Learning to assemble geometric shapes into a larger target structure is a pivotal task in various practical applications. In this work, we tackle this problem by establishing local correspondences between point clouds of part shapes in both coarse- and fine-levels. To this end, we introduce Proxy Match Transform (PMT), an approximate high-order feature transform layer that enables reliable matching between mating surfaces of parts while incurring low costs in memory and computation. Building upon PMT, we introduce a new framework, dubbed Proxy Match TransformeR (PMTR), for the geometric assembly task. We evaluate the proposed PMTR on the large-scale 3D geometric shape assembly benchmark dataset of Breaking Bad and demonstrate its superior performance and efficiency compared to state-of-the-art methods. Project page: https://nahyuklee.github.io/pmtr.
@article{arxiv.2407.10542,
title = {3D Geometric Shape Assembly via Efficient Point Cloud Matching},
author = {Nahyuk Lee and Juhong Min and Junha Lee and Seungwook Kim and Kanghee Lee and Jaesik Park and Minsu Cho},
journal= {arXiv preprint arXiv:2407.10542},
year = {2024}
}