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Perceptual Organization A Mathematical Approach Based on scale, orientation and curvature

Perceptual Organization A Mathematical Approach Based on scale, orientation and curvature. Remco Duits. Perceptual Organization: The organization of local image image fragments into the global structure. Outline. 1 . Scale Space Repr. 2. Orientation Score. Part 1. Scale Space.

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Perceptual Organization A Mathematical Approach Based on scale, orientation and curvature

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  1. Perceptual OrganizationA Mathematical Approach Based on scale, orientation and curvature Remco Duits

  2. Perceptual Organization:The organization of local image image fragments into the global structure

  3. Outline 1. ScaleSpace Repr. 2. Orientation Score

  4. Part 1. Scale Space The notion of scale :

  5. Scale Space Theory Axioms Gaussian scale space ? - NO ! Axioms

  6. Scale Space Theory Generator: Gaussian SS: Poisson SS:

  7. Scale Space Theory

  8. Deep Structure: Top-points:

  9. Top-point Reconstruction Gelfand Triples Sobolev/Traj. Spaces Reproducing Kernels

  10. If energy is norm on Hilbert space exact solution is obtained by orthogonal projection :

  11. Fast Top-point Reconstruction on large images,cooperation with Frans Kanters, Bart Janssen : Cooperation with Frans Kanters, Bart Janssen

  12. Part 2. Orientation Scores

  13. Stability Transformations : Reducible Generalization wavelet theory :

  14. Perceptual organization via orientation scores:

  15. Processing on Orientation Scores image score processed image processed score Euclidean-invariant iff Left-invariant

  16. Left-invariant Evolutions on :

  17. Application Automatic Closure of Gaps: Collision probability of forward and backward proces:

  18. Orientation scores of 3D images (Euler angles) image orientation score

  19. 3D Proper Wavelets allowing stable inverse transform :

  20. Line enhancement in 3D via invertible orientation scores Application: Enhancement Adam-Kiewitz vessel

  21. Robust orientation estimation Channel representations: (steerable) Tensor voting :

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