1 / 129

Shape Descriptors I

Shape Descriptors I. Thomas Funkhouser CS597D, Fall 2003 Princeton University. 3D Representations. What properties are required for analysis and retrieval?. Retrieval. Analysis. Display. Editing. Property. Intuitive specification Yes No No No Guaranteed continuity Yes No No No

bond
Download Presentation

Shape Descriptors I

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. Shape Descriptors I Thomas Funkhouser CS597D, Fall 2003Princeton University

  2. 3D Representations • What properties are required for analysis and retrieval? Retrieval Analysis Display Editing Property Intuitive specification YesNo No No Guaranteed continuity YesNo No No Guaranteed validity YesNo No No Efficient boolean operations YesNoNo No Efficient rendering Yes YesNo No Accurate Yes Yes ? ? Concise ? ? ? Yes StructureYes Yes Yes Yes

  3. Shape Analysis Problems 1) • Examples: • Feature detection • Segmentation • Labeling • Registration • Matching • Retrieval • Recognition • Classification • Clustering 2) 3) Query 4) Ranked Matches “How can we find 3D models best matching a query?”

  4. Shape • Definition from Merriam-Webster’s Dictionary: • a: the visible makeup characteristic of a particular item or kind of item b : spatial form or contour

  5. Shape • Shape is independent of similarity transformation (rotation, scale, translation, mirror) =

  6. Shape Similarity • Need a shape distance function d(A,B) that: • matches our intuitive notion of shape similarity • can be computed robustly and efficiently • Perhaps, shape distance function should be a metric: • Non-negative: d(A,B)  0 for all A and B • Identity: d(A,B) = 0 if and only if A=B • Symmetry: d(A,B) = d(B,A) for all A and B • Triangle inequality: d(A,B) + d(B,C)  d(A,C)

  7. Example Distance Functions • Lp norm: • Hausdorff distance: • Others (Fréchet, etc.)

  8. Shape Matching • Compute shape distance function for pair of 3D models • Can matching two objects • Can find most similar object among a small set Are these the same chair?

  9. Shape Retrieval • Find 3D models with shape most similar to query • Searching large database must take less than O(n) Is this blue chair in the database?

  10. Shape Retrieval • Build searchable shape index Geometric Query Shape Analysis Shape Descriptor Similar Objects ShapeRetrieval Database of 3D Models Shape Index Shape Analysis

  11. Shape Retrieval • Find 3D models with shape similar to query 3D Query Best Matches 3D Database

  12. Challenge • Need shape descriptor that is: • Concise to store • Quick to compute • Efficient to match • Discriminating 3D Query ShapeDescriptor BestMatches 3D Database

  13. Challenge • Need shape descriptor that is: • Concise to store • Quick to compute • Efficient to match • Discriminating 3D Query ShapeDescriptor BestMatches 3D Database

  14. Challenge • Need shape descriptor that is: • Concise to store • Quick to compute • Efficient to match • Discriminating 3D Query ShapeDescriptor BestMatches 3D Database

  15. Challenge • Need shape descriptor that is: • Concise to store • Quick to compute • Efficient to match • Discriminating 3D Query ShapeDescriptor BestMatches 3D Database

  16. Challenge • Need shape descriptor that is: • Concise to store • Quick to compute • Efficient to match • Discriminating 3D Query ShapeDescriptor BestMatches 3D Database

  17. Challenge • Need shape descriptor that is: • Concise to store • Quick to compute • Efficient to match • Discriminating • Invariant to transformations • Insensitive to noise • Insensitive to topology • Robust to degeneracies Different Transformations(translation, scale, rotation, mirror)

  18. Challenge Image courtesy ofRamamoorthi et al. • Need shape descriptor that is: • Concise to store • Quick to compute • Efficient to match • Discriminating • Invariant to transformations • Insensitive to noise • Insensitive to topology • Robust to degeneracies Scanned Surface

  19. Challenge Images courtesy of Viewpoint & Stanford • Need shape descriptor that is: • Concise to store • Quick to compute • Efficient to match • Discriminating • Invariant to transformations • Insensitive to noise • Insensitive to topology • Robust to degeneracies Different Genus Different Tessellations

  20. Challenge Images courtesy of Utah & De Espona • Need shape descriptor that is: • Concise to store • Quick to compute • Efficient to match • Discriminating • Invariant to transformations • Insensitive to noise • Insensitive to topology • Robust to degeneracies No Bottom! &*Q?@#A%!

  21. Taxonomy of Shape Descriptors • Structural representations • Skeletons • Part-based methods • Feature-based methods • Statistical representations • Voxels, moments, wavelets, … • Attributes, histograms, ... • Point descriptors

  22. Taxonomy of Shape Descriptors Images courtesy of Amenta & Osada • Structural representations • Skeletons • Part-based methods • Feature-based methods • Statistical representations • Voxels, moments, wavelets, … • Attributes, histograms, ... • Point descriptors

  23. Taxonomy of Shape Descriptors Image courtesy of De Espona • Structural representations • Skeletons • Part-based methods • Feature-based methods • Statistical representations • Voxels, moments, wavelets, … • Attributes, histograms, ... • Point descriptors ?

