Research map / Point clouds / Shape and surface completion
3D Geometric Shape Assembly via Efficient Point Cloud Matching
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes Proxy Match Transform (PMT), a sub-quadratic approximation of second-order (high-order) feature transforms, and builds the PMTR coarse-to-fine point cloud matcher for 3D geometric shape assembly on Breaking Bad.
Problem
Geometric shape assembly requires high-resolution pairwise correspondence between mating surfaces of parts, but high-order feature transforms (convolution/attention over pairwise correlations) have quadratic cost and are infeasible at fine resolution.
Approach
PMT approximates a 2nd-order convolution over two point clouds by routing information through a shared low-dimensional learnable proxy tensor (with orthonormal/zero constraints), avoiding construction of the pairwise correlation matrix, giving sub-quadratic complexity; it is used in a coarse-to-fine matcher.
Key results
- On Breaking Bad everyday pairwise assembly, PMTR reaches CRD 0.39e-2 and CD 0.25e-3 vs. GeoTransformer's 0.61e-2 and 0.51e-3.
- Multi-part assembly on everyday: PMTR CRD 6.51e-2 and PA_CD 70.56% vs. Jigsaw's 14.13e-2 and 60.26%.
- PMT as coarse-level matcher uses about 21.5x fewer FLOPS than GeoTransformer's matcher (0.45G vs 9.67G for coarse-only).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add PMT layers as the fine-level matcher (vs. none) (ablation) | PMTR coarse-level PMT · Breaking Bad everyday (pairwise) | CRD: 0.53 -> 0.39 (x10^-2) | Helped |
| Share one proxy tensor across the two PMT transforms vs. separate proxies (ablation) | PMT · Breaking Bad everyday (pairwise) | CRD: 0.44 -> 0.39 (x10^-2) | Helped |
| Remove proxy tensor from PMT (ablation) | PMT · Breaking Bad everyday (pairwise) | CRD: 0.39 -> 0.53 (x10^-2) | Hurt |
| Add orthonormal and zero losses on proxy tensors (ablation) | PMT · Breaking Bad everyday (pairwise) | CRD: 0.43 (neither) -> 0.39 (both) | Helped |
| Replace fine-level PMT with linear or MLP layer (no inter-feature exchange) (ablation) | PMTR fine-level matcher · Breaking Bad everyday (pairwise) | CRD: 0.39 -> 0.47 (Linear), 0.49 (MLP) | Hurt |
| Replace fine-level PMT with HDC or GeoTransformer (ablation) | PMTR fine-level matcher · Breaking Bad everyday (pairwise) | CRD: out of memory | Hurt |
| Use PMTR (PMT matching) instead of GeoTransformer on pairwise assembly | Pairwise assembly · Breaking Bad everyday and artifact | CRD and CD: CRD 0.61->0.39 (everyday), CD 0.51->0.25 (everyday) | Helped |
| PMT-based coarse+fine matching vs GeoTransformer matcher (efficiency) | PMTR vs GeoTransformer matcher · Matcher efficiency (backbone excluded) | FLOPS (G): 9.67 -> 0.78 (Coarse+Fine) | Helped |
Surprising findings
- Vanilla high-order convolution (HDC) and GeoTransformer matchers run out of memory when used at fine level, so PMT is the only feasible option there.
- Jigsaw achieves the best translation RMSE (T) on pairwise everyday/artifact results, beating PMTR on that single metric.
Limitations
- Accuracy can drop with extremely low overlap between point clouds.
- Requires extensive training on domain-specific datasets.
- Only evaluated on geometric shape assembly, not other applications.
Experimental setup
Datasets: Breaking Bad
Benchmarks: Breaking Bad
Metrics: CRD CD RMSE (R) RMSE (T) PA_CRD PA_CD
Baselines: Global LSTM DGL NSM GeoTransformer Jigsaw HDC
Builds on: KPConv-FPN GeoTransformer neighborhood consensus (NC-Net) Jigsaw PerViT
Closest papers by meaning
- Partial-to-Partial Shape Matching with Geometric Consistency (CVPR 2024 · similarity 0.88)
- Category-Level Multi-Part Multi-Joint 3D Shape Assembly (CVPR 2024 · similarity 0.86)
- SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency (CVPR 2024 · similarity 0.85)
- EchoMatch: Partial-to-Partial Shape Matching via Correspondence Reflection (CVPR 2025 · similarity 0.85)
- DV-Matcher: Deformation-based Non-rigid Point Cloud Matching Guided by Pre-trained Visual Features (CVPR 2025 · similarity 0.85)
- Wormhole Loss for Partial Shape Matching (NeurIPS 2024 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.