Tracking Surfaces with Evolving Topology

Tracking Surfaces with Evolving TopologyMorten Bojsen-HansenIST AustriaHao Li Columbia UniversityChris WojtanIST Austria

Topological Change

Marching cubehttp://www.cs.carleton.edu/cs_comps/0405/shape/marching_cubes.htmlback split and merge 32IntroductionNo correspondence information

Extracting correspondences between time-varying meshes

?Input:time-varying meshes framesOutputCorrespondences between mesh frames

The correspondences are useful

5Basic ideaframe1Mesh MDeform M to frame n;n=n+1;deformed mesh M;Save M;M=MShow a sequence of fluid simulation, and animate them

Frame1 template, Frame2 Frame3

6Basic ideaLet just consider two successive framesnon-rigid alignmentTopological changeRecord correspondence information

Frame t (M)Frame t+1 (N)

alignment

Topological change1.

two shapes to correspond in the presence of topology changesand find the most appropriate mapping between consecutive pairsof input surfaces.

non-rigid alignment (dont consider topology change)

7

Non-Rigid AlignmentHao Li Columbia UniversityCoarse Non-Linear AlignmentFine-Scale Linear Alignment

Robust single-view geometry and motion reconstruction,2009,togNon-Rigid AlignmentM->N1 deformation graph Gconstructed by uniformly sub-sampling M2 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 transformations9Non-Rigid AlignmentM->N (Coarse Non-Linear Alignment)

Non-Rigid AlignmentM->N (Fine-Scale Linear Alignment)

11Basic ideaLet just consider two successive framesnon-rigid alignmentTopological changeRecord correspondence informationFrame t (M)Frame t+1 (N)

alignment

Topological changetwo shapes to correspond in the presence of topology changesand find the most appropriate mapping between consecutive pairsof input surfaces.

non-rigid alignment (dont consider topology change)

12Topological ChangeDeforming meshes that split and merge,2009,TOG

Chris WojtanIST AustriaTopological ChangeFor mesh Mvolumetric gridCompute signed distance functiontopologically complex cellthe intersection of M with the cell is more complex than what can be represented by a marching cubes reconstruction inside the celltriangles of M inside such cells will be replaced by marching cubes triangles Deforming meshes that split and merge

14Topological Change

Deforming meshes that split and merge,2009,TOG

Basic ideaLet just consider two successive framesnon-rigid alignmentTopological changeRecord correspondence informationFrame t (M)Frame t+1 (N)

alignment

Topological changetwo shapes to correspond in the presence of topology changesand find the most appropriate mapping between consecutive pairsof input surfaces.

non-rigid alignment (dont consider topology change)

16Record correspondence informationA Few vertices which were created or destroyed due to topology event listAdding new geometry: propagate information from the vertices on the boundaryDeleting vertices: march inward from the boundary of the deleted vertices and propagate informationevent list17Full PipelineMesh M = LoadTargetMesh(S1)ImproveMesh(M)for frame n = 2 -> N do{LoadTargetMesh(Sn) ImproveMesh(M) ImproveMesh(M)SaveEventListToDisk(n)SaveMeshToDisk(M)}non-rigid registrationchanging surface mesh topologyCoarseNonRigidAlignment(M, Sn)FineLinearAlignment(M, Sn)(M) := CalculateSignedDistance(M)ConstrainTopology(M; M ) (Sn) := alculateSignedDistance(Sn)ConstrainTopology(M; (Sn))

Mesh improvement ( non-rigid registration, topology mesh )

event list

18ApplicationsColor

ApplicationsMorph

Distance field20ApplicationsDisplacement Maps

ApplicationsWave simulation

ApplicationsPerformance Capture

Evolution

Evolution

Time

contributionsthe 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 simulation algorithm 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 generatedno template

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 surfaceslimitations28DoneThanks!triangle mesh improvementedges become too short; triangle interior angles become too small; dihedral angles become too smalledge collapse by replacing an edge with a single vertex

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