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Distribution Fields

Distribution Fields. A Unifying Representation for Low-Level Vision Problems Erik Learned-Miller with Laura Sevilla Lara, Manju Narayana , Ben Mears . Unifying Low-Level Vision. Tracking Optical Flow Affine invariant matching Stereo Backgrounding Registration

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Distribution Fields

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  1. Distribution Fields A Unifying Representation for Low-Level Vision Problems Erik Learned-Millerwith Laura Sevilla Lara, ManjuNarayana, Ben Mears

  2. Unifying Low-Level Vision • Tracking • Optical Flow • Affine invariant matching • Stereo • Backgrounding • Registration • Image StitchingWhat kind of representation serves all these problems well?

  3. Unifying Descriptors and Representations • HOG, SIFT, Shape Contexts • Geometric blur • Multi-scale methods • Mixture of Gaussian backgrounding • Bilateral filter • Joint alignment (congealing)

  4. Tracking

  5. Basics of Tracking Frame T Frame T+d

  6. Basics of Tracking Frame T Frame T+d

  7. Basics of Tracking Frame T Frame T+d

  8. Basics of Tracking Frame T Frame T+d

  9. The Core Matching Problem Find best match of patch I to image J,for some set of transformations. image J patch I

  10. Key issues • Large “basin of attraction” in gradient descent • Robustness to appearance changes of target

  11. Local optimum problem in alignment Stuck in a local optimum Unaligned

  12. Common solution to gradient descent matching • Blur images? • “Spreads information” • Also destroys information through averaging

  13. Exploding an image One plane for each feature value.

  14. Spatial Blur: 3d convolution with 2d Gaussian

  15. Spatial Blur: 3d convolution with 2d Gaussian KEY PROPERTY: doesn't destroy information through averaging

  16. Properties of Distribution Field Representation • Much larger basin of attraction than other descriptors. • A useful probability model from a single image. • Inherently multi-scale. • Extension and unification of many popular descriptors. • State of the art performance from extremely simple algorithms.

  17. Properties of Distribution Field Representation • Much larger basin of attraction than other descriptors. • A useful probability model from a single image. • Inherently multi-scale. • Extension and unification of many popular descriptors. • State of the art performance with extremely simple algorithms. • THANKS!

  18. The likelihood match

  19. Sharpening match

  20. Understanding the sharpening match What standard deviation maximizes the likelihood of a given point under a zero-mean Gaussian?

  21. Intuition behind sharpening match • Increase standard deviation until it matches “average distance” to matching points.

  22. Properties of the sharpening match • A patch has probability of 1.0 under its own distribution field. • Probability of an image patch degrades gracefully as it is translated away from best position. • Optimum “sigma” value gives a very intuitive notion of the quality of the image match.

  23. Basin of attraction studies

  24. Basin of attraction studies GIVEN A RANDOM PATCH...

  25. Basin of attraction studies AND A RANDOM DISPLACEMENT...

  26. Basin of attraction studies

  27. Basin of attraction studies

  28. Basin of attraction results

  29. Tracking results • State of the art results on tracking with standard sequences • Very simple code • Trivial motion model • Simple memory model

  30. Closely Related work • Mixture of Gaussian backgrounding (Stauffer...) • Shape contexts (Belongie and Malik) • Congealing (me) • Bilateral filter • SIFT (Lowe), HOG (Dalal and Triggs) • Geometric Blur (Berg) • Rectified flow techniques (Efros, Mori) • Mean-shift tracking • Kernel tracking • and many others...

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