SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularization

Tianwei Ye, Xiaoguang Mei, Yifan Xia, Fan Fan, Jun Huang, Jiayi Ma†

Wuhan University

ECCV 2026

† Corresponding Author

(Left): Colormap transfer on the SHREC'19 dataset demonstrates that incorporating semantic features resolves ambiguity and yields globally consistent correspondences. (Right): Vertex transfer on the SMAL dataset shows that the proposed conditional flow matching regularization promotes spatially smooth correspondences.

Key Observation

Geometry alone is ambiguous.

Intrinsic descriptors can confuse symmetric or self-similar parts, such as left-right limbs, because local geometry does not always identify semantic correspondence.

Flow matching regularization visualization

Point-wise recovery needs local coherence.

Spectral functional maps provide a compact matching space, but dense projection can still introduce local mismatches that appear as noisy correspondence transitions.

Abstract

Establishing accurate point-to-point correspondences between non-rigid 3D shapes remains a critical challenge, particularly under non-isometric deformations and topological noise. Existing functional map pipelines suffer from ambiguities that geometric descriptors alone cannot resolve, and spatial inconsistencies inherent in the projection of truncated spectral bases to dense pointwise correspondences. In this paper, we introduce SGMatch, a learning-based framework that couples 3D-lifted semantic cues with trajectory-level feature transport regularization. Specifically, we design a Semantic-Guided Local Cross-Attention module that integrates semantic features from vision foundation models into geometric descriptors while preserving local structural continuity. Furthermore, we adapt conditional flow matching as a time-conditioned feature transport regularizer that promotes spatially coherent point-wise recovery. Experimental results on multiple benchmarks demonstrate that SGMatch achieves competitive performance across near-isometric settings and consistent improvements under non-isometric deformations and topological noise.

Method

SGMatch combines lifted semantic cues, local feature fusion, functional maps, and flow-based feature transport to recover accurate and spatially coherent non-rigid correspondences.

Overview of SGMatch. Given a pair of shapes, we extract geometric and semantic features, fuse them via SGLCA, estimate functional maps, and regularize correspondences through spectral heat diffusion and conditional flow matching.

3D-Lifted Semantics

Depth- and normal-guided multi-view renderings are encoded by frozen DINOv2 and back-projected to mesh vertices, providing semantic cues that complement DiffusionNet geometry.

Local Semantic Fusion

SGLCA uses semantic-guided gates and local cross-attention to inject part-level context while preserving neighborhood structure on the surface.

Flow-Regularized Recovery

Fused descriptors estimate bidirectional functional maps, while heat diffusion and conditional flow matching regularize dense point-wise recovery through coherent feature transport.

Results

SGMatch matches state-of-the-art performance in near-isometric settings and brings clearer gains under non-isometric deformation and topological noise, where semantic cues and flow regularization are most beneficial.

Near-Isometric Shape Matching

Mean geodesic error (×100) on FAUST, SCAPE (near-isometric) and SHREC'19 (cross-dataset generalization).

Method	FAUST	SCAPE	SHREC'19
Axiomatic Methods
ZoomOut	6.1	7.5	-
Smooth Shells	2.5	4.2	-
DiscreteOp	5.6	13.1	-
Supervised Methods
FMNet	11.0	33.0	-
GeomFMaps	2.6	3.0	7.9
Unsupervised Methods
Deep Shell	1.7	2.5	21.1
DUO-FMNet	2.5	4.2	6.4
AttnFMaps	1.9	2.2	5.8
ULRSSM	1.6	1.9	4.6
HybridFMap	1.5	1.8	3.6
DenoisFMap	1.7	2.1	3.6
DiffuMatch	1.9	4.4	3.9
DeepFAFM	1.5	1.9	3.6
Ours	1.4	1.8	3.3

Non-Isometric Shape Matching

Mean geodesic error (×100) on SMAL and DT4D-H. Our method achieves the best overall performance on SMAL, surpassing the previous state-of-the-art by 24%.

