CS 468 Data-driven Shape Analysis. Shape Descriptors

Transcription

1 CS 468 Data-driven Shape Analysis Shape Descriptors April 1, 2014

2 What Is A Shape Descriptor? Shapes Shape Descriptor F1=[f1, f2,.., fn] F2=[f1, f2,.., fn] F3=[f1, f2,.., fn]

3 What Is A Shape Descriptor? Shapes Shape Descriptor F1=[f1, f2,.., fn] F2=[f1, f2,.., fn] F3=[f1, f2,.., fn] Hopefully F2 F1 and F2 F3

4 What Is A Shape Descriptor? Shapes Shape Descriptor F1=[f1, f2,.., fn] What Is A Good SD? F2=[f1, f2,.., fn] F3=[f1, f2,.., fn] Hopefully F2 F1 and F2 F3

5 What Is A Good SD? Desired Properties Automatic Discriminative Robust w.r.t. noise (e.g. due to scanning) Cheap to compute Easy to compare (e.g. few features, L2 distance) Invariant to transformations, e.g.: - Rotation - Translation - Scale

6 What Is A Good SD? Desired Properties Automatic Discriminative Robust w.r.t. noise (e.g. due to scanning) Cheap to compute Easy to compare (e.g. few features, L2 distance) Invariant to transformations, e.g.: - Rotation - Translation - Scale Toy Example: per-vertex positions, # i.e. [x1, y1, z1, x2, y2, z2,, xn, yn, zn]

7 What Is A Good SD? Desired Properties Automatic Discriminative Robust w.r.t. noise (e.g. due to scanning) Cheap to compute Easy to compare (e.g. few features, L2 distance) Invariant to transformations, e.g.: Rotation Translation Scale Toy Example: per-vertex positions, # i.e. [x1, y1, z1, x2, y2, z2,, xn, yn, zn]

8 What Is A Good SD? Desired Properties Automatic Discriminative Robust w.r.t. noise (e.g. due to scanning) Cheap to compute Easy to compare (e.g. few features, L2 distance) Invariant to transformations, e.g.: - Rotation - Translation - Scale Toy Example: shape diameter,# i.e. maximal distance between any two points: [d]

9 What Is A Good SD? Desired Properties Automatic Discriminative Robust w.r.t. noise (e.g. due to scanning) Cheap to compute Easy to compare (e.g. few features, L2 distance) Invariant to transformations, e.g.: Rotation Translation Scale Toy Example: shape diameter,# i.e. maximal distance between any two points: [d]

10 What Is A Good SD? Desired Properties Automatic Discriminative Robust w.r.t. noise (e.g. due to scanning) Cheap to compute Easy to compare (e.g. few features, L2 distance) Invariant to transformations, e.g.: - Rotation - Translation - Scale How about looking at statistics # over all pairs of points?

11 Shape Descriptors Shape Descriptors Shape Distributions (D2) Spin Images Lightfield Descriptor Intrinsic Methods Applications Retrieval Classification Exploration

12 Shape Distributions (D2) D2 Probability Density Distance Between a Pair

13 Shape Distributions (D2) Guess: A Line Segment? D2 Probability Density Distance Between a Pair

14 Shape Distributions (D2) Guess: A Line Segment? D2 Probability Density Distance Between a Pair

15 Shape Distributions (D2) Guess: A Circle? D2 Probability Density Distance Between a Pair

16 Shape Distributions (D2) Guess: A Circle? D2 Probability Density Distance Between a Pair

17 Shape Distributions (D2) Guess: A Car? :) D2 Probability Density Distance Between a Pair

18 Shape Distributions (D2) Distributions for 6 different cars D2 Probability Density Distance Between a Pair

19 Shape Distributions (D2) Some Other Examples D2

20 Good SD? Desired Properties Automatic Discriminative Robust w.r.t. noise (e.g. due to scanning) Cheap to compute Easy to compare (e.g. few features, L2 distance) Invariant to transformations, e.g.: - Rotation - Translation - Scale

21 Evaluation Metrics Examples Precision/Recall Confusion Mtx Artificial noise

22 Evaluation Metrics Examples Precision/Recall Confusion Mtx Artificial noise TP FN FP TN Want all Filled Dots to be# retrieved by the Ellipse

23 Evaluation Metrics Examples Precision/Recall Confusion Mtx Artificial noise TP FN FP TN Want all Filled Dots to be# retrieved by the Ellipse For N retrieved results:# Precision = TP / (TP + FP) Recall = TP / (TP + FN)

24 Evaluation Metrics Examples Precision/Recall Confusion Mtx Artificial noise TP FN FP TN Want all Filled Dots to be# retrieved by the Ellipse For N retrieved results:# Precision = TP / (TP + FP) Recall = TP / (TP + FN)

25 Evaluation Metrics Examples Precision/Recall Confusion Mtx Artificial noise

26 Evaluation Metrics For example: Examples Precision/Recall Confusion Mtx Artificial noise What would you choose?

27 Shape Descriptors Shape Descriptors Shape Distributions (D2) Spin Images Lightfield Descriptor Intrinsic Methods Applications Retrieval Classification Exploration

28 α - radial dist. β - elevation Spin Images

29 Spin Images Works for partial# matching too! Large Support Small Support

30 Spin Images

31 Spin Images We will discuss the details of shape matching later

32 Good SD? Desired Properties Automatic Discriminative Robust w.r.t. noise (e.g. due to scanning) Cheap to compute Easy to compare (e.g. few features, L2 distance) Invariant to transformations, e.g.: - Rotation - Translation - Scale

33 Good SD? Desired Properties Automatic Discriminative Robust w.r.t. noise (e.g. due to scanning) Cheap to compute Easy to compare (e.g. few features, L2 distance) Invariant to transformations, e.g.: - Rotation - Translation - Scale NOTE: there is a trick here Still expensive:# requires shape matching

34 Shape Descriptors Shape Descriptors Shape Distributions (D2) Spin Images Lightfield Descriptor Intrinsic Methods Applications Retrieval Classification Exploration

35 Lightfield Descriptor Image distances under the best rotation

36 Lightfield Descriptor

37 Good SD? Desired Properties Automatic Discriminative Robust w.r.t. noise (e.g. due to scanning) Cheap to compute Easy to compare (e.g. few features, L2 distance) Invariant to transformations, e.g.: - Rotation - Translation - Scale

38 References Shape Distributions. R. Osada, T. Funkhouser, B. Chazelle, D. Dobkin. Trans. on Graphics 2002 Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors. M. Kazhdan, T. Funkhouser, S. Rusinkiewicz. SGP 2004 Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes. A. Johnson, M. Hebert. Trans. PAMI 1999 On Visual Similarity Based 3D Model Retrieval. D-Y. Chen, X-P. Tian, Y-T. Shen, and M. Ouhyoung. Eurographics 2003