# Elastic Net Constraints for Shape Matching

@article{Rodol2013ElasticNC, title={Elastic Net Constraints for Shape Matching}, author={E. Rodol{\`a} and A. Torsello and T. Harada and Y. Kuniyoshi and D. Cremers}, journal={2013 IEEE International Conference on Computer Vision}, year={2013}, pages={1169-1176} }

We consider a parametrized relaxation of the widely adopted quadratic assignment problem (QAP) formulation for minimum distortion correspondence between deformable shapes. In order to control the accuracy/sparsity trade-off we introduce a weighting parameter on the combination of two existing relaxations, namely spectral and game-theoretic. This leads to the introduction of the elastic net penalty function into shape matching problems. In combination with an efficient algorithm to project onto… Expand

#### 53 Citations

Relaxations for Minimizing Metric Distortion and Elastic Energies for 3D Shape Matching

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- 2013

We present two methods for non-rigid shape matching. Both methods formulate shape matching as an energy minimization problem, where the energy measures distortion of the metric defined on the shapes… Expand

Partial Matching of Deformable Shapes

- Computer Science
- 3DOR@Eurographics
- 2016

This paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods in this benchmark, the biggest and most challenging of its kind. Expand

Matching of Deformable Shapes with Topological Noise

- Computer Science
- 3DOR@Eurographics
- 2016

This track of the SHREC'16 contest evaluates shape matching algorithms that operate on 3D shapes under synthetically produced topological changes and describes the different methods and the contest results. Expand

SHREC ’ 16 : Partial Matching of Deformable Shapes

- 2016

Matching deformable 3D shapes under partiality transformations is a challenging problem that has received limited focus in the computer vision and graphics communities. With this benchmark, we… Expand

Consistent Partial Matching of Shape Collections via Sparse Modeling

- Mathematics, Computer Science
- Comput. Graph. Forum
- 2017

A novel approach to obtain consistent matches without requiring initial pairwise solutions to be given as input is introduced by optimizing a joint measure of metric distortion directly over the space of cycle‐consistent maps. Expand

Applying Random Forests to the Problem of Dense Non-rigid Shape Correspondence

- Computer Science
- Perspectives in Shape Analysis
- 2016

This work introduces a novel dense shape matching method for deformable, three-dimensional shapes which achieves significant improvements over the baseline approach and obtains state-of-the-art results while keeping a low computational cost. Expand

Matching Deformable Objects in Clutter

- Mathematics, Computer Science
- 2016 Fourth International Conference on 3D Vision (3DV)
- 2016

This work considers the problem of deformable object detection and dense correspondence in cluttered 3D scenes using the functional maps framework, and seeks for the most regular nearly-isometric parts in the model and the scene that minimize correspondence error. Expand

Fully Spectral Partial Shape Matching

- Computer Science
- Comput. Graph. Forum
- 2017

An efficient procedure for calculating partial dense intrinsic correspondence between deformable shapes performed entirely in the spectral domain is proposed and a variant of the JAD problem with an appropriately modified coupling term allows to construct quasi‐harmonic bases localized on the latent corresponding parts. Expand

Partial Functional Correspondence

- Mathematics, Computer Science
- Comput. Graph. Forum
- 2017

P perturbation analysis is used to show how removal of shape parts changes the Laplace–Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Expand

Dense Non-rigid Shape Correspondence Using Random Forests

- Mathematics, Computer Science
- 2014 IEEE Conference on Computer Vision and Pattern Recognition
- 2014

A shape matching method that produces dense correspondences tuned to a specific class of shapes and deformations that achieves significant improvements over the baseline approach and obtains state-of-the-art results while keeping short computation times. Expand

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