We tested whether the rod interacts with the frame in building an estimate of head orientation in space, and hence causing a bias in the subjective visual vertical. We replaced the classical rod with an ellipse whose eccentricity (roundness) we varied to manipulate the uncertainty in the orientation of its main axis. Results show that the effect of the ellipse eccentricity on the SVV uncertainty was greater when the frame was upright and that the bias in the SVV was not affected by this manipulation. This provides evidence that the ellipse does not interact with the frame as part of a global visual process that biases the estimation of the head-in-space orientation, and thus the SVV. This refutes our interaction hypothesis. Instead, our results favor the addition hypothesis by suggesting that the uncertainty about the ellipse orientation on the retina plays a role at a later processing stage, adding variance when ellipse orientation on the retina is combined with eye-in-head and head-in-space orientation signals to transform it into world coordinates.
This assumption of additive retinal orientation noise was already incorporated in our models a decade ago (Alberts et al.,
2016; Clemens et al.,
2011; De Vrijer et al.,
2008,
2009; Vingerhoets et al.,
2008). In all our Bayesian optimal-integration models, an estimate of head-in-space orientation is constructed based on noisy information from the otoliths (De Vrijer et al.,
2008,
2009), somatosensory organs (Alberts et al.,
2016; Clemens et al.,
2011), visual contextual information (Alberts et al.,
2016; Vingerhoets et al.,
2008), and prior experiences. In an SVV task, of which the rod-and-frame task is a special case, the head-in-space estimate has to be transformed into a probability distribution of how a vertical line will fall onto the retina, using both the eye-in-head orientation and the uncertainty about the line on retina. Because the line-on-retina uncertainty is small (Vandenbussche, Vogels, & Orban,
1986) compared to the uncertainty associated with other sensory modalities, it is normally omitted in the modeling. This choice is also made to reduce the number of parameters in the model and make the model tractable (see De Vrijer et al.,
2009). However, this simplification also implies that the noise levels of the individual sensory signals are not distinguishable, at the expense of attributing the retinal uncertainty to other sensory systems involved in the integration process. Although we argue that these simplifying assumptions are justified when modeling the standard rod-and-frame task, such a Bayesian model, which assumes a noiseless signal about line orientation on the retina, is not warranted in modeling the current experiment: We artificially increased the line-orientation uncertainty, in an attempt to segregate the noise associated to the line on retina and study its effect on the percept of head orientation in the presence of contextual visual cues.
In order to quantify the uncertainty of the ellipse-on-retina orientation, one would have to run a separate psychophysical experiment. For example, Vandenbussche et al. (
1986) measured just-noticeable difference levels for orientation discrimination of <1°. In a preliminary experiment (see
Supplementary File S1) leading up to the experiment presented here, we psychophysically tested how precisely subjects perceive the orientation of ellipses with different eccentricities (i.e., 0.6, 0.745, 0.788, 0.821, 0.846, 0.866, 0.968, 0.992, 0.997) in the absence of a visual frame. We observed a hyperbolically decreasing precision curve (see
Supplementary Figure S1) that leveled off at an eccentricity of about 0.96 at a precision of about 0.7°, which is in the range reported by Vandenbussche et al. Based on the precision curve, we selected the three eccentricity values of 0.74, 0.82, and 0.99 for the main experiment, corresponding to 1.2°, 1.0°, and 0.7° uncertainty, respectively. As shown in
Figure 4 (right panel), the decrease in perceptual uncertainty about the SVV with increasing eccentricity of the ellipse in the presence of an upright frame is in the same range.
Our data are in line with the addition hypothesis: The effect of the eccentricity of the ellipse on the SVV uncertainty is larger when the frame is upright, and the effect is insignificant for the tilted frames. This could be due to the fact that the higher uncertainty induced by the frame completely masks the contribution of orientation uncertainty of the ellipse. As to the bias of the SVV, the modulation induced by the frame was on average 2° across all ellipse eccentricities. This limited effect is comparable to the previous findings of our group, using the same frame size and rod length (Alberts et al.,
2016). Antonucci, Fanzon, Spinelli, and Zoccolotti (
1995) have also reported such values, whereas Zoccolotti, Antonucci, Daini, and Martelli (
1997) documented a slightly larger value of about 5°, perhaps reflecting different experimental factors (Zoccolotti et al.,
1992). Importantly, the bias did not change with orientation uncertainty of the ellipse, indicating that visual orientation noise of the rod is more likely added to than integrated with a visual percept of head orientation in space. While we replaced the rod with a visual ellipse to probe spatial orientation, other studies have shown that orientations of objects, which are more important for perceptual recognition, are influenced more by visual context and body orientation (Dyde, Jenkin, & Harris,
2006). For future work, it would be interesting to manipulate the variability of such probes and see if they behave in the same way as the line probe investigated here.