of local speed repulsion serves as a mechanism-level explanation not only for the decrease of DAE-LOCAL when test orientation changes, but also for the generation of DAE-LOCAL when test orientations are the same as adapting ones in the LOCAL condition in Experiments 1A and 1B
Results from Experiment 3 may lead to two questions. The first question is whether the repulsive DAE found on a single plaid (Schrater & Simoncelli, 1998) can be effectively generalized to a multiple-plaid pattern. One may doubt this because of the decrease in DAE when the stimulus was changed from Gabor to Plaid. However, a significant DAE, although weaker, was still observed for the Plaid stimulus, suggesting that certain mechanisms within the motion system must be involved in generating the repulsive DAE for plaids. But the questions of where in the motion system and how remain open as they cannot be addressed directly based on data from Experiment 3 alone. 
The second question is whether the difference in DAE strength can be explained by the difference in pooling of motion signals between Gabor and Plaid elements. When both adapting and test elements are plaid at each location, the element signals an unambiguous 2-D motion direction and speed. The visual system could be using a different pooling strategy under such situation (Amano et al., 2009) than for Gabor elements, which could potentially explain the weaker DAE-LOCAL in the Plaid condition than in the Gabor condition. This is closely related to the issue discussed above in the section about computational rule. However, results from the present study are not sufficient to address this issue. The deeper question of how motion pooling may be related to aftereffects needs to be addressed by future studies that focus specifically on motion signal pooling and motion adaptation. 
Effects of attention on DAE
Previous studies have demonstrated that attention can modulate motion aftereffects (Boynton et al., 2006; Chaudhuri, 1990; Culham et al., 2000). However, in Experiment 4, it was found that attending to test-element locations during adaptation did not affect subsequent DAE-LOCAL. This finding is consistent with that in Morgan's (2011) study, in which MAE was measured using a bias-free two-alternative, forced-choice task on contrast discrimination. He found that MAE strength remained largely unchanged between different conditions of attention load. 
Although the direction-discrimination task used in the present study was not bias-free, there are still other explanations for the results from Experiment 4. One possible explanation is that such modulation by attention requires the observer to focus his or her attention to the global adapting direction. In most previous studies that found significant attention modulation of MAE, observers were usually instructed to pay attention to a specific motion direction that was clearly visible. However, in Experiment 4 of the present study, global adapting direction was rendered imperceptible by multiple directions in the adapting pattern. Moreover, observer's attention was directed toward a specific location in the entire pattern instead of the global direction, which may further reduce attention modulation effect (if any). Based on the paradigm and findings of the present study, future studies can explore how attention may differentially modulate aftereffects generated from the adaptation of different levels of processing. 
Effects adapt-test specificity on DAE
Results from Experiment 5 show that DAE strength depends on both the level at which adaptation occurs and the level at which the aftereffect is tested. If a single-element test stimulus is taken as a local-level probe (because the resulting DAE does not require integration) and a multiple-element test pattern is taken as a global-level probe (because the resulting DAE requires integration), results from Experiment 5 have two important implications. First, these results further demonstrate that the adaptation paradigm used in the present study is effective in independently inducing adaptation at local and global levels of motion processing. The effects of level-specific adaptation can be separately measured by using stimuli that specifically probe the level at which adaptation is induced as demonstrated in Experiment 5
Second, these results are consistent with the idea that aftereffect is the strongest when tested at the level at which adaptation occurs. For many artificial motion stimuli, such as random dots (e.g., Curran et al., 2006) and multiple-aperture patterns (e.g., Amano et al., 2009), as well as for many real-life motion signals (e.g., object motion, optic flow patterns), which require global motion integration, findings from the present study suggest that global adaptation has a greater contribution in generating the perception of repulsive DAE. However, it should be noted that the DAE observed when tested with a single grating (e.g., Schrater & Simoncelli, 1998), which requires minimal global motion integration, could possibly be driven more by the adaptation of local, orientation-specific mechanisms. 
Multiple levels of adaptation, one percept of aftereffect
