Robust Nonrigid Registration by Convex

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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

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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

Optimize by gradient descent
Easily stuck at bad local minima (GMDS)

Optimization Let and be points densely sampled over and
Optimize labeling ( is a set of m labels) (GMDS) (Discrete MRF) Continuous Markov random field (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 disambiguates intrinsic symmetry

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
[Kim et al. 2011] Random forest
[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/

Robust Nonrigid Registration by Convex

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