Deep functional maps: intrinsic structured prediction for dense shape correspondence

Michael Bronstein
USI Lugano, Switzerland
/ Tel Aviv University, Israel / Intel Perceptual Computing, Israel

Recently, there has been a keen interest in the computer graphics community to adopt successful deep learning methods for dealing with geometric data, in particular, to address the problem of shape correspondence. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label produced by a deep neural network, identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. The key drawback of such approaches is that the neural network does not impose any structure on the output correspondence at inference time, resulting in correspondence that is not guaranteed to be smooth.
In this talk, I will present a structured prediction model in the space of functional maps (linear operators that provide a compact representation of the correspondence in the spectral domain). We model the learning process via a deep residual network which takes dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects. The proposed approach achieves state-of-the-art results on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and missing parts.

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