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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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3 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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4 Scale Space:
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5 Critical Points and Paths Maxima Minimum Saddles
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6 Scale Space Theory Axioms Gaussian scale space ? Axioms NO!
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7 Differences with Different
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8 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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9 Part2: Orientation, Invertible Orientation scores image orientation score
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10 Perceptual organization via orientation scores: Simple modelling of visual illusions Enhancement elongated structures in medical images
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11 Application Automatic Closure of Gaps: Collision probability of forward and backward process:
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12 Original ImageNoisy ImageImproved MapGround Truth Orientation Map Robust Orientation Estimation
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13 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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15 Scale Space Theory Generator: Gaussian SS: Poisson SS:
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16 If energy is norm on Hilbert space exact solution is obtained by orthogonal projection :
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