Psychophysics Thurs. Feb. 22, 2018 1 How do we measure how well - - PowerPoint PPT Presentation

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Psychophysics Thurs. Feb. 22, 2018 1 How do we measure how well - - PowerPoint PPT Presentation

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COMP 546 Lecture 13 Psychophysics Thurs. Feb. 22, 2018 1 How do we measure how well someone can perform a vision task? E.g. How well can one discriminate color or luminance (intensity) orientation depth from binocular

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COMP 546

Lecture 13

Psychophysics

  • Thurs. Feb. 22, 2018
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How do we measure how well someone can perform a vision task? E.g. How well can one discriminate …

  • color or luminance (intensity)
  • orientation
  • depth from binocular disparity
  • 2D velocity
  • 3D surface shapes (slant, tilt, curvature, …)
  • …..
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"Psychophysics" : (loose definition) the study of mappings from physical variables to perceptual variables, as measured by behavioral response stimulus (physical) response (perceptual -- measured by behavior)

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Psychometric function

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response stimulus

(independent variable, set by experimenter)

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Example 1a: discriminate brightness (increment or decrement?)

Percent response “increment”

𝐽0 𝐽0 + ∆𝐽

100

𝐽0 + ∆𝐽 𝐽0

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Example 1b: detect a brightness increment (left or right?)

Percent correct

𝐽0 𝐽0 + ∆𝐽

50 100

𝐽0 + ∆𝐽 𝐽0

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A: Q: Why are psychometric curves not step functions ?

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A:

  • Noise/randomness in the display or stimulus
  • Noise/randomness in the sensors/brain
  • Limited resolution: finite samples
  • Subjects press the wrong button (stop paying attention)

Q: Why are psychometric curves not step functions ?

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Example 1c: detect a brightness increment left or right? (with added noise)

50 100

𝐽0 𝐽0 + ∆𝐽

Percent correct (left or right?)

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Ideal Observer

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Even an “ideal observer” who knows the code used to generate the images would not get 100% correct, because code uses a random number generator. One can compare human performance to that of an ideal observer. (Technical details omitted.)

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Psychophysical threshold 𝜐

stimulus variable 𝑡

percentage response 75 50 100

𝑡0 𝑡0 + 𝜐

Defines the stimulus level that gives a particular performance level e.g. 75% correct.

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Psychophysical threshold 𝜐

stimulus variable 𝑡

percentage correct 75 50 100

𝑡0 𝑡0 + 𝜐

Defines the stimulus level that gives a particular performance level e.g. 75% correct.

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How to estimate a threshold 𝜐 ?

stimulus variable 𝑡

percentage correct 75 50 100

𝑡0

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How to estimate a threshold 𝜐 ? Fit a (sigmoid shaped) curve.

stimulus variable 𝑡

percentage correct 75 50 100

𝑡0

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Overview

  • Psychometric function
  • Threshold
  • Examples
  • Contrast Sensitivity
  • Depth discrimination (binocular disparity)
  • 2D Motion
  • Slant from texture

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Luminance Contrast revisited (Assignment 1)

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≡ 𝐽𝑛𝑏𝑦 − 𝐽𝑛𝑗𝑜 𝐽𝑛𝑏𝑦 + 𝐽𝑛𝑗𝑜

Michelson Contrast

It is always between 0 and 1.

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∆𝐽 𝐽 = (𝐽𝑛𝑏𝑦 − 𝐽𝑛𝑗𝑜)/2 (𝐽𝑛𝑏𝑦+ 𝐽𝑛𝑗𝑜)/2

Michelson contrast is commonly used for sine functions.

𝐽𝑛𝑗𝑜 𝐽𝑛𝑏𝑦

𝐽

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Example : Detecting a 2D sinusoid grating

(vertical or horizontal?)

