Deep functional map

Dr Abhishek Sharma



3D Shape matching is a fundamental problem in computer vision and graphics with significant applications on biological data. In this project, we will take a closer look at Deep Functional Map (DFM) [1,2] paradigm for 3D shape matching.  You will become familiar with unsupervised DFM frameworks [2] and investigate a couple of directions less explored in the DFM literature. First, most DFM literature strongly relies on precomputed Laplacian Beltrami (LB) eigenbasis. There have been some recent attempts to learn an embedding [3,4] instead. However, it is not entirely clear in which circumstances learned embedding is more robust and useful than LB eigenbasis. Secondly, we will investigate cycle consistency constraints in DFM that provide a strong regularization by jointly optimizing the maps over a collection of shapes. By the end of the project, you should better understand these topics from both theoretical and practical perspectives.


[1] Litany et al., Deep Functional Map: Structure prediction for dense shape correspondence, ICCV 2017

[2] Roufosse et al., Unsupervised Deep Learning for 3D shape Matching, ICCV 2019

[3] Marin et al., Correspondence Learning via Linearly Invariant Embedding, Neurips 2020

[4] Sharma & Ovsjanikov, Joint Symmetry Detection and Shape Matching for Non-rigid Point Cloud, arXiv