From cortical anisotropy to failures of 3-D shape constancy Qasim Zaidi Elias H. Cohen State University of New York College of Optometry
Jan 21, 2016
From cortical anisotropy to failures of 3-D shape constancyQasim Zaidi Elias H. Cohen
State University of New YorkCollege of Optometry
Shape is the geometrical property of an object that is invariant to location, rotation and scale.The ability to perceive the shape of a rigid object as constant across viewpoints has been considered essential to perceiving objects accurately.The visual system does not discount all perspective distortions, so the shapes of many 3-D objects change with viewpoint. Can shape constancy be expected for rotations of the image plane?
VerticalObliqueConvexConcaveDoes rotating from vertical to oblique preserve perceived depth?3-D Shape Constancy across image rotations?
VerticalObliqueConvexConcaveStimuliPerspective projection of convex and concave wedges (in circular window).
Experiment 1 compared 5 vertical shapes to 5 oblique shapes in depth (concave to concave & convex to convex). Shapes
Exp 1 Failures of 3-D shape constancy Vertical vs. Oblique comparison task.Subjects view two shapes sequentially.
Which shape is greater in depth?
Exp 1: Shape Comparison ResultsThe same shape was perceived to be deeper when it was oriented vertically than when it was oriented obliquely.Oblique shapes were matched to vertical shapes of 0.77 times depth of the oblique shape (S.E. = .007).
3D Shape From Texture Perception of shape from texture depends on patterns of orientation flows (Li & Zaidi, 2001; 2004)
Origins of oblique bias for 3D shape Is the 3D OB explained by an OB for 2D oriented components?
Exp 2 Failures of 2-D angle constancy Vertical vs. Oblique comparison task.Subjects view two shapes sequentially.
Which angle is sharper?
Exp 2: Angle Comparison ResultsThe same angle was perceived to be sharper when it was oriented vertically than when it was oriented obliquely.Oblique angles were matched to vertical angles 4.5 shallower on average.
Predicting the 3-D depth bias from the 2-D angle bias
The average ratio of perceptually equivalent 2-D slopes = 0.862 (SE = .001)
Ratio of perceptually equivalent 3-D depths = 0.771 (SE = .007)
3-D depth inconstancy can be explained by anisotropy in perception of 2-D features.
irrespective of h.
Orientation anisotropies in cat V1 cells (Li et al 2003)Oriented energy in natural images (Hansen & Essock, 2004)
Stimulus orientation decoded from cortical responsesThe probability that an orientation-tuned cell will give a spike in response to an orientation is determined by its tuning curve f() (Sanger, 1996):The probability of the cell giving ni spikes is given by a Poisson distribution: For independently responding neurons, the probability of ni spikes each from k cells is given by the product of the probabilities:
Stimulus orientation decoded from cortical responsesUsing Bayes formula, the optimal estimate of the stimulus is the peak of the posterior probability distribution (P() = Probability of in natural images) :Equivalently the peak of the log of the posterior:Given di cells tuned to each orientation i the equation is grouped using average responses:
Stimulus angle decoded from cortical responsesUsing orientation tuned cells in V1, plus cross-orientation inhibition, we derived a matrix valued tuning function for (V4?) cells selective for angles W composed of two lines p and q :For the prior P(W) we made the rough approximation:Finally, stimulus angles were decoded from the population responses of orientation tuned cells using an equation similar to that for orientations:
ASSUMPTION: Observer perceives an angle equal to the optimally decoded angle, i.e. the peak of the posterior probability distributionStimulus angle 140 Decoded oblique angle 142 Decoded vertical angle 138
From cortical anisotropy to shape inconstancyWe show an oblique bias for 3-D appearance.
The 3-D effect can be explained by an oblique bias for 2-D angles.
Simulations show that the anisotropy in orientation tuning of cortical neurons plus cross-orientation inhibition explains the 2-D oblique bias.
Anisotropy in numbers of cells predicts the opposite bias.
The predictions were insensitive to the prior distribution.
Consequences of the oblique bias for angle perceptionZucker et alFleming et alCohen & SinghTse
ConclusionsIf the perception of 3D shape depends on the extraction of simple image features, then bias in the appearance of the image features will lead to bias in the appearance of 3D shape.
Variations in properties within neural populations can have direct effects on visual percepts, and need to be included in neural decoding models.REFERENCECohen EH and Zaidi Q Fundamental failures of shape constancy due to cortical anisotropy. Journal of Neuroscience (Under review).
If the balconies of a building switch from tilting up to tilting down depending on viewpoint, it is clear that the change is not in the building, but in the percept. Such illusions are explained in terms of perceptual assumptions that enable the visual system to disambiguate 2D images into likely 3D scenes. A very large number of such assumptions have been identified, but the mechanisms by which the visual system chooses the best assumption have been much less studied, especially the case where competing assumptions lead to incompatible percepts.