Subspace Gradient Domain Mesh Deformation

Subspace Gradient Domain Mesh Deformation Presented by Xinguo Liu( 刘新国 ) State Key Lab of CAD&CG, Zhejiang Univ. To Appear in ACM SIGGRAPH 2006 Jin Huang, Xiaohan Shi, Xinguo Liu, Kun Zhou,Li-Yi Wei, Shang-Hua Teng, Hujun Bao, Baining Guo, Heung-Yeung Shum CAD&CG MSRA Boston Univ.

Brief Introduction to Some Sample Works

Sample works High quality real time rendering 3 SIGGRAPH (2001, 2003,2006) 1 IEEE TVCG (2004) 1 EGSR (2004) Geometric Processing 2 SIGGRAPH (2005,2006) 1 IEEE CVPR (2003) 1 ACM SPM (2005) 1 EG Point Based Graphics (2005) 1 Computer & Graphics (2006) 1 J. CAVW (2006) 1 Pacific Graphics (2006) 3

Rendering Synthesizing Bidirectional Texture Functions for Real-world Surfaces. [ACM SIGGRAPH 2001] Xinguo Liu, et al. Biscale Radiance Transfer [SIGGRAPH 2003] Peter-Pike Sloan, Xinguo Liu, et al. Synthesis and Rendering of Bidirectional Texture Functions on Arbitrary Surfaces. [IEEE TVCG 10(3), 2004] Xinguo Liu et al. 4

Rendering All-Frequency Precomputed Radiance Transfer for Glossy Objects [Eurographics Symposium on Rendering 2004] Xinguo Liu et al. Real-time Soft Shadows in Dynamic Scenes using Spherical Harmonic Exponentiation. [SIGGRAPH 2006] Zhong Ren, Rui Wang, John Snyder, Kun Zhou, Xinguo Liu, et al. 5

Biscale Radiance Transfer [SIGGRAPH 2003] Lighting 6

Biscale Radiance Transfer [SIGGRAPH 2003] 7

Biscale Radiance Transfer [SIGGRAPH 2003] 8

All-Frequency Precomputed Radiance Transfer for Glossy Objects [GSR04] 9

All-Frequency Precomputed Radiance Transfer for Glossy Objects [EGSR04] 10

Real-time soft shadows in dynamic scenes using spherical harmonic exponentiation [SIGGRAPH 2006] Video 11

Geometric Preprocessing Directional Histogram Model for Three- Dimensional Shape Similarity. [IEEE CVPR 2003] Xinguo Liu, et al. Computing Variation Modes for Point Set Surfaces. [Eurographics Symposium on Point-Based Graphics 2005] Lanfang Miao, Jin Huang, Xinguo Liu et al. 12

Geometric Processing Large mesh deformation using the volumetric graph Laplacian [SIGGRAPH 2005] Kun Zhou, Jin Huang, John Snyder, Xinguo Liu, et al. Clustering method for fast deformation with constraints. [ACM SPM 2005] Jin Huang, Xinguo Liu, et al. 13

Directional Histogram Model for Three-Dimensional Shape Similarity [IEEE CVPR 2003] 14

Directional Histogram Model for Three-Dimensional Shape Similarity [IEEE CVPR 2003] 15

Large mesh deformation using the volumetric graph Laplacian [SIGGRAPH 2005] 16

An Efficient Large Deformation Method using Domain Decomposition [Computer & Graphics, 2006] 17

An Efficient Large Deformation Method using Domain Decomposition [Computer & Graphics, 2006] 18

Deformation Orginal twisting bending 20

Mesh Deformation Scanned Models Preserve surface details 21

Mesh Deformation Scanned Model Dense samples High quality Arbitrarily shape In triangular meshes 22

Related Work Mesh Deformation Traditional method (blend, interpolation) Skeleton skinning FFD: Free form deformation Multiresolution mesh editing Gradient domain method (linear least square) Poisson Mesh Editing Laplacian Mesh Editing Volumetric Graph Laplacian 23

Gradient Domain Method Differential coordinates (Laplacian) 24

Gradient Domain Method (Cont.) Differential coordinates in local frame get the local transformation through intepolation/diffusing/fitting... Linear least square reconstruction 25

Gradient Domain Method Local Transforms User rotate some handles Other vertices obtain their transformation by Transformation Propagation Harmonic Guidance Field Linear Rotation Invariant Need users input 26

Gradient Domain Method Local transformations must be consistent with deformation. 27

Our Method Non-linear least square energy Get rid of transformation (of user input) Nontrivial to handle useful constraints skeleton projection volume Subspace solver Stable, fast convergence 28

Our Method (Cont.) Video 29

Encoding Differential Coordinates We need the consistent direction of differential coordinates. Express it by neighbor vertices: 30

Encoding Differential Coordinates (Cont.) Calculate the direction: Rescale back to original length: 31

Non-linear Linear Square For preserving surface detail (differential coordinates), we have: Add soft position constraints: 32

Quasi-Linear Object energy: Linear: Non-linear: Quasi-linear: 33

Inexact Gauss-Newton Gauss-Newton Inexact Gauss-Newton 34

Video Walking Dinosaur 35

Constraints Skeleton Soft Projection Hard Volume Hard 36

Skeleton Constraints Extremely useful when deforming articulated figures 37

Skeleton Constraints (Cont.) Create skeleton by stroking 38

Skeleton Constraints (Cont.) Video 39

Skeleton Constraints (Cont.) Keeping straightness and length: Reform to... Make it quasi-linear: 40

Projection Constraints Manipulate the object interactively in only one view 41

Projection Constraints Video 42

Volume Constraints Keep/control the object's volume exactly 43

Volume Constraints Video 44

Solve Hard Constraints Projection and volume constraints are hard constrains. Apply Lagrange multipliers at each iteration: 45

Instability Video 46

Deformation Space The deformation space can be spanned by a lower dimensional linear space. low frequency deformation is what we want. high frequency deformation means surface detail changes 47

Deformation Space (Cont.) Subspace can be constructed using the eigen vectors of the Laplacian matrix SVD is costly for models with large number of vertices. 48

Deformation Space (Cont.) Create a coarse control mesh Using 3D mean value interpolation 49

Subspace Solver Can be viewed as a simple variable replacement: Then 50

Subspace Solver Fast and stable Much better condition number. Smooth out non-linear factor. 51

Subspace Solver Video 52

Objects with multiple components Components are binded together in the subspace 53

Multi-part Object Video 54

Comparison with FFD FFD Ours 55

More Results 56

More Results 57

Future Work Subspace construction Better methods, e.g. based on user specified deformation examples Local support basis for subspace lower cost for more DOFs local surface editing Multigrid hierachical constraints remove the residua for better results 58

Thanks! Xinguo Liu, xgliu@cad.zju.edu.cn http://www.cad.zju.edu.cn/home/xgliu