large mesh deformation using the volumetric graph laplacian kun zhou jin huang* john snyder^ xinguo...
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![Page 1: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/1.jpg)
Large Mesh Deformation Using the
Volumetric Graph Laplacian
Large Mesh Deformation Using the
Volumetric Graph Laplacian
Kun Zhou Jin Huang* John Snyder^ Xinguo Liu
Hujun Bao* Baining Guo Heung-Yeung Shum
Microsoft Research Asia
*Zhejiang University
^Microsoft Research
Kun Zhou Jin Huang* John Snyder^ Xinguo Liu
Hujun Bao* Baining Guo Heung-Yeung Shum
Microsoft Research Asia
*Zhejiang University
^Microsoft Research
![Page 2: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/2.jpg)
Mesh DeformationMesh Deformation
• Smooth geometry
– Freeform deformation [Barr84, Singh98, Bendels03]
– Energy minimization [Welch94, Taubin95, Botsch04]
• Detailed geometry
– Multi-resolution editing [Zorin97, Kobbelt98, Guskov99]
– Differential domain methods:
• Poisson mesh editing [Yu04]
• Laplacian surface editing [Sorkine04, Lipman05]
![Page 3: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/3.jpg)
Large Mesh DeformationLarge Mesh Deformation
• Challenge to existing techniques
– Local self-intersection, unnatural volume change
Bending Twisting
![Page 4: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/4.jpg)
Large Mesh DeformationLarge Mesh Deformation
• Challenge to existing techniques
– Local self-intersection, unnatural volume change
Poisson Mesh Editing VGL
![Page 5: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/5.jpg)
Large Mesh DeformationLarge Mesh Deformation
• Challenge to existing techniques
– Local self-intersection, unnatural volume change
Poisson Mesh Editing VGL
![Page 6: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/6.jpg)
Large Deformation: Why Difficult?Large Deformation: Why Difficult?
• Differential domain methods [Yu04, Sorkine04]
Uniform error distribution using least-squares optimization
Only surface details, volume ignored
• Displacement volumes [Botsch03]
Volumetric constraints
Iterative relaxation produces artifacts
Solution: Volumetric Constraints &Least-Squares Optimization
![Page 7: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/7.jpg)
Poisson Mesh EditingPoisson Mesh Editing
Step 1: Specify control curve Step 2: Edit control curve
F
F’
![Page 8: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/8.jpg)
Poisson Mesh EditingPoisson Mesh Editing
Step 3: Propagate local frame transformations
Step 4: Solve Poisson equation
![Page 9: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/9.jpg)
Surface Details & LaplacianSurface Details & Laplacian
N(i)j
jjiiiM pwp)(pL ,-
![Page 10: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/10.jpg)
Surface Details & LaplacianSurface Details & Laplacian
iiiM
ppL
i
2)(min
![Page 11: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/11.jpg)
Surface Details & LaplacianSurface Details & Laplacian
iiiM
ppL
i
2)(min
![Page 12: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/12.jpg)
Volumetric Details & LaplacianVolumetric Details & Laplacian
N(i)j
jjiiiG pwp)(pL ,-
![Page 13: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/13.jpg)
Volumetric Details & LaplacianVolumetric Details & Laplacian
iiiG
ppL
i
2)(min
![Page 14: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/14.jpg)
Quadric Energy FunctionQuadric Energy Function
k
kkGj
jji
iiM δpLqppL222
)()(
Surface Details Volumetric DetailsPosition Constraints
iiiGiM pLpL )( )(
jj qp
kkG pL )(
bxA bAx 1
![Page 15: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/15.jpg)
1. Construct the volumetric graph
2. Compute Laplacian coordinates
3. Compute and apply local transformation
4. Solve the sparse linear system
Deformation Using VGLDeformation Using VGL
kkk δTδ iii T
![Page 16: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/16.jpg)
Volumetric Graph ConstructionVolumetric Graph Construction
![Page 17: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/17.jpg)
Volumetric Graph ConstructionVolumetric Graph Construction
• Construct an inner shell
![Page 18: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/18.jpg)
Volumetric Graph ConstructionVolumetric Graph Construction
• Embed both the mesh and shell in a lattice
![Page 19: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/19.jpg)
Volumetric Graph ConstructionVolumetric Graph Construction
• Build edge connections
![Page 20: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/20.jpg)
Volumetric Graph ConstructionVolumetric Graph Construction
• Simplify and smooth the graph
Not Tetrahedral Mesh
![Page 21: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/21.jpg)
Deformation ComparisonDeformation Comparison
Laplacian surface[Sorkine04]
Poisson mesh [Yu04]
VGL
![Page 22: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/22.jpg)
Poisson mesh [Yu04]
Laplacian surface[Sorkine04]
Deformation ComparisonDeformation Comparison
VGL
![Page 23: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/23.jpg)
Deformation ComparisonDeformation Comparison
Original model Poisson mesh VGL
![Page 24: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/24.jpg)
Deformation InterfaceDeformation Interface
• 3D space manipulation [Yu04]
– Tedious and require artistic skill
• 2D sketch-based interface
– Modeling: Teddy [Igarashi99]
– Editing: [Zelinka04, Kho05, Nealen05]
“Teddy-like” deformation:intuitive and easy to use
![Page 25: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/25.jpg)
2D Sketch-based Deformation2D Sketch-based Deformation
![Page 26: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/26.jpg)
Deformation RetargetingDeformation Retargeting
![Page 27: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/27.jpg)
Deformation RetargetingDeformation Retargeting
![Page 28: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/28.jpg)
ResultsResults
![Page 29: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/29.jpg)
ResultsResults
![Page 30: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/30.jpg)
ResultsResults
![Page 31: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/31.jpg)
ResultsResults
![Page 32: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/32.jpg)
ResultsResults
![Page 33: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/33.jpg)
ConclusionConclusion
• Volumetric graph Laplacian (VGL)
– Volumetric constraints
– Least squares minimization
– No tetrahedral mesh construction
• 2D sketch-based deformation system
– “Teddy-like” deformation system
– Cartoon deformation retargeting
![Page 34: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/34.jpg)
Future WorkFuture Work
• Anchor-based deformation
• Dynamic connectivity
• Automatic contour tracking
![Page 35: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/35.jpg)
AcknowledgementAcknowledgement
• Cartoons from Disney Feature Animation and Dongyu Cao
• 3D models from Stanford, MIT, Cyberware
• Xin Sun, Jianwei Han
• Steve Lin, Bo Zhang
• NSFC and 973 Program of China
![Page 36: Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft](https://reader038.vdocuments.us/reader038/viewer/2022103111/5514782a550346b0158b53b2/html5/thumbnails/36.jpg)
Thank You !Thank You !