Although converging evidence suggests that adaptation in the processing hierarchy cascades through the levels, it is unclear how such propagation is carried out. An intuitive proposal is that low-level adaptation creates local illusory signals that are then integrated by later stages of processing to produce an aftereffect percept. Indeed, such an “integration of illusions” account is appealing because of its parsimony (as it builds on how the system integrates “real” signals) and its power in explaining aftereffect phenomena. For example, it can explain why the percept of MAE is always integrated after adapting to bidirectional transparent motion (Vidnyánszky, Blaser, & Papathomas, 2002). 
However, findings from the present study may provide some counterevidence to this account. The manipulation in both Experiments 2 and 3 aimed to strengthen illusory local DAE signals so that, if they could be integrated by some high-level units in later stages of processing, the final DAE percept could be strengthened. However, the observed DAE strength did not increase and even appeared to decrease when local DAEs were strengthened. This seems to go against the proposal that low-level effects of adaptation are propagated via integration of local illusory signals. If it is not the local illusory signals that are integrated, how are effects of adaptation propagated downstream? 
One possibility is that neural activities at early stages of processing do not contribute in producing conscious perception, so that they do not directly produce “local illusory signals.” However, activity patterns at these early levels are later integrated internally to produce altered activity patterns in neurons at higher levels from which a percept of, say, motion direction is read out. For example, local motion detectors are orientation-selective, and therefore, so is the effect of adaptation at the local level. Probing the local level with test orientations that are far away from the adapting orientation may reduce the effect of adaptation on altering neural activity. The integration of these less-altered activity patterns is then fed to later stages of motion processing and, thus, produces a less biased, weaker DAE percept. 
In short, findings from the present study seem to suggest that there may be no perceptual readout at the local level of motion processing—at least in the case of the generation of DAE. This idea is consistent with the idea that conscious perception resides at a higher level of processing than at low levels (Crick & Koch, 1995; Kanwisher, 2001). It is also consistent with a previous adaptation study in which adaptation to oriented gratings with imperceptibly high spatial frequency was found to produce the tilt aftereffect (He & MacLeod, 2001). 
How can the present findings be reconciled with the idea about integrating illusory signals to produce perceptual aftereffect? One possible interpretation is that the existence of local illusory signals is just a shorthand representation of the population response pattern produced by adapted local motion detectors during testing. In particular, for motion adaptation, when the test stimulus is stationary, population response at the local stage of processing can be represented as an “illusory” motion signal that is opposite to the adapting one. The apparent discrepancy can be resolved if one views the propagation mechanism as propagating neural signals instead of illusory motion signals. 
Finally, findings from the present study do not rule out the possibility that the integration mechanism for generating DAE is different from that for generating static MAE. As noted in many previous psychophysical studies (for review, see Mather, Pavan, Campana, & Casco, 2008), stationary and dynamic test stimuli may actually be probing different levels of motion processing. DAE, by definition, must be measured by a dynamic test stimulus. Results from Experiment 5 further confirm that the level at which aftereffect percepts are read out depends on the test stimulus: When the test is stationary, local illusory percepts are first read out and then integrated; when the test is dynamic, an aftereffect percept is read out only at the global level from the integrated neural responses. However, this flexible propagation strategy may be less general and parsimonious than a “late readout” strategy. 
Conclusion
Repulsive DAE is the result of the adaptation of a hierarchical motion-processing system. It depends on the level(s) of motion processing at which adaptation occurs and at which the aftereffect is tested. The paradigm described in the present study, minimizing global adaptation using a multidirectional adapting pattern and minimizing local adaptation by testing at nonadapted locations, is a powerful tool for isolating the contribution from level-specific adaptation in generating repulsive DAE. 
Acknowledgments
I would like to thank Hongjing Lu and Joey Cham for their feedback and suggestions on the manuscript. I would also like to thank all the research assistants at both UCLA and Lingnan University (especially Angela, Ashlyn, Carly, Frankie, Kitty, Mona, and Ziwi) for their help in data collection. 
This research was supported by the Initial Research Activities Fund (102236) from Lingnan University, Hong Kong. 
Commercial relationships: none. 
Corresponding author: Alan L. F. Lee. 
Address: Department of Applied Psychology, Lingnan University, Hong Kong. 
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Supplementary Material
Supplementary Movie S1. Demo movie for BOTH condition. 
Supplementary Movie S2. Demo movie for GLOBAL condition. 
Supplementary Movie S3. Demo movie for LOCAL condition. 
Supplementary Movie S4. Demo movie for NEITHER condition. 
Figure 1
 