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Luminance contrast thresholds depend on spatial frequency

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contrast spatial frequency k

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Luminance contrast thresholds depend on spatial frequency

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contrast spatial frequency k

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spatial frequency k (cycles per degree)

Measure threshold at each spatial frequency. (For 2D sinusoid e.g. 20x20 degrees)

contrast detection threshold

minimum threshold at 3-5 cycles per degree

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spatial frequency (k cycles per degree)

Contrast sensitivity ≡

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contrast detection threshold

Contrast sensitivity

peak sensitivity at 3-5 cycles per degree

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Why?

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spatial frequency (k cycles per degree)

Contrast sensitivity

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Assignment 1 Q2a

  • -

+

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Assignment 1 Q2a lecture 4 The shape of the contrast sensitivity function is believed to be a result of the range of DOG receptive fields (starting at the retina).

  • -

+

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Example 2a: Depth discrimination from binocular disparity

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Is square closer or farther than background?

anaglyph Δ𝑎

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Assignment 2

Q1 (binocular disparity) Even if there is no noise added, there is uncertainty in the disparity.

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Example 2b: Depth discrimination for 2D sinusoidal binocular disparity

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[Bradshaw and Rogers 1999]

Why this dependence ?

Example 2b: Depth discrimination for 2D sinusoidal binocular disparity

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[Bradshaw and Rogers 1999]

Lowest threshold occurs at much lower (about

1 10 )

spatial frequency than for luminance contrast. Why ?

Example 2b: Depth discrimination for 2D sinusoidal binocular disparity

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𝜖 𝐽 𝜖𝑦

𝑤𝑦 +

𝜖 𝐽 𝜖𝑧 𝑤𝑧 + 𝜖 𝐽 𝜖𝑢 = 0

𝑤𝑦 𝑤𝑧

Example 3: 2D velocity estimation

(How to think about image noise in this task?)

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𝜖 𝐽 𝜖𝑦

𝑤𝑦 + 𝜖 𝐽

𝜖𝑧 𝑤𝑧 + 𝜖 𝐽 𝜖𝑢 = 0

𝑤𝑦 𝑤𝑧

One must estimate image derivatives (subject to “noise”)

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This creates uncertainty in motion constraint line.

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Recall: Intersection of Constraints (IOC)

𝑤𝑦 𝑤𝑧

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Uncertainty in the motion constraint lines leads to uncertain in the 2D velocity estimates.

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Assignment 2

Q5, Q6 (motion): Images are filtered with “shift detector” cells. Even if there is no noise added, there is uncertainty in the 2D velocity estimate.

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Example 4: Slant from texture

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Given two images of slanted surfaces, which surface has greater slant ?

𝜄+Dq 𝜄

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Slant discrimination threshold ∆𝜄

slant

percentage response 75 50 100

𝜄 𝜄 + ∆𝜄 Which is more slanted? 𝜄 versus 𝜄 + ∆𝜄 ?

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Thresholds ∆𝜄 depend on slant 𝜄. How and why?

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0 deg 65 deg 65 deg 0 deg

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Results: Dq threshold is larger when q is smaller.

Dq Dq q q

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Recall: Texture cues for slant & tilt

(lecture 11)

  • size gradient (scale)
  • density gradient (position)
  • foreshortening gradient

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  • How reliable are the size, density, foreshortening

cues for an ideal observer ? (What assumptions need to hold to make to estimate slant from these cues?)

  • Do human observers have similar pattern of

responses as ideal observers?

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human observers “ideal” observers who know the probability model used to generate texture and who use various combinations of cues: size, density, foreshortening

Dq threshold is large when q is small for both human and ideal observers.

[Knill, 1998]

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Overview

  • Psychometric function
  • Threshold
  • Examples
  • Contrast Sensitivity
  • Depth discrimination (binocular disparity)
  • 2D Motion
  • Slant from texture

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Summary

Discrimination thresholds can tell us about:

  • underlying mechanisms

(how the brain codes of luminance, color, 2D orientation, disparity, 2D velocity, slant & tilt…)

  • inherent difficulty of the computational problem

that is due to randomness (“noise”)

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