Product Manifold Filter: Non-rigid Shape Correspondence via Kernel Density Estimation in the Product Space

By Matthias Vestner, Roee Litman, Emanuele Rodolà, A. Bronstein, Daniel Cremers. 2017

139 citations recorded by the source corpus.

Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a post-processing stage in the functional correspondence framework. Such frequently used techniques implicitly make restrictive assumptions (e.g., nearisometry) on the considered shapes and in practice suffer from lack of accuracy and result in poor surjectivity. We propose an alternative recovery technique capable of guaranteeing a bijective correspondence and producing significantly higher accuracy and smoothness. Unlike other methods our approach does not depend on the assumption that the analyzed shapes are isometric. We derive the proposed method from the statistical framework of kernel density estimation and demonstrate its performance on several challenging deformable 3D shape matching datasets.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition, Representation & Self-Supervised Learning

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Michael M. Bronstein
2. Emanuele Rodolà
3. A. Bronstein
4. Or Litany
5. Federico Monti
6. Davide Boscaini
7. Jonathan Masci
8. Edmond Boyer

In Computer Graphics and Computer-Aided Design

1. Michael M. Bronstein
2. Emanuele Rodolà
3. Or Litany
4. Jonathan Masci
5. A. Bronstein
6. Federico Monti
7. Davide Boscaini
8. Edmond Boyer

In Computer Vision and Pattern Recognition

1. Michael M. Bronstein
2. A. Bronstein
3. Luc Van Gool
4. Or Litany
5. Emanuele Rodolà
6. Xiaogang Wang
7. Dacheng Tao
8. Jonathan Masci

In Representation & Self-Supervised Learning

1. A. Bronstein
2. Emanuele Rodolà
3. Michael M. Bronstein
4. Jakob Verbeek
5. Edmond Boyer
6. Nitika Verma
7. Jonathan Masci
8. Davide Boscaini

Citations in the corpus

• Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs (2016, methodology): “The output of the network was refined using the intrinsic product manifold filter [40] in order to remove some local outliers.”
• Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks (2017, methodology): “While in this work we apply multi-graph CNNs in the context of recommender systems to the graphs of users and items, however, our architecture is generic and can be used in other applications, such as neuroscience (autism detection with network of people and brain connectivity [31, 23]), computer gr”
• Deep Functional Maps: Structured Prediction for Dense Shape Correspondence (2017, methodology): “The results are reported in Figure 7; here, all methods were post-processed with the correspondence refinement technique of [40].”
• FeaStNet: Feature-Steered Graph Convolutions for 3D Shape Analysis (2017, methodology): “MoNet [15], w/ refinement [29] SHOT 88.”
• Dynamic Filters in Graph Convolutional Networks (2017, methodology): “Besides evaluating the quality of the matches directly predicted by our model, we also assessed the impact of a post-processing the matches using a correspondence refinement algorithm [23].”
• Self-supervised Learning of Dense Shape Correspondence (2018, methodology): “0 0.02 0.04 0.06 0.08 0.1 0 20 40 60 80 100 Geodesic error % C or re sp on de nc es TOSCA Ours RF [37] PMF [44] BIM [24] SGMDS [4] FM [33] Reference Figure 6.”