# Deep Functional Maps: Structured Prediction for Dense Shape Correspondence

## TL;DR

This paper presents a novel deep learning framework for dense shape correspondence that leverages structured prediction in the space of functional maps, improving accuracy across various challenging 3D shape datasets.

## Contribution

It introduces a deep residual network that predicts soft functional maps directly from dense descriptors, shifting from label-based to structured prediction for shape correspondence.

## Key findings

- Accurate correspondence on multiple challenging benchmarks
- Effective handling of synthetic and real 3D scans with artifacts
- Outperforms existing methods in dense shape matching

## Abstract

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.