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 language | English (US) |
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Title of host publication | 2019 IEEE/CVF International Conference on Computer Vision (ICCV) |
Publisher | IEEE |
Pages | 8587-8596 |
Number of pages | 10 |
ISBN (Print) | 9781728148038 |
DOIs | |
State | Published - Feb 27 2020 |
Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2022-06-30Acknowledged KAUST grant number(s): CRG-2017-3426
Acknowledgements: Parts of this work were supported by the ERC Starting Grant StG-2017-758800 (EXPRO-TEA), KAUST OSR Award CRG-2017-3426 a gift from the Nvidia Corporation, a Vannevar Bush Faculty Fellowship, NSF grant DMS-1546206, a Google Research award and gifts from Adobe and Autodesk. The authors thank Davide Boscaini and Etienne Corman for their help with baseline comparisons.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.