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Page 1: From cortical anisotropy to failures of 3-D shape constancy

From cortical anisotropy to failures of 3-D shape

constancy

Qasim Zaidi Elias H. Cohen

State University of New YorkCollege of Optometry

Page 2: From cortical anisotropy to failures of 3-D shape constancy

Shape Constancy

•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? North view South view

The Future Building, Manhattan

(Griffiths & Zaidi, 2000)

Page 3: From cortical anisotropy to failures of 3-D shape constancy

Vertical

Oblique

Convex Concave

Does rotating from vertical to oblique preserve perceived depth?

3-D Shape Constancy across image rotations?

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Vertical

Oblique

Convex Concave

Stimuli

Perspective 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

Sine-wave gratings• 3 spatial frequencies, 1,3,6 cpd.• Oriented at 90, ± 67.5, ± 45, & ± 22.5 degrees ( wrt 3D axis).• Added in randomized phases to make 10 different textures per shape.

Texture

Page 5: From cortical anisotropy to failures of 3-D shape constancy

Exp 1

Failures of 3-D shape constancy

Vertical vs. Oblique comparison task.Subjects view two shapes sequentially.

Which shape is greater in depth?

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500 msec

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500 msec

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500 msec

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500 msec

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500 msec

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Exp 1: Shape Comparison Results

The 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).

Page 13: From cortical anisotropy to failures of 3-D shape constancy

3D Shape From Texture Perception of shape from texture depends on patterns of

orientation flows (Li & Zaidi, 2001; 2004)

Textured shape with no orientation component orthogonal to axis of curvature.

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Is there a corresponding OB for single 2D angles?

Origins of oblique bias for 3D shape

Is the 3D OB explained by an OB for 2D oriented components?

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Exp 2

Failures of 2-D angle constancy

Vertical vs. Oblique comparison task.Subjects view two shapes sequentially.

Which angle is sharper?

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500 msec

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500 msec

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500 msec

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500 msec

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500 msec

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Exp 2: Angle Comparison Results

The 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.

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Predicting the 3-D depth bias from the 2-D angle bias

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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.

Page 23: From cortical anisotropy to failures of 3-D shape constancy

Orientation anisotropies in cat V1 cells (Li et al 2003)

Oriented energy in natural images (Hansen & Essock, 2004)

Page 24: From cortical anisotropy to failures of 3-D shape constancy

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Stimulus orientation decoded from cortical responses

The probability that an orientation-tuned cell will give a spike in response to an orientation θ is determined by its tuning curve f(θ) (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:

Page 25: From cortical anisotropy to failures of 3-D shape constancy

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Stimulus orientation decoded from cortical responses

Using Bayes formula, the optimal estimate of the stimulus is the peak of the posterior probability distribution (P(θ) = Probability of θ in natural images) :

Equivalently the peak of the log of the posterior:

Given di cells tuned to each orientation θi the equation is grouped using average responses:

Page 26: From cortical anisotropy to failures of 3-D shape constancy

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Stimulus angle decoded from cortical responses

Using orientation tuned cells in V1, plus cross-orientation inhibition, we derived a matrix valued tuning function for (V4?) cells selective for angles composed of two lines θp and θq :

For the prior P() 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:

Page 27: From cortical anisotropy to failures of 3-D shape constancy

ASSUMPTION: Observer perceives an angle equal to the optimally decoded angle, i.e. the peak of the posterior probability distribution

Stimulus angle 140º

Decoded oblique angle 142º Decoded vertical angle 138º

Page 28: From cortical anisotropy to failures of 3-D shape constancy

From cortical anisotropy to shape inconstancy

1. We show an oblique bias for 3-D appearance.

2. The 3-D effect can be explained by an oblique bias for 2-D angles.

3. Simulations show that the anisotropy in orientation tuning of cortical neurons plus cross-orientation inhibition explains the 2-D oblique bias.

4. Anisotropy in numbers of cells predicts the opposite bias.

5. The predictions were insensitive to the prior distribution.

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Consequences of the oblique bias for angle perception

Zucker et al

Fleming et al

Cohen & Singh

Tse

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Conclusions

1. If 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.

2. 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).


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