Report

Tracking Surfaces with Evolving Topology Morten Bojsen-Hansen IST Austria Hao Li Columbia University Chris Wojtan IST Austria Introduction • Implicit surfaces are extremely popular for representing time-evolving surfaces Fluid simulation Morphing Introduction • No correspondence information ? • Extracting correspondences between timevarying meshes • Input: – time-varying meshes frames • Output – Correspondences between mesh frames The correspondences are useful Basic idea Mesh M frame1 Deform M to frame n; n=n+1; M=M’ deformed mesh M’; Save M’; Basic idea • Let just consider two successive frames – non-rigid alignment – Topological change – Record correspondence information Frame t (M) Frame t+1 (N) alignment Topological change Non-Rigid Alignment • Coarse Non-Linear Alignment • Fine-Scale Linear Alignment Hao Li Columbia University • Robust single-view geometry and motion reconstruction,2009,tog 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 Non-Rigid Alignment • M->N (Coarse Non-Linear Alignment) Non-Rigid Alignment • M->N (Fine-Scale Linear Alignment) Basic idea • Let just consider two successive frames – non-rigid alignment – Topological change – Record correspondence information Frame t (M) Frame t+1 (N) alignment Topological change Topological Change Chris Wojtan IST Austria • Deforming meshes that split and merge,2009,TOG 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 Topological Change • Deforming meshes that split and merge,2009,TOG Basic idea • Let just consider two successive frames – non-rigid alignment – Topological change – Record correspondence information Frame t (M) Frame t+1 (N) alignment Topological change 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 • • • • • • • • • • • • • • • • Full Pipeline Mesh M = LoadTargetMesh(S1) ImproveMesh(M) for frame n = 2 -> N do { LoadTargetMesh(Sn) CoarseNonRigidAlignment(M, Sn) FineLinearAlignment(M, Sn) non-rigid registration ImproveMesh(M) Ф(M) := CalculateSignedDistance(M) ConstrainTopology(M; фM ) ф (Sn) := alculateSignedDistance(Sn) ConstrainTopology(M; ф (Sn)) ImproveMesh(M) SaveEventListToDisk(n) SaveMeshToDisk(M) } changing surface mesh topology Applications • Color Applications • Morph Applications • Displacement Maps Applications • Wave simulation Applications • Performance Capture Evolution Evolution Time 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 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 generated – no template 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 Done • Thanks! triangle mesh improvement Edges become too long split them in half by adding a new vertex at the midpoint 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 Topological Change • Marching cube http://www.cs.carleton.edu/cs_comp s/0405/shape/marching_cubes.html back