Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
This addresses shape correspondence for computer graphics and vision, offering a new paradigm that improves accuracy in handling deformations and noise.
The paper tackles the problem of learning dense correspondence between deformable 3D shapes by introducing a structured prediction model in the functional maps space, resulting in accurate correspondence on challenging benchmarks with synthetic models, real scans, and partial data.
We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. 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 resulting correspondence is shown to be accurate on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and partiality.