Warping and Morphing. Ligang Liu Graphics&Geometric Computing Lab USTC

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1 Warping and Morphing Ligang Liu Graphics&Geometric Computing Lab USTC

2 Metamorphosis "transformation of a shape and its visual attributes" Intrinsic in our environment Deformations in nature Man made deformations Powerful concept Comparison of shapes

3 Shape Change In Nature Plant Growth Erosion Industrial object

4 Graphical Objects Components Shape geometric support (vertex coordinates ) Attributes visual properties (color, texture ) Examples Particle systems, drawings, images, surfaces, volumes, animations

5 Warping and Morphing Warping continuous family of transformations of a graphical object Source object, no target object Morphing warping between two graphical objects Source object, target object

6 Shape Transformations Warping: Unary Op Given Object A and F(t), find Object B F(t)? A Morphing: Binary Op Given Object A and Object B, find F(t) A? B

7 Warping Examples F 1 F 2

8 Morphing Example?

9 Morphing: Example 1

10 Morphing: Example 2

11 Applications Modeling Animation Special Effects Shape Analysis

12

13 Image Warping and Morphing Demo

14 Warping Pipeline Geometry deformation Attribute generation

15 Morphing Pipeline Morphing = warping + blending

16 Morphing Pipeline

17 Cross Dissolve Linear color interpolation

18 Feature Warping Shape warp + attribute blending

19 Aligning Features

20 Point features User Specifications: Warping

21 User Specifications: Warping Vector features

22 Simple Transformations Affine transformation Perspective transformation

23 Warping Problem Scattered point interpolation Given the values on some points, compute the value on arbitrary other point

24 Interpolation Methods Inverted distance method Shepard, 1965 Spline surface fitting Thin plate spline Finite element method

25 Radial Basis Functions

26 Radial Basis Functions

27 RBF Examples

28 Point features User Specifications: Morphing

29 Vector features User Specifications: Morphing

30 Partition User Specifications: Morphing

31 Morphing Example

32 Morphing Example

33 Discussions

34 Polygon Morphing

35 Problem? Source polygon shape Target polygon shape

36 Two Subproblems Correspondence problem find a correspondence between vertices of the two shapes Path problem find paths that the corresponding vertices traverse during the morphing process Dependent on each other

37 1. Correspondence Problem Matching Problem

38 Finding Correspondence Finding similarity function between local features of the two shapes Dynamic programming

39 Physically Based Method Stretching work Bending work Sederberg et al. 1992

40 Fuzzy Approach Zhang 1996

41 Curve Matching Cohen et al. 1997

42 Feature Based Method Hui and Li 1998

43 Approximated Skeleton Mortara et al. 2001

44 Curve Aligning Sebastian et al. 2003

45 Perceptually Based Method Liu et al. 2004

46 Matching Results

47 2. Path Problem

48 Linear Interpolation Simple and easy Drawbacks Shrinkage

49 Unnatural Results in Linear Interpolation

50 Intrinsic Approach Intrinsic variables edge lengths turning angles Sederberg et al. 1993

51 Fourier Approach Chen et al. 2001

52 Wavelet Approach Wavelet decomposition Zhang et al. 2000

53 Warp Guided Method Warp + linear interpolation Camel et al. 1997

54 Scale Invariant Intrinsic Approach Scaling invariant intrinsic variables Ren et al Li 1 e i 1 p i L θ i i p θ i 1 e i+1 + i L e i + 1 i+1 p i+2 p i 1 r = L L i i i 1

55 Interior Based Approach Based on compatible triangulation [Gotsman and Surazhsky, ] As rigid as possible [Alexa et al. 2000]

56 Compatible Triangulation [Aronov et al. 1994]

57 Examples

58 Star Skeleton Representation [Shapira et al. 1995]

59 Star Shaped Polygon Decomposition Star shaped, star points

60 Compatible Star Decompositions

61 Morphing Stick Figures [Surazhsky et al. 2001]

62 Morphing between Different Topologies Liu et al. 2005

63 More Surface reconstruction from slices

64 Implicit function from an X shape Implicit Approaches

65 Discussions