Combinative Matching
for Geometric Shape Assembly

ICCV 2025 Highlight ✨
Nahyuk Lee1*      Juhong Min1,2*      Junhong Lee1     Chunghyun Park1     Minsu Cho1,3
1 POSTECH        2 Samsung Research America        3 RLWRLD       
(* equal contribution)
arXiv (TBA) Poster (TBA) Code (TBA) BibTex

Abstract

This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces between the parts as in conventional shape matching and registration. In contrast, we explicitly model two distinct properties of interlocking shapes: 'identical surface shape' and 'opposite volume occupancy.' Our method thus learns to establish correspondences across regions where their surface shapes appear identical but their volumes occupy the inverted space to each other. To facilitate this process, we also learn to align regions in rotation by estimating their shape orientations via equivariant neural networks. The proposed approach significantly reduces local ambiguities in matching and allows a robust combination of parts in assembly. Experimental results on geometric assembly benchmarks demonstrate the efficacy of our method, consistently outperforming the state of the art.

What's this project about?

Traditional shape matching methods like GeoTransformer [CVPR'23] and PMTR [ICML'24] rely on equative matching, which assumes that mating parts resemble each other at their surfaces. While technically sound, this approach often falls short in geometric shape assembly, where parts are not merely visually similar—as in point cloud registration—but are structurally complementary.
Then, what do we miss? 🤔
Geometric shape assembly requires more than visual resemblance—it demands complementary properties: surfaces must not only look alike but also fit by occupying opposite volumes.

Learning to interlock parts: Combinative Matching

We introduce Combinative Matching, a novel approach that addresses the dual requirements of geometric assembly: identical surface shape and opposite volume occupancy. To ensure consistent matching under arbitrary part poses, it first aligns (1) local orientations between surface points, establishing a shared reference frame. Within this frame, the method jointly performs (2) shape matching to find visually similar regions and (3) occupancy matching to enforce volumetric complementarity—allowing parts to interlock properly.

Combinative Matching Network (CMNet)

Building upon the concept of combinative matching, we introduce a new framework, Combinative Matching Network (CMNet), designed for robust geometric shape assembly. CMNet jointly leverages surface resemblance and volumetric complementarity to establish reliable correspondences on mating surfaces. The proposed architecture consists of four main components: (1) feature extraction and orientation alignment, (2) surface shape matching, (3) volume occupancy matching, and (4) transformation estimation.

Quantitative Comparison

🔉 NOTE: In main paper, we conducted experiments on the volume-constrained Breaking Bad dataset in which the volume of every piece is at least 1/40 of the total shape volume, reducing extreme point density imbalance. Results on vanilla version are provided in the supplementary material.

Qualitative Comparison

BibTeX

@inproceedings{lee2025combinative,
      author    = {Lee, Nahyuk and Min, Juhong and Lee, Junhong and Park, Chunghyun and Cho, Minsu},
      title     = {Combinative Matching for Geometric Shape Assembly},
      booktitle = {Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)},
      year      = {2025},
    }