Zorah Lähner

Zorah Lähner

Assistant Professor (tenure track), Geometry in Machine Learning Group

Efficient Globally Optimal 2D-to-3D Deformable Shape Matching

Published in Conference on Computer Vision and Pattern Recognition (CVPR), 2016

Zorah Lähner, Emanuele Rodolà, Frank R. Schmidt, Michael M. Bronstein, Daniel Cremers

Teaser Image

Abstract

We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D query shape as well as a 3D target shape and the output is a continuous matching curve represented as a closed contour on the 3D shape. We cast the problem as finding the shortest circular path on the product 3-manifold of the two shapes. We prove that the optimal matching can be computed in polynomial time with a (worst-case) complexity of O(mn^2 log(n)), where m and n denote the number of vertices on the 2D and the 3D shape respectively. Quantitative evaluation confirms that the method provides excellent results for sketch-based deformable 3D shape retrieval.

Resources

[pdf] [arxiv] [github]

Data

(dataset parameter tuning, 2.7GB) based on MPI FAUST

(dataset retrieval, 2.9GB) based on TOSCA high-res

(retrieval matchings, 267kB)

Additional Code

(matching code, 281MB) Matlab/C++ Code, example with precomputed data reproducing one matching

(retrieval code, 270kB) Matlab Code, code outline to run retrieval on a new data set, needs matching code

Bibtex

@InProceedings{laehner2016elastic2D3D,
  author       = {Zorah L\"ahner and Emanuele Rodol\`a and Frank R. Schmidt and Michael M. Bronstein and Daniel Cremers},
  title        = { Efficient Globally Optimal 2D-to-3D Deformable Shape Matching },
  booktitle    = { Proc. of IEEE Conference on Computer Vision and Pattern Recognition (CVPR) },
  month        = { June },
  year         = { 2016 },
}