Searching Dense Point Correspondences via Permutation Matrix Learning

TL;DR

This paper introduces a novel deep learning approach for dense 3D point cloud correspondence estimation, formulating the problem as a differentiable permutation matrix learning task that enforces one-to-one matching.

Contribution

It proposes a differentiable permutation matrix learning framework for dense 3D point cloud correspondence, addressing the non-differentiability of classical assignment solutions.

Findings

Achieves state-of-the-art performance on dense correspondence tasks.

Works effectively on both rigid and non-rigid 3D point clouds.

Introduces a differentiable matching module for deep learning.

Abstract

Although 3D point cloud data has received widespread attentions as a general form of 3D signal expression, applying point clouds to the task of dense correspondence estimation between 3D shapes has not been investigated widely. Furthermore, even in the few existing 3D point cloud-based methods, an important and widely acknowledged principle, i.e . one-to-one matching, is usually ignored. In response, this paper presents a novel end-to-end learning-based method to estimate the dense correspondence of 3D point clouds, in which the problem of point matching is formulated as a zero-one assignment problem to achieve a permutation matching matrix to implement the one-to-one principle fundamentally. Note that the classical solutions of this assignment problem are always non-differentiable, which is fatal for deep learning frameworks. Thus we design a special matching module, which solves a doubly stochastic matrix at first and then projects this obtained approximate solution to the desired permutation matrix. Moreover, to guarantee end-to-end learning and the accuracy of the calculated loss, we calculate the loss from the learned permutation matrix but propagate the gradient to the doubly stochastic matrix directly which bypasses the permutation matrix during the backward propagation. Our method can be applied to both non-rigid and rigid 3D point cloud data and extensive experiments show that our method achieves state-of-the-art performance for dense correspondence learning.