Method	SMAL	DT4D-H (intra)	DT4D-H (inter)
Axiomatic Methods
ZoomOut	38.4	4.0	29.0
Smooth Shells	30.0	1.2	6.4
DiscreteOp	38.1	3.6	27.6
Supervised Methods
FMNet	42.0	9.6	38.0
GeomFMaps	8.4	1.9	4.2
Unsupervised Methods
Deep Shell	29.3	3.4	31.1
DUO-FMNet	6.7	2.6	15.8
AttnFMaps	5.4	1.7	11.6
ULRSSM	3.9	0.9	4.1
HybridFMap	3.3	1.0	3.5
DenoisFMap	4.3	5.8	16.9
DiffuMatch	10.1	1.8	8.6
DeepFAFM	3.8	0.9	3.9
Ours	2.5	1.0	3.4

Matching with Topological Noise

Mean geodesic error (×100) on TOPKIDS. Our method achieves a 42% improvement over the previous best.

Method	TOPKIDS
Axiomatic Methods
ZoomOut	33.7
Smooth Shells	10.8
DiscreteOp	35.5
Unsupervised Methods
Deep Shell	13.7
AttnFMaps	23.4
ULRSSM	9.2
HybridFMap	5.0
DeepFAFM	6.2
Ours	2.9

PCK curves and AUC values on SMAL, DT4D-H inter-class, and TOPKIDS. SGMatch consistently improves the area under the curve in challenging non-isometric and topology-noisy settings.

Map Smoothness

Beyond point-wise geodesic accuracy, we evaluate the local smoothness of recovered maps using conformal distortion, surface coverage, Dirichlet energy, and bijectivity. SGMatch improves most metrics, with the clearest gains on non-isometric and topology-noisy datasets where intrinsic geometry is less reliable.

Metric	Method	FAUST	SCAPE	SHREC'19	SMAL	DT4D-inter	TOPKIDS
Conf. ↓	HybridFMap	0.654	0.779	1.030	2.473	1.866	3.201
Conf. ↓	Ours	0.639	0.764	0.787	1.956	1.563	2.517
Cov. (%) ↑	HybridFMap	83.3	82.5	75.9	65.0	67.1	63.3
Cov. (%) ↑	Ours	83.5	81.9	76.1	71.2	66.3	63.9
Dir.E ↓	HybridFMap	2.96	3.11	12.30	19.29	8.44	98.30
Dir.E ↓	Ours	2.95	3.27	6.30	10.20	8.70	48.33
Bij. ↓	HybridFMap	0.0049	0.0060	—	0.0285	0.0130	—
Bij. ↓	Ours	0.0052	0.0064	—	0.0175	0.0166	—

Conformal-distortion-based smoothness comparison on SMAL, DT4D-H inter-class, and TOPKIDS. Higher curves indicate more correspondences under a given distortion threshold.

Regularization and Ablation

We isolate the contribution of CFM by comparing it with endpoint matching, cycle consistency, and synchronous diffusion under the same SGMatch backbone. We also ablate the main feature-fusion components on SMAL.

Alternative Smoothness Regularizers

Variant	SMAL					TOPKIDS
Variant	Geo. ↓	Conf. ↓	Dir.E ↓	Bij. ↓	Cov. ↑	Geo. ↓	Conf. ↓	Dir.E ↓	Cov. ↑
w/o CFM	2.7	2.32	10.55	0.0210	66.8	3.4	2.92	45.64	63.5
Endpoint-only	2.7	2.46	14.37	0.0225	65.0	3.4	2.76	50.92	63.8
Cycle-consistency	2.8	2.29	10.53	0.0201	67.2	3.4	2.75	42.42	63.7
Sync. Diff.	2.6	2.45	13.48	0.0221	64.7	3.5	2.79	50.14	63.8
Ours	2.5	1.96	10.20	0.0175	71.2	2.9	2.52	48.33	63.9

Ablation Study

Variant	Gating	Attention	Geo.Err ↓
Geo. only	—	—	3.2
Sem. only	—	—	21.2
Gating only		none	3.6
Local attention only		local	2.6
Gating + global attention		global	2.6
w/o heat diffusion		local	3.0
Ours		local	2.5

Qualitative Results

Qualitative results on SMAL and DT4D-H. Comparison of our method against DeepFAFM and HybridFMap via texture transfer. Our method produces more accurate and coherent correspondences.

BibTeX

@inproceedings{ye2026sgmatch,
  title     = {SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularization},
  author    = {Ye, Tianwei and Mei, Xiaoguang and Xia, Yifan and Fan, Fan and Huang, Jun and Ma, Jiayi},
  booktitle = {European Conference on Computer Vision (ECCV)},
  year      = {2026}
}