1 / 37

Images Similarity by Relative Dynamic Programming

Images Similarity by Relative Dynamic Programming. M. Sc. thesis by Ady Ecker Supervisor: prof. Shimon Ullman. Overview. The similarity problem The Method: Overlapping patches Combining evidences Relative dynamic programming Analysis. Part 1: The Problem. Old problem. Important.

caldwell-flores
Télécharger la présentation

Images Similarity by Relative Dynamic Programming

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Images Similarity by Relative Dynamic Programming M. Sc. thesis by Ady Ecker Supervisor: prof. Shimon Ullman

  2. Overview • The similarity problem • The Method: • Overlapping patches • Combining evidences • Relative dynamic programming • Analysis

  3. Part 1: The Problem

  4. Old problem. Important. Difficult. Natural to humans. The similarity problem

  5. What is similarity? • Similarity has many aspects, e.g. shape, color, size, outline, texture. • Relative and context dependent. • Depends on experience with classes in the real world.

  6. Similarity is not a metric Minimality Triangle inequality Symmetry

  7. Previous approaches to similarity computation • Distance functions (L2, correlation). • Features detection, image signatures. • Minimal energy aligning transformation. • Dynamic programming measures. • Overlapping fragments (Ullman and Sali).

  8. Motivation • Point-wise methods fail on very simple examples.

  9.                                  Motivation • We propose: common substructures of multiple sizes at multiple scales.

  10. B2 B1 A1 A2 C1 C2 Similarity of sub-patchesat the local level A1 A2 B1 B2 C1 C2

  11. Part 2: The method

  12. Overlapping sub-patches • overlapping fragments impose similar structure.

  13. Hierarchical decomposition • Allows the sub-patches to move a little.

  14. Hierarchical alignment

  15. Similarity indicators • Each indicator has its marginal distribution, but the joint distribution is too complex. • The indicators are dependent. FX X normalization by 1-D distribution

  16. Generalization groups example   45º length ratio  2 The similarity is related to the intersection of the groups:Pr(   (A,B)  length ratio  ratio(A,B) )

  17. z F 1 1 z F (x3,y3) 1 (x0,y0) (x0,y0) (x1,y1) (x1,y1) z F z F z (x,y) F z 0 0 area zprob. F F 0 1 0 1 0 0 1 Graphical illustration of the similarity score independent case estimation error general case

  18. Empirical example • 10,000 points from 2D normal distribution. • Normalization:x → Pr ( X  x )y → Pr ( Y  y ) • Only 233 points between the two curves.

  19. x1 y1 x2 z y2 x3 The similarity score • The score combines several similarity indicators. • The score is relative. • Since the score is normalized, it can be used in hierarchical construction:

  20. Dynamic programming in 2D? Vertical movement Horizontal and vertical movements

  21. Relative Dynamic Programming (RDP) • Works in 2D like dynamic programming algorithms, but: • Scores are relative. • No explicit objective function. • Start from many points simultaneously.

  22. The similarity table T(i,d) D(x,x+3) D(x,x+2) 3 D(x,x+1) 2 D(x,x) 1 I1 I2 0 -1 D(x,x-1) D(x,x-2) -2 D(x,x-3) -3 x x

  23. projected index delta The minima table • Allow flexible movements. • Costs keep movement coherence. • Used for efficiency. • Bi-directional (two tables).

  24. Combining evidences

  25. Flowchart Basic similarity measure Input images Set patch size = 2 Geometric mean of sub-patches' scores Store scores in similarity table Double the patch size Build minima tables No Patch size = N? Normalization Yes Output the similarity score

  26. Weighting patches

  27. Multi-scale • Two dimensions, cross-resolution: T(r,z,i1,i2,d1,d2)=min(P, Vhigh-low, Vlow-low) Vlow-low low resolution: Vhigh-low P high resolution:

  28. Distributions • Distributions are sampled empirically. • The sampling is done layer by layer. distribution of the weighted geometric mean of real images distribution of the geometric mean of independent uniform variables

  29. Part 3: Analysis

  30. Performance • The complexity is O(N2D2). • The number of operations is governed by the operations on the original resolution. • Basic-similarity operations: 3232171716  4,735,000. • Minima operations: 3232171792  5,327,000. • Total  10,000,000. • Takes a second on 1.5GH p.c.

  31. Results L2 RDP correlation

  32. Results

  33. Experimental conclusions • The algorithm is superior to point-wise distance functions (L2, correlation), even when the images are aligned by a global transformation. • The current implementation neglects important parts such as outlines and topology.

  34. Qualitative properties • Similarity by parts. • Captures variety of transformations. • Weights the salient parts. • Adaptive to distributions in the domain.

  35. Properties of the design • Robust. • Simple operations. • Can be implemented in parallel and neural-networks. • Intuitive. • Extendible to deal with many aspects of similarity.

  36. Summary • We presented a new scheme to the similarity problem in general. • The scheme is based on the systematic evaluation of similarity on overlapping sub-patches. • Scores are relative. Scores are combined hierarchically using empiric normalizations. • The implementation captures aspects of perceptual similarity, but is still inferior to human’s judgment.

  37. The End

More Related