Sparse Geometric Representation Through Local Shape Probing

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Julie Digne   Sébastien Valette    Raphaëlle Chaine

Resampling a shape with curve parts and surface parts.

Abstract

We propose a new shape analysis approach based on the non-local analysis of local shape variations. Our method relies on a novel description of shape variations, called Local Probing Field (LPF), which describes how a local probing operator transforms a pattern onto the shape. By carefully optimizing the position and orientation of each descriptor, we are able to capture shape similarities and gather them into a geometrically relevant dictionary over which the shape decomposes sparsely. This new representation permits to handle shapes with mixed intrinsic dimensionality (e.g., shapes containing both surfaces and curves) and to encode various shape features such as boundaries. Our shape representation has several potential applications; here we demonstrate its efficiency for shape resampling and point set denoising for both synthetic and real data.

Application of Local Probing Fields to the point cloud denoising problem. Mixed dimensions case.

Bibtex

@article{lpf2018,
author={Digne, Julie and Valette, Sébastien and Chaine, Raphaëlle},
journal={IEEE Transactions on Visualization and Computer Graphics},
title={Sparse Geometric Representation Through Local Shape Probing},
year={2018},
volume={24},
number={7},
pages={2238-2250},
doi={10.1109/TVCG.2017.2719024},
ISSN={1077-2626},
month={July},}

Acknowledgements

Research funded by ANR, PAPS project (ANR-14-CE27-0003)