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Shape Analysis

Contact: Dr. Frank R. Schmidt

Over the last years, the availability of devices for the acquisition of three-dimensional data like laser-scanners, RGB-D Vision or medical imaging devices has dramatically increased. This brings about the need for efficient algorithms to analyze three-dimensional shapes.

Our research is focused on reliable and efficient methods for the automatic interpretation of non-rigid three-dimensional shapes. In particular, we have been working on novel approaches to Shape Matching and on the design of Feature Descriptors.

Matching

The goal of shape matching is to register corresponding surface regions of two given three-dimensional shapes. This means for example to identify the hands, the feet and the head of two human figures. Once two shapes are registered, one can infer morphs between them. The video shows examples of such morphs, e.g. interpolating between a samba dancer and a hip hop dancer. In each of these example sequences, a registration of the first and the last shape has been computed, all intermediate frames are obtained by linear interpolation. The colors visualize regions which have been identified with each other.

A registration of two shapes can be the building block for measuring similarity of shapes and for performing shape statistics.

Mathematically, the task is to find a mapping from the boundary surface of one shape to the other one. This typically results in a very difficult, highly non-convex optimization problem.

We are currently working on efficient algorithms for shape matching with a focus on geometric consistency guarantees and on global optimization.

Feature Descriptors

The goal of feature descriptors is to characterize each point on an object's surface regarding its relation to the entire shape. The feature vectors of four different points of a cat are shown above.

In our research we aim at feature descriptors which are robust to shape articulations while capturing as much information as possible. A very powerful mathematical tool for this task is the eigendecomposition of the Laplace–Beltrami operator.


