Operatornet: Recovering 3D shapes from difference operators

Ruqi Huang, Marie Julie Rakotosaona, Panos Achlioptas, Leonidas Guibas, Maks Ovsjanikov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

Abstract

This paper proposes a learning-based framework for reconstructing 3D shapes from functional operators, compactly encoded as small-sized matrices. To this end we introduce a novel neural architecture, called OperatorNet, which takes as input a set of linear operators representing a shape and produces its 3D embedding. We demonstrate that this approach significantly outperforms previous purely geometric methods for the same problem. Furthermore, we introduce a novel functional operator, which encodes the extrinsic or pose-dependent shape information, and thus complements purely intrinsic pose-oblivious operators, such as the classical Laplacian. Coupled with this novel operator, our reconstruction network achieves very high reconstruction accuracy, even in the presence of incomplete information about a shape, given a soft or functional map expressed in a reduced basis. Finally, we demonstrate that the multiplicative functional algebra enjoyed by these operators can be used to synthesize entirely new unseen shapes, in the context of shape interpolation and shape analogy applications.
Original languageEnglish (US)
Title of host publication2019 IEEE/CVF International Conference on Computer Vision (ICCV)
PublisherIEEE
Pages8587-8596
Number of pages10
ISBN (Print)9781728148038
DOIs
StatePublished - Feb 27 2020
Externally publishedYes

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