Stimulus and design of the experiments. Left: Illustration of the adapting stimulus. Dashed circles (not shown in actual stimuli) highlight the locations without Gabor elements (i.e., the nonadapted locations). Number of elements has been reduced for illustration purposes. The actual stimulus contained about four times more elements. Right (adopted from Lee & Lu, 2014): The illustrations of the conditions resulting from the 2 × 2 design based on the example pattern on the right panel. Under “Adapting pattern,” each circle represents a Gabor element. Colors represent different sets that were assigned different global adapting directions (indicated by the arrow within each empty circle). Elements with the same color were assigned the same global adapting direction. In this example, red represents the reference set (see description of stimulus in Stimulus and apparatus for details). Under “Test locations,” solid circles represent locations at which elements were presented during the test phase. Red and black colors correspond to the reference-set locations and the nonadapted locations (i.e., the dashed circles on the left panel), respectively.
Figure 1
 
Stimulus and design of the experiments. Left: Illustration of the adapting stimulus. Dashed circles (not shown in actual stimuli) highlight the locations without Gabor elements (i.e., the nonadapted locations). Number of elements has been reduced for illustration purposes. The actual stimulus contained about four times more elements. Right (adopted from Lee & Lu, 2014): The illustrations of the conditions resulting from the 2 × 2 design based on the example pattern on the right panel. Under “Adapting pattern,” each circle represents a Gabor element. Colors represent different sets that were assigned different global adapting directions (indicated by the arrow within each empty circle). Elements with the same color were assigned the same global adapting direction. In this example, red represents the reference set (see description of stimulus in Stimulus and apparatus for details). Under “Test locations,” solid circles represent locations at which elements were presented during the test phase. Red and black colors correspond to the reference-set locations and the nonadapted locations (i.e., the dashed circles on the left panel), respectively.
Figure 2
 
Results of Experiment 1A (n = 36, n = 9 in each condition). (A) Bias curves across all 16 test directions relative to the adapting direction. Each column represents one of the four conditions. Top row shows the biases in the Test-only session. Bottom panel shows the biases in the Adapt-Test sessions. Thin lines show biases of individual observers. Thick lines represent the means across observers in each session. (B) Fitting of bias curves for the Adapt-Test session for four example observers, one from each condition. (C) Bias indices for the four conditions in the Adapt-Test session. Error bars are ±1 between-subjects SEM.
Figure 2
 
Results of Experiment 1A (n = 36, n = 9 in each condition). (A) Bias curves across all 16 test directions relative to the adapting direction. Each column represents one of the four conditions. Top row shows the biases in the Test-only session. Bottom panel shows the biases in the Adapt-Test sessions. Thin lines show biases of individual observers. Thick lines represent the means across observers in each session. (B) Fitting of bias curves for the Adapt-Test session for four example observers, one from each condition. (C) Bias indices for the four conditions in the Adapt-Test session. Error bars are ±1 between-subjects SEM.
Figure 3
 
Results of Experiment 1B. (A) Psychometric curves of one example observer (RH) from the constant-stimuli procedure (n = 5). For each observer, responses were fitted independently for each of the four conditions (BOTH: magenta, solid symbols, thick line; GLOBAL: red, open symbols; LOCAL: blue, solid symbols; NEITHER: black, open symbols, dashed line). (B) Independent tracks of PSE estimates for the four conditions (BOTH: top left magenta; GLOBAL: bottom left red; LOCAL: top right blue; NEITHER: bottom right black) of one example observer (TM) from the adaptive-staircase procedure (n = 12). The thick line in each small panel traces through the estimated PSE across trials. Test stimulus directions presented at each trial are marked by open symbols and connected by thin lines. (C) Averaged PSEs for all participants (n = 17). Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 3
 
Results of Experiment 1B. (A) Psychometric curves of one example observer (RH) from the constant-stimuli procedure (n = 5). For each observer, responses were fitted independently for each of the four conditions (BOTH: magenta, solid symbols, thick line; GLOBAL: red, open symbols; LOCAL: blue, solid symbols; NEITHER: black, open symbols, dashed line). (B) Independent tracks of PSE estimates for the four conditions (BOTH: top left magenta; GLOBAL: bottom left red; LOCAL: top right blue; NEITHER: bottom right black) of one example observer (TM) from the adaptive-staircase procedure (n = 12). The thick line in each small panel traces through the estimated PSE across trials. Test stimulus directions presented at each trial are marked by open symbols and connected by thin lines. (C) Averaged PSEs for all participants (n = 17). Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 4
 
Results of Experiment 2 and simulation. Left: Results of the LOCAL condition (labeled as “Same”) in Experiment 1B were replotted in the figure for easy comparison. Results from the constant-stimuli experiment for the three conditions. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Each bar shows the PSE estimate for each condition, averaged across observers. Error bars represent ±1 SEM. Right: Results from the simulation of local speed repulsion. Open bars show the simulated DAE for each condition averaged over 5,000 runs of simulation.
Figure 4
 
Results of Experiment 2 and simulation. Left: Results of the LOCAL condition (labeled as “Same”) in Experiment 1B were replotted in the figure for easy comparison. Results from the constant-stimuli experiment for the three conditions. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Each bar shows the PSE estimate for each condition, averaged across observers. Error bars represent ±1 SEM. Right: Results from the simulation of local speed repulsion. Open bars show the simulated DAE for each condition averaged over 5,000 runs of simulation.
Figure 5
 
Results of Experiment 3. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 5
 
Results of Experiment 3. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 6
 
Results of Experiment 4. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 6
 
Results of Experiment 4. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 7
 
Results of Experiment 5. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Figure 7
 
Results of Experiment 5. Positive PSE refers to a PSE shift toward the adapted direction (i.e., a repulsive DAE). Bars represent averages across observers in each condition. Error bars represent ±1 SEM.
Supplement 1
Supplement 2
Supplement 3
Supplement 4
Supplement 5
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