In this paper, we propose a fully differentiable pipeline for estimating accurate dense correspondences between 3D point clouds. The proposed pipeline is an extension and a generalization of the functional maps framework. However, instead of using the Laplace-Beltrami eigenfunctions as done in virtually all previous works in this domain, we demonstrate that learning the basis from data can both improve robustness and lead to better accuracy in challenging settings. We interpret the basis as a learned embedding into a higher dimensional space. Following the functional map paradigm the optimal transformation in this embedding space must be linear and we propose a separate architecture aimed at estimating the transformation by learning optimal descriptor functions. This leads to the first end-to-end trainable functional map-based correspondence approach in which both the basis and the descriptors are learned from data. Interestingly, we also observe that learning a canonical embedding leads to worse results, suggesting that leaving an extra linear degree of freedom to the embedding network gives it more robustness, thereby also shedding light onto the success of previous methods. Finally, we demonstrate that our approach achieves state-of-the-art results in challenging non-rigid 3D point cloud correspondence applications.

Correspondence Learning via Linearly-invariant Embedding / Marin, Riccardo; Rakotosaona, Marie-Julie; Melzi, Simone; Ovsjanikov, Maks. - (2020). (Intervento presentato al convegno Conference on Neural Information Processing Systems tenutosi a Montreal; Canada).

Correspondence Learning via Linearly-invariant Embedding

Riccardo Marin
Primo
;
Simone Melzi
Penultimo
;
2020

Abstract

In this paper, we propose a fully differentiable pipeline for estimating accurate dense correspondences between 3D point clouds. The proposed pipeline is an extension and a generalization of the functional maps framework. However, instead of using the Laplace-Beltrami eigenfunctions as done in virtually all previous works in this domain, we demonstrate that learning the basis from data can both improve robustness and lead to better accuracy in challenging settings. We interpret the basis as a learned embedding into a higher dimensional space. Following the functional map paradigm the optimal transformation in this embedding space must be linear and we propose a separate architecture aimed at estimating the transformation by learning optimal descriptor functions. This leads to the first end-to-end trainable functional map-based correspondence approach in which both the basis and the descriptors are learned from data. Interestingly, we also observe that learning a canonical embedding leads to worse results, suggesting that leaving an extra linear degree of freedom to the embedding network gives it more robustness, thereby also shedding light onto the success of previous methods. Finally, we demonstrate that our approach achieves state-of-the-art results in challenging non-rigid 3D point cloud correspondence applications.
2020
Conference on Neural Information Processing Systems
3D Shape Matching; Deep Learning; Geometry Processing; Virtual Humans
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
Correspondence Learning via Linearly-invariant Embedding / Marin, Riccardo; Rakotosaona, Marie-Julie; Melzi, Simone; Ovsjanikov, Maks. - (2020). (Intervento presentato al convegno Conference on Neural Information Processing Systems tenutosi a Montreal; Canada).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1556596
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