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Tracking Surfaces with Evolving Topology

Tracking Surfaces with Evolving Topology. Morten Bojsen-Hansen IST Austria. Chris Wojtan IST Austria. Hao Li Columbia University. Introduction. I mplicit surfaces are extremely popular for representing time-evolving surfaces. Fluid simulation. Morphing. Introduction.

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Tracking Surfaces with Evolving Topology

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  1. Tracking Surfaces with Evolving Topology MortenBojsen-Hansen IST Austria Chris Wojtan IST Austria Hao Li Columbia University

  2. Introduction • Implicit surfaces are extremely popular for representing time-evolving surfaces • Fluid simulation • Morphing

  3. Introduction • No correspondence information • Extracting correspondences between time-varying meshes ?

  4. Input: • time-varying meshes frames • Output • Correspondences between mesh frames

  5. The correspondences are useful

  6. Basic idea frame1 Mesh M Deform M to frame n; n=n+1; M=M’ deformed mesh M’; Save M’;

  7. Basic idea • Let just consider two successive frames • non-rigid alignment • Topological change • Record correspondence information alignment • Topological change Frame t (M) Frame t+1 (N)

  8. Non-Rigid Alignment • Coarse Non-Linear Alignment • Fine-Scale Linear Alignment • Robust single-view geometry and motion reconstruction,2009,tog Hao Li Columbia University

  9. Non-Rigid Alignment • M->N • 1 deformation graph G • constructed by uniformly sub-sampling M • 2 Find affine an affine transformation (Ai; bi) for each graph node. • 3 the motion of Xi is defined as a linear combination of the computed graph node transformations

  10. Non-Rigid Alignment • M->N (Coarse Non-Linear Alignment)

  11. Non-Rigid Alignment • M->N (Fine-Scale Linear Alignment)

  12. Basic idea • Let just consider two successive frames • non-rigid alignment • Topological change • Record correspondence information alignment • Topological change Frame t (M) Frame t+1 (N)

  13. Topological Change • Deforming meshes that split and merge,2009,TOG Chris Wojtan IST Austria

  14. Topological Change • For mesh M • volumetric grid • Compute signed distance function • topologically complex cell • the intersection of M with the cell is more complex than what can be represented by a marching cubes reconstruction inside the cell • triangles of M inside such cells will be replaced by marching cubes triangles

  15. Topological Change • Deforming meshes that split and merge,2009,TOG

  16. Basic idea • Let just consider two successive frames • non-rigid alignment • Topological change • Record correspondence information alignment • Topological change Frame t (M) Frame t+1 (N)

  17. Record correspondence information • A Few vertices which were created or destroyed due to topology • event list • Adding new geometry: propagate information from the vertices on the boundary • Deleting vertices: march inward from the boundary of the deleted vertices and propagate information

  18. Full Pipeline • Mesh M = LoadTargetMesh(S1) • ImproveMesh(M) • for frame n = 2 -> N do • { • LoadTargetMesh(Sn) • ImproveMesh(M) • ImproveMesh(M) • SaveEventListToDisk(n) • SaveMeshToDisk(M) • } CoarseNonRigidAlignment(M, Sn) FineLinearAlignment(M, Sn) non-rigid registration Ф(M) := CalculateSignedDistance(M) ConstrainTopology(M; фM ) ф (Sn) := alculateSignedDistance(Sn) ConstrainTopology(M; ф (Sn)) changing surface mesh topology

  19. Applications • Color

  20. Applications • Morph

  21. Applications • Displacement Maps

  22. Applications • Wave simulation

  23. Applications • Performance Capture

  24. Evolution

  25. Evolution

  26. Time

  27. contributions • the first comprehensive framework for tracking a series of closed surfaces where topology can change • greatly enhance existing datasets with valuable temporal correspondence information. • a novel topology-aware wave simulationalgorithm for enhancing the appearance of existing liquid simulations while significantly reducing the noise present in similar approaches. • extracts surface information from input data alone, • no assumptions about how the data was generated • no template

  28. limitations • unable to track surfaces invariant under our energy functions; a surface with no significant geometric features (like a rotating sphere) will not be tracked accurately • limited to closed manifold surfaces

  29. Done • Thanks!

  30. triangle mesh improvement • Edges become too long • split them in half by adding a new vertex at the midpoint

  31. triangle mesh improvement • edges become too short; triangle interior angles become too small; dihedral angles become too small • edge collapse by replacing an edge with a single vertex Back

  32. Topological Change • Marching cube http://www.cs.carleton.edu/cs_comps/0405/shape/marching_cubes.html back

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