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

Transcription

1 Shape Descriptors I Thomas Funkhouser CS597D, Fall 2003 Princeton University 3D Representations Property Editing Display Analysis Retrieval Intuitive specification Yes No No No Guaranteed continuity Yes No No No Guaranteed validity Yes No No No Efficient boolean operations Yes No No No Efficient rendering Yes Yes No No Accurate Yes Yes?? Concise??? Yes Structure Yes Yes Yes Yes

2 Shape Analysis Problems! " " Query ) 2) 3) 4) Ranked Matches How can we find 3D models best matching a query? Shape #! $ %# & & 2

3 Shape '( (() = Shape Similarity * '+(,) - ( *$ '+(,).+, / '+(,)0.+0, '+(,)0',(+)+, '+(,)2',(") '+(") 3

4 Example Distance Functions 3 p ( a ) p i b i d( A, B) = d ~ ( A, B) = max min a a A b B b ( ) d( A, B) = max d ~ ( A, B), d ~ ( B, A) 4 '5 ( 6) i i Shape Matching " 7# "8 9 " 9 Are these the same chair? 4

5 Shape Retrieval 7# 8 & 4') Is this blue chair in the database? Shape Retrieval, Geometric Query Shape Analysis Shape Descriptor Database of 3D Models Shape Analysis Shape Index Shape Retrieval Similar Objects 5

6 Shape Retrieval 7# 8 3D Query Best Matches 3D Database Challenge * " :& # 3D Query Shape Descriptor 3D Database Best Matches 6

7 Challenge * " :& # 3D Query Shape Descriptor 3D Database Best Matches Challenge * " :& # 3D Query Shape Descriptor 3D Database Best Matches 7

8 Challenge * " :& # 3D Query Shape Descriptor 3D Database Best Matches Challenge * " :& # 3D Query Shape Descriptor 3D Database Best Matches 8

9 Challenge * " :& # / / / Different Transformations (translation, scale, rotation, mirror) Challenge * " :& # / / / Scanned Surface Image courtesy of Ramamoorthi et al. 9

10 Challenge * " :& # / / / Images courtesy of Viewpoint & Stanford Different Genus Different Tessellations Challenge * " :& # / / / No Bottom! Images courtesy of Utah & De Espona &*Q?@#A%! 0

11 Taxonomy of Shape Descriptors & -$ $ ; ( (8 (< + ((666 - Taxonomy of Shape Descriptors & -$ $ Images courtesy of Amenta & Osada ; ( (8 (< + ((666 -

12 Taxonomy of Shape Descriptors Image courtesy of De Espona & -$ $ ; ( (8 (< + ((666 -? Taxonomy of Shape Descriptors & -$ $ ; ( (8 (< + ((666 -? 2

13 Statistical Shape Descriptors + $ ;! =/ + / + $ 3 Feature Vectors Image courtesy of Mao Chen! $ Tables Feature Desks File cabinets Feature 2 3

14 Feature Vectors Image courtesy of Mao Chen " (( > ( Tables What feature vectors? Feature Desks File cabinets Feature 2 Voxels? ' ) * 7 ' ) '+(,)0@@+$,@@ * ( ) d =, A B A-B N 4

15 Voxels Image courtesy of Misha Kazhdan " '#) A +, Surface Distance Transform Voxels Image courtesy of Misha Kazhdan " '#) A +, Surface Distance Transform 5

16 Voxels Image courtesy of Daniel Keim, SIGMOD 999 " 66(!/;!; Voxel Retrieval Experiment ; 8 A(BC. (BD 53 dining chairs 25 livingroom chairs 6 beds 2 dining tables 8 chests 28 bottles 39 vases 36 end tables 6

17 Evaluation Metric - $ - 0 EEFE 0 EEFEE Precision Recall Evaluation Metric - $ - 0.F. 0.FD Precision Query Ranked Matches Recall 7

18 Evaluation Metric - $ - 0AFA 0AFD Precision Query Ranked Matches Recall Evaluation Metric - $ - 0GF7 0GFD Precision Query Ranked Matches Recall 8

19 Evaluation Metric - $ - 07FD 07FD Precision Query Ranked Matches Recall Evaluation Metric - $ - 0HFI 0HFD Precision Query Ranked Matches Recall 9

20 Evaluation Metric - $ - 0DFC 0DFD Precision Query Ranked Matches Recall Voxel Retrieval Experiment ; 8 A(BC. (BD 53 dining chairs 25 livingroom chairs 6 beds 2 dining tables 8 chests 28 bottles 39 vases 36 end tables 20

21 Voxel Retrieval Results 0.8 Voxels Random Precision Recall Voxels - # / / :& J " J / 2

22 Wavelets Image courtesy of Jacobs, Finkelstein, & Salesin # 88 6,000 coefficients 400 coefficients 00 coefficients 20 coefficients Wavelets Jacobs, Finkelstein, & Salesin SIGGRAPH 95 # A = ***( ***

23 Wavelets Jacobs, Finkelstein, & Salesin SIGGRAPH 95 # A = ***( *** 8 3 # G > :> $> 2AKA Jackie Chan Example 4/ 'GDLGDL) 23

24 Truncated And Quantized to 5000 Truncated And Quantized to

25 Truncated And Quantized to 500 Truncated 00 25

26 Truncated 50 Truncated 0 26

27 Torus Example Torus Truncated to

28 Torus Truncated to 000 Torus Truncated to

29 Torus Truncated to 00 Torus Truncated to 50 29

30 Wavelets Jacobs, Finkelstein, & Salesin SIGGRAPH 95 # A d( A, B) = w A i i, j, k [, j, k] B[ i, j k] i, j, k, 8 +M(9(&N,M(9(&N > 8 (9(& 8 ( 6 Wavelets Jacobs, Finkelstein, & Salesin SIGGRAPH 95 # G d( A, B) = [, j, k] B[ i, j, k] wi, j, k ( A i ) i, j, k: A( i, j, k )

31 Wavelets Jacobs, Finkelstein, & Salesin SIGGRAPH 95 - / / :& " # J / Moments # m pqr = x surface p y q z r dxdydz 3

32 Moments Retrieval Experiment ; 8 A(BC. (BD 53 dining chairs 25 livingroom chairs 6 beds 2 dining tables 8 chests 28 bottles 39 vases 36 end tables Moments Retrieval Results 0.8 Voxels Moments [Elad et al.] Random Precision Recall 32

33 Moments Retrieval Results 0.8 Voxels Moments [Elad et al.] Random Precision Recall Moments - / :& " J / J / J # 33

34 Extended Gaussian Image # 8 / 9 3D Model EGI EGI Retrieval Experiment ; 8 A(BC. (BD 53 dining chairs 25 livingroom chairs 6 beds 2 dining tables 8 chests 28 bottles 39 vases 36 end tables 34

35 EGI Retrieval Results Precision Voxels Moments [Elad et al.] EGI [Horn 84] Random Recall Extended Gaussian Images - / :& " J / J J / J # 35

36 Other Rotation-Dependent Descriptors Spherical Extent Functions (Vranic & Saupe, 2000) Shape Histograms (sectors) (Ankherst, 999) 36