Robust Nonrigid Registration by Convex Optimization

Robust Nonrigid Registration by Convex Optimization

Robust Nonrigid Registration by Convex Optimization Qifeng Chen Stanford University Vladlen Koltun Intel Labs Nonrigid Registration

Intra-subject registration Nonrigid Registration Inter-subject registration Uses of Nonrigid Registration Loop

closure in dynamic reconstruction Shape analysis Propagation of material properties

across 3D models Surface completion Prior work Intrinsic descriptors

Heat kernel signature [Sun et al. 2009] Wave kernel signature [Aubry et al. 2011] Global point signature [Rustamov 2007] Spectral descriptors [Litman et al. 2014] Optimal descriptors [Windheuser et al. 2014]

Prior work Generalized multidimensional scaling (GMDS) [Bronstein et al. 2006] Given two surfaces Compute mapping Minimize highly nonconvex objective (GMDS

) Optimize by gradient descent Easily stuck at bad local minima Optimization Let

and be points densely sampled over and Optimize labeling ( is a set of m labels) Continuous Markov random field (MRF) (GMDS

) (Discrete MRF) Optimization (Discrete MRF) (Linear program) where

Optimization (Linear program) (Dual LP) Optimization (Linear program) (Dual LP)

TRW-S [Kolmogorov 2006] Objective Penalty Objective where symmetry

disambiguates intrinsic Implementation Preprocessing Poisson reconstruction for geodesic distance farthest point sampling Global optimization

sample hundreds of points random permutation of the nodes for best solution Upsampling and refinement (optional) upsample mapping to thousands of

correspondences refine the correspondences by fusion moves FAUST Dataset FAUST [Bogo et al. 2014] Results Our

approach outperforms a large body of prior work by a factor of 3 Results Results Blended intrinsic maps Random forest

[Kim et al. 2011] [Rodola et al. 2014] Our approach Summary Simple but robust no descriptors

convex optimization outperforms a large body of prior work by a multiplicative factor Future work partial surface registration joint analysis of non-isometric shapes

Questions? Matlab, C++ code, and data http://www.stanford.edu/~cqf/ convex/

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