  24. Taxonomy of Shape Descriptors • Structural representations • Skeletons • Part-based methods • Feature-based methods • Statistical representations • Voxels, moments, wavelets, … • Attributes, histograms, ... • Point descriptors ?

  25. Alignment-dependent Voxels Wavelets Moments Extended Gaussian Image Spherical Extent Function Spherical Attribute Image Alignment-independent Shape histograms Harmonic descriptor Shape distributions Statistical Shape Descriptors

  26. Feature Vectors Image courtesy ofMao Chen • Map shape onto point in multi-dimensional space • Similarity measure is distance in feature space Tables Feature 1 Desks File cabinets Feature 2

  27. Feature Vectors Image courtesy ofMao Chen • Cluster, classify, recognize, and retrieve similarfeature vectors using standard methods What feature vectors? Tables Feature 1 Desks File cabinets Feature 2

  28. Voxels • Use voxel values as feature vector (shape descriptor) • Feature space has N3 dimensions (one dimension for each voxel) • d(A,B) = ||A-B||N • Example: = d , A-B A B N

  29. Voxels Image courtesy ofMisha Kazhdan • Can store distance transform (DT) in voxels • ||A-DT(B)||1 represents sum of distances from every point on surface of A to closest point on surface of B Surface Distance Transform

  30. Voxels Image courtesy ofMisha Kazhdan • Can store distance transform (DT) in voxels • ||A-DT(B)||1 represents sum of distances from every point on surface of A to closest point on surface of B Surface Distance Transform

  31. Voxels Image courtesy ofDaniel Keim, SIGMOD 1999 • Can build hierarchical search structure • e.g., interior nodes store MIV and MSV

  32. Voxel Retrieval Experiment • Test database is Viewpoint household collection1,890 models, 85 classes 153 dining chairs 25 livingroom chairs 16 beds 12 dining tables 8 chests 28 bottles 39 vases 36 end tables

  33. 1 0.8 0.6 Precision 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Recall Evaluation Metric • Precision-recall curves • Precision = retrieved_in_class / total_retrieved • Recall = retrieved_in_class / total_in_class

  34. 1 0.8 0.6 Precision 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Recall Evaluation Metric • Precision-recall curves • Precision = 0 / 0 • Recall = 0 / 5 1 2 3 4 5 6 Query 7 8 9 Ranked Matches

  35. 1 0.8 0.6 Precision 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Recall Evaluation Metric • Precision-recall curves • Precision = 1 / 1 • Recall = 1 / 5 1 2 3 4 5 6 Query 7 8 9 Ranked Matches

  36. 1 0.8 0.6 Precision 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Recall Evaluation Metric • Precision-recall curves • Precision = 2 / 3 • Recall = 2 / 5 1 2 3 4 5 6 Query 7 8 9 Ranked Matches

  37. 1 0.8 0.6 Precision 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Recall Evaluation Metric • Precision-recall curves • Precision = 3 / 5 • Recall = 3 / 5 1 2 3 4 5 6 Query 7 8 9 Ranked Matches

  38. 1 0.8 0.6 Precision 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Recall Evaluation Metric • Precision-recall curves • Precision = 4 / 7 • Recall = 4 / 5 1 2 3 4 5 6 Query 7 8 9 Ranked Matches

  39. 1 0.8 0.6 Precision 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Recall Evaluation Metric • Precision-recall curves • Precision = 5 / 9 • Recall = 5 / 5 1 2 3 4 5 6 Query 7 8 9 Ranked Matches

  40. Voxel Retrieval Experiment • Test database is Viewpoint household collection1,890 models, 85 classes 153 dining chairs 25 livingroom chairs 16 beds 12 dining tables 8 chests 28 bottles 39 vases 36 end tables

  41. 1 0.8 0.6 Precision 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Recall Voxel Retrieval Results Voxels Random

  42. Voxels • Properties • Discriminating • Insensitive to noise • Insensitive to topology • Robust to degeneracies • Quick to compute • Efficient to match? • Concise to store • Invariant to transforms

  43. Wavelets Image courtesy ofJacobs, Finkelstein, & Salesin • Define shape with wavelet coefficients 16,000 coefficients 400 coefficients 100 coefficients 20 coefficients

  44. Wavelets Jacobs, Finkelstein, & SalesinSIGGRAPH 95 • Descriptor 1: • Given an NxNxN grid, generate an NxNxN array of the wavelet coefficients for the standard Haar basis functions

  45. Wavelets Jacobs, Finkelstein, & SalesinSIGGRAPH 95 • Descriptor 1: • Given an NxNxN grid, generate an NxNxN array of the wavelet coefficients for the standard Haar basis functions • Descriptor 2: • Truncate: Find the m largest coefficients and set all others equal to zero • Quantize: Set the non-zero coefficients to +1 or –1 depending on their sign

  46. Jackie Chan Example • Original Image (256x256)

  47. Truncated And Quantized to 5000

  48. Truncated And Quantized to 1000

  49. Truncated And Quantized to 500

  50. Truncated 100

More Related