From local motion estimates to global ones physiology:

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From local motion estimates to global ones -
physiology
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Motion fields for more complex patterns
Hildreth (1985) Smoothness of velocity field
along the contour
True motion field
Local motion estimates
Smoothest Velocity field
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Motion fields for more complex patterns (contd.)
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Motion fields for more complex patterns (contd.)
Ellipse demo
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Recovering 3D structure from motion
Kinetic Depth Effect Wallach, 1953
Another possible percept
Percept
Inference The human visual system has a
preference for rigid interpretations
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Ullmans model for recovering 3D structure from
motion

• Establish correspondence between features in
  different frames
• Recover transformation matrix and z values of
  points

Key result For a rigid structure, 4 non-coplanar
points in 3 frames are sufficient to solve
for all the unknowns Ullman, 1979
Open questions 1. Do these bounds apply to
human observers too? 2. Does the rigidity
assumption always hold? 3. How do we recover the
3D structure of non-rigid dynamic objects?
Video 1 NR rotating object Video 2 Johansson
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Ullmans incremental rigidity scheme
Allows structure recovery even for gradually
deforming objects.
However 1. Humans are able to recover 3D
structures even with just 2 frames. It is unclear
how this is accomplished. 2. Correspondence is
not an easy problem. Errors in correspondence
lead to errors In structure recovery.
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Processing Framework Proposed by Marr
Recognition
3D structure motion characteristics surface
properties
Shape From stereo
Motion flow
Shape From motion
Color estimation
Shape From contour
Shape From shading
Shape From texture
Edge extraction
Image
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Color
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Color Estimation
Goal To recover the intrinsic surface
reflectance of an object.
And yet, we have good lightness constancy!
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Lightness Constancy
The constancy in perceived surface reflectance
regardless of differences in illumination.
Luminance (L) Reflectance (R) Illumination (I)
Goal Given L, recover R. Clearly
underconstrained. Assumptions are needed for
unique solutions.
Helmholtzs theory Observer knows I through
past experience. Hering, Wallach, Land McCann
Observer computes luminance ratios across
edges. (some important hidden assumptions
here)
Explain fig above
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The perceptual importance of luminance ratios at
edges
Cornsweet Illusion
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Explaining simultaneous contrast illusions via
edge ratios
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TANGENT ALERT!
Are ratios taken with actual or perceived
luminances?
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Land and McCanns Retinex theory
I

R
L
Given L, recover R
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Land and McCanns Retinex theory - Assumptions

• The world is flat and all sharp
• luminance variations are due
• to changes in reflectance.
• Reflectance always changes
• abruptly.
• Illumination changes gradually
• across a scene.

Basic idea Preserve luminance ratios at edges
and discard slow variations.