Related publications

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Journal Articles Conference and Workshop Papers 
Journal Articles
2016
White Matter MS-Lesion Segmentation Using a Geometric Brain Model (M. Strumia, F. R. Schmidt, C. Anastasopoulos, C. Granziera, G. Krueger, T. Brox), In IEEE Transactions on Medical Imaging, volume 35, 2016. [bib] [pdf]
Non-Rigid Puzzles (O. Litany, E. Rodola, A. M. Bronstein, M. M. Bronstein, D. Cremers), In Computer Graphics Forum, Wiley, volume 35, 2016. [bib] [pdf]Received the Best Paper Award at SGP 2016
Anisotropic Diffusion Descriptors (D. Boscaini, J. Masci, E. Rodola, M. M. Bronstein, D. Cremers), In Computer Graphics Forum - Proc. EUROGRAPHICS, Wiley, volume 35, 2016. [bib] [pdf]
Consistent Partial Matching of Shape Collections via Sparse Modeling (L. Cosmo, E. Rodola, A. Albarelli, F. Memoli, D. Cremers), In Computer Graphics Forum, Wiley, 2016. [bib] [pdf]
Partial Functional Correspondence (E. Rodola, L. Cosmo, M. M. Bronstein, A. Torsello, D. Cremers), In Computer Graphics Forum, Wiley, 2016. [bib] [pdf]
2015
A Simple and Effective Relevance-based Point Sampling for 3D Shapes (E. Rodola, A. Albarelli, D. Cremers, A. Torsello), In Pattern Recognition Letters, Elsevier, volume 59, 2015. [bib] [pdf] [code]
Fast and Accurate Surface Alignment through an Isometry-Enforcing Game (A. Albarelli, E. Rodola, A. Torsello), In Pattern Recognition, Elsevier, volume 48, 2015. [bib] [pdf] [doi]
2014
Robust Region Detection via Consensus Segmentation of Deformable Shapes (E. Rodola, S. Rota Bulo, D. Cremers), In Computer Graphics Forum, Wiley, volume 33, 2014. [bib] [pdf] [code]
2013
A Scale Independent Selection Process for 3D Object Recognition in Cluttered Scenes (E. Rodola, A. Albarelli, F. Bergamasco, A. Torsello), In International Journal of Computer Vision, Springer US, volume 102, 2013. [bib] [pdf] [doi]
2011
Large-Scale Integer Linear Programming for Orientation-Preserving 3D Shape Matching (T. Windheuser, U. Schlickewei, F. R. Schmidt, D. Cremers), In Computer Graphics Forum (Proceedings Symposium Geometry Processing), Eurographics, volume 30, 2011. [bib] [pdf]
Journal Articles Conference and Workshop Papers 
Conference and Workshop Papers
2016
A Convex Solution to Spatially-Regularized Correspondence Problems (T. Windheuser, D. Cremers), In European Conference on Computer Vision (ECCV), 2016. [bib] [pdf]
2015
Point-wise Map Recovery and Refinement from Functional Correspondence (E. Rodola, M. Moeller, D. Cremers), In Proceedings Vision, Modeling and Visualization (VMV), 2015. [bib] [pdf]Received the Best Paper Award
2014
Learning Similarities for Rigid and Non-Rigid Object Detection (A. Kanezaki, E. Rodola, D. Cremers, T. Harada), In International Conference on 3D Vision (3DV), 2014. [bib] [pdf]
Optimal Intrinsic Descriptors for Non-Rigid Shape Analysis (T. Windheuser, M. Vestner, E. Rodola, R. Triebel, D. Cremers), In British Machine Vision Conference (BMVC), 2014. [bib] [pdf]
Dense Non-Rigid Shape Correspondence Using Random Forests (E. Rodola, S. Rota Bulo, T. Windheuser, M. Vestner, D. Cremers), In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2014. [bib] [pdf] [code]
2013
Relaxations for Minimizing Metric Distortion and Elastic Energies for 3D Shape Matching (D. Cremers, E. Rodola, T. Windheuser), In Actes des recontres du CIRM: Courbure discrete: théorie et applications, volume 3, 2013. [bib] [pdf]
Elastic Net Constraints for Shape Matching (E. Rodola, A. Torsello, T. Harada, Y. Kuniyoshi, D. Cremers), In IEEE International Conference on Computer Vision (ICCV), 2013. [bib] [pdf] [code]
Efficient Shape Matching using Vector Extrapolation (E. Rodola, T. Harada, Y. Kuniyoshi, D. Cremers), In British Machine Vision Conference (BMVC), 2013. [bib] [pdf]
2012
A game-theoretic approach to deformable shape matching (E. Rodola, A.M. Bronstein, A. Albarelli, F. Bergamasco, A. Torsello), In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2012. [bib] [pdf] [doi]
2011
The Wave Kernel Signature: A Quantum Mechanical Approach To Shape Analysis (M. Aubry, U. Schlickewei, D. Cremers), In IEEE International Conference on Computer Vision (ICCV) - Workshop on Dynamic Shape Capture and Analysis (4DMOD), 2011. [bib] [pdf] [code]
On a linear programming approach to the discrete Willmore boundary value problem and generalizations (T. Schoenemann, S. Masnou, D. Cremers), In Curves and Surfaces 2011 (J.-D. Boissonnat et al., ed.), 2011. [bib] [pdf]
Pose-Consistent 3D Shape Segmentation Based on a Quantum Mechanical Feature Descriptor (M. Aubry, U. Schlickewei, D. Cremers), In Pattern Recognition (Proc. DAGM), Springer, 2011. [bib] [pdf]
Geometrically Consistent Elastic Matching of 3D Shapes: A Linear Programming Solution (T. Windheuser, U. Schlickewei, F. R. Schmidt, D. Cremers), In IEEE International Conference on Computer Vision (ICCV), 2011. [bib] [pdf]
Sampling Relevant Points for Surface Registration (A. Torsello, E. Rodola, A. Albarelli), In International Conference on 3D Imaging, Modeling, Processing, Visualization and Transmission (3DIMPVT), 2011. [bib] [pdf] [doi]
A Non-Cooperative Game for 3D Object Recognition in Cluttered Scenes (A. Albarelli, E. Rodola, A. Torsello), In International Conference on 3D Imaging, Modeling, Processing, Visualization and Transmission (3DIMPVT), 2011. [bib] [pdf] [doi]
2010
Loosely Distinctive Features for Robust Surface Alignment (A. Albarelli, E. Rodola, A. Torsello), In European Conference on Computer Vision (ECCV), 2010. [bib] [pdf] [doi]
A Game-Theoretic Approach to Fine Surface Registration without Initial Motion Estimation (A. Albarelli, E. Rodola, A. Torsello), In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2010. [bib] [pdf] [doi]
2009
Efficient Planar Graph Cuts with Applications in Computer Vision (F. R. Schmidt, E. Toeppe, D. Cremers), In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2009. (Note: This version of the paper is modified with respect to the published one: In the published version we had only cited the PhD thesis [2], as the conference paper [3] does not mention Step 13 of Algorithm 2 that restores the important property of T being a rooted tree.) [bib] [pdf]Received a CVPR Doctoral Spotlight Award
2007
Efficient Shape Matching via Graph Cuts (F. R. Schmidt, E. Toeppe, D. Cremers, Y. Boykov), In Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), Springer, volume 4679, 2007. [bib] [pdf]
Intrinsic Mean for Semimetrical Shape Retrieval via Graph Cuts (F. R. Schmidt, E. Toeppe, D. Cremers, Y. Boykov), In Pattern Recognition (Proc. DAGM), Springer, volume 4713, 2007. [bib] [pdf]
Fast Matching of Planar Shapes in Sub-cubic Runtime (F. R. Schmidt, Dirk Farin, D. Cremers), In IEEE International Conference on Computer Vision (ICCV), 2007. [bib] [pdf]
2006
Shape Matching by Variational Computation of Geodesics on a Manifold (F. R. Schmidt, M. Clausen, D. Cremers), In Pattern Recognition (Proc. DAGM), Springer, volume 4174, 2006. [bib] [pdf]
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Last edited 07.03.2016 10:09 by Frank R. Schmidt