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Perceptual Organization
A Mathematical Approach Based on scale and orientation
Remco Duits
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Perceptual Organization
:
The organization of
local image fragments into
the global structure
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Part1: Scale
Painting by Dali
• Objects exist at certain ranges of scale.
• It is not known a priory at what scale to look.
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Scale Space:
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Critical Points and Paths
Maxima
Minimum
Saddles
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Scale Space Theory
Axioms Gaussian scale space ?
Axioms
NO!
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Differences with
Different
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Reconstruction
• It is possible to reconstruct the image by using a limited number of points from the Deep Structure.
Drastically Improved Reconstruction by Reproducing Kernel Theory and Gelfand Triples
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Part2: Orientation, Invertible Orientation scores
image orientation score
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Perceptual organization via orientation scores:Simple modelling of visual
illusions
Enhancement elongated structures in medical images
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Application Automatic Closure of Gaps:Collision probability of forward and backward
process:
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Original ImageNoisy Image Improved MapGround TruthOrientation MapOrientation Map
Robust Orientation Estimation
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1. New scale space theory obeying scale space axioms
2. Improved reconstruction by means of Gelfand-Triples
3. New wavelet theory for invertible orientation scores
4. New theory/applications for stochastic completion fields.
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Scale Space Theory
Generator:
Gaussian SS:
Poisson SS:
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If energy is norm on Hilbert space exact
solution is obtained by orthogonal projection :