A Computational Model for Perception of Two-dimensional Pattern - - PowerPoint PPT Presentation

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A Computational Model for Perception of Two-dimensional Pattern - - PowerPoint PPT Presentation

Aug 21, 2023 429 likes •587 views

A Computational Model for Perception of Two-dimensional Pattern Velocities Eero P. Simoncelli The Media Laboratory EECS Department, MIT David J. Heeger NASA-Ames Research Center Psychology Department, Stanford University Outline

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A Computational Model for Perception of Two-dimensional Pattern Velocities Eero P. Simoncelli The Media Laboratory EECS Department, MIT NASA-Ames Research Center Psychology Department, Stanford University David J. Heeger

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Simoncelli & Heeger, ARVO-92

Outline

  • Computational model: Bayesian velocity estimator
  • Simple two-stage model implementation
  • Model response to plaid stimuli
  • Comparison to psychophysical data:
  • Ferrera & Wilson, 1990, 1991
  • Stone, Watson, Mulligan, 1990
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Simoncelli & Heeger, ARVO-92

  • Gradient measurement equation, with noise model:

Ix (v - n1)+ It + n2 = 0

  • Prior probability distribution on velocity:

P(v) ~ N(0, σv2)

  • Bayes' rule gives probability distribution on velocity:

Bayesian Velocity Estimator (σe2 +Ix2) (Ix v + It)2 σv2 v2 log P(v | I) ∝

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Simoncelli & Heeger, ARVO-92

+ Implementation: Stage 1

  • Linear filtering, using spatio-

temporally oriented operators

  • Energy computation (squaring)
  • Divisive normalization, with semi-

saturation parameter, σe

  • Outputs are spatio-temporally

tuned ÷ ÷

  • σe2

. . . . . .

Input: image intensities

. . .

Output: normalized "energy"

Simoncelli & Heeger, ARVO-92

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Simoncelli & Heeger, ARVO-92

Implementation: Stage 2

  • Weighted summation of stage 1

energies over space, frequency bands

  • Some of the summations include

prior variance parameter, σv

  • Outputs are velocity tuned

+ + σv-2

Input: spatio-temporal energies

. . .

  • Output: "velocity"

Simoncelli & Heeger, ARVO-92

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Simoncelli & Heeger, ARVO-92

Grating Examples

Vx Vy

stimulus idealization model

Vy Vx Vx Vy Vx Vy

Simoncelli & Heeger, ARVO-92

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Simoncelli & Heeger, ARVO-92

Plaids: Effect of Relative Contrast

Vx Vy

stimulus idealization model

Vy Vx Vx Vy Vx Vy

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Simoncelli & Heeger, ARVO-92

4 3 2 1

  • 5

5 10 15 20

Model

Log Contrast Ratio

4 3 2 1

  • 5

5 10 15 20

5% 10% 20% 40% Total Contrast

Subject

Log Contrast Ratio Perceived Direction Bias (degrees)

Stone et al. 1990

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Simoncelli & Heeger, ARVO-92

Plaids: Effect of Grating Angles

Vx Vy

stimulus idealization model

Vy Vx Vx Vy Vx Vy

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Simoncelli & Heeger, ARVO-92

Sym m etr i c I Asym m etr i c I Type I I 2 4 6 8

subject model

Ferrera & Wilson, 1990

Plaid Type Perceived Direction Bias (degrees)

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Simoncelli & Heeger, ARVO-92

90 60 30 0. 2 0. 4 0. 6 0. 8 1.

subject2 cosine model

Ferrera & Wilson, 1991

Plaid angle (degrees) Perceived Speed (relative to IOC)

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Simoncelli & Heeger, ARVO-92

Summary of Model

  • Derived as a Bayesian estimator
  • Starting from image intensities, computes response of

a population of velocity-tuned units

  • Implemented in two simple stages of computation
  • Velocity estimates are consistent with psychophysics
  • f plaid perception
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Simoncelli & Heeger, ARVO-92

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Simoncelli & Heeger, ARVO-92

y t x Example Receptive Field x

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Simoncelli & Heeger, ARVO-92

x Spatio-temporal Filter Bank ωx ωt y x t