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Segmentation and Perceptual Grouping

Segmentation and Perceptual Grouping. The problem Gestalt Edge extraction: grouping and completion Image segmentation. Camouflage. Kanizsa Triangle. The image of this cube contradicts the optical image. Perceptual Organization. Atomism, reductionism:

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Segmentation and Perceptual Grouping

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  1. Segmentation and Perceptual Grouping • The problem • Gestalt • Edge extraction: grouping and completion • Image segmentation

  2. Camouflage

  3. Kanizsa Triangle

  4. The image of this cube contradictsthe optical image

  5. Perceptual Organization • Atomism, reductionism: • Perception is a process of decomposing an image into its parts. • The whole is equal to the sum of its parts. • Gestalt (Wertheimer, Köhler, Koffka 1912) • The whole is larger than the sum of its parts.

  6. Mona Lisa

  7. Mona Lisa

  8. Proximity Gestalt Principles

  9. Proximity Similarity Gestalt Principles

  10. Proximity Similarity Continuity Gestalt Principles

  11. Closure Proximity Similarity Continuity Gestalt Principles

  12. Proximity Similarity Continuity Closure Common Fate Gestalt Principles

  13. Proximity Similarity Continuity Closure Common Fate Simplicity Gestalt Principles

  14. Smooth Completion • Isotropic • Smoothness • Minimal curvature • Extensibility

  15. Elastica • Elastica is not scale invariant

  16. Elastica • Scale invariant measure • Approximation

  17. Finding lines from points

  18. Parametric methods: RANSAC

  19. RANSAC • RANdom SAmple Concensus • Complexity: • Need to go over all pairs: O(n2) • For each pair check how many more points are consistent: O(n) • Total complexity: O(n3 )

  20. RANSAC • Another application of RANSAC: Find transformation between images • Example: compute homography • Compute homography for every 4 pairs of corresponding points • Choose the homography that best explains the image • m4n4 sets should be tested • Another example: compute epipolar lines • How many correspondences are needed?

  21. Hough Transform

  22. Hough Transform • Linear in the number of points • Describe lines as • Or better • Prepare a 2D table c θ

  23. Hough Transform c +1 +1 +1 +1 +1 θ

  24. Hough Transform c 13 16 θ What if we want to find circles?

  25. Curve Salience

  26. Saliency Network Encourage • Length • Low curvature • Closure

  27. Saliency Network

  28. Tensor Voting • Every edge element votes to all its circular edge completions • Vote attenuates with distance: e-αd • Vote attenuates with curvature: e-βk • Determine salience at every point using principal moments

  29. Tensor Voting

  30. Stochastic Completion Field • Random walk: • In addition, a particle may die with probability:

  31. Stochastic Completion Fields

  32. Stochastic Completion Fields • Most probable path: with • Can be implemented as a convolution

  33. Stochastic Completion Fields

  34. Stochastic Completion Fields

  35. Snakes • Given a curve Г(s)=(x(s),y(s)), define: with

  36. Extremum: Calculus of Variation • Given a functional • A condition for a local extrimum is obtained using the Euler-Lagrange equation • Curve evolution is defined • Solution obtained when

  37. Curve evolution

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