TransLAP: Non‐Isometric Shape Matching Using Transformer Based Linear Assignment Problem

Amirreza Amirfathiyan; Hossein Ebrahimnezhad

doi:10.1049/ipr2.70333

journal article Open Access Jan 01, 2026

TransLAP: Non‐Isometric Shape Matching Using Transformer Based Linear Assignment Problem

Amirreza Amirfathiyan Hossein Ebrahimnezhad

IET Image Processing Vol. 20 No. 1 · Institution of Engineering and Technology (IET)

View at Publisher Save 10.1049/ipr2.70333

Abstract

ABSTRACT
Establishing correspondences between 3D shapes under challenging conditions, such as mixed pose and non‐isometric deformations, is critical for applications like shape registration in computer vision and graphics. Existing methods, including geodesic‐based, orientation‐preserving, and deep learning approaches, often falter in handling intrinsic symmetries and significant deformations, as evidenced in benchmarks like SHREC’20 and TOSCA. We introduce TransLAP, a transformer‐based linear assignment solver that directly operates on hybrid geometric features (geodesic distances + Dirichlet‐to‐Neumann eigenfunctions) to produce bijective mappings in a CPU‐efficient manner. TransLAP estimates soft assignment matrices using stacked self‐ and cross‐attention layers with assurance‐based early stopping, followed by Jonker–Volgenant optimisation and the Voting‐Based Consensus Algorithm (VBCA) refinement. Evaluated on TOSCA, SHREC’20, SMAL, and DT4D datasets, our method achieves average geodesic errors of 0.0932, 0.1094, 0.0614, and 0.0663, respectively — outperforming state‐of‐the‐art approaches (e.g., SSL, ConsistFMaps, DGFM, FM‐Net and Diffusion‐Net) by up to 60%. Qualitative results demonstrate effective matching for non‐isometric pairs (e.g., human‐gorilla, pig‐dog). Ablation studies confirm the role of each component in our proposed method, with TransLAP contributing approximately 50% and the Mapping Modifier contributing over 20%. Our method runs on a CPU with less than 3 GB of memory, making it practical for low‐resource settings.

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References

45

[1]

Bronstein A. M. "Generalized Multidimensional Scaling: A Framework for Isometry‐invariant Partial Surface Matching" Proceedings of the National Academy of Sciences (PNAS) (2006) 10.1073/pnas.0508601103

[2]

Dubrovina A. "Approximately Isometric Shape Correspondence by Matching Pointwise Spectral Features and Global Geodesic Structures" Advances in Adaptive Data Analysis (2011) 10.1142/s1793536911000829

[3]

10.1016/j.cag.2020.08.008

[4]

G.ShamaiandR.Kimmel “Geodesic Distance Descriptors ” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition (arXiv 2017) 6410–6418. 10.1109/cvpr.2017.386

[5]

10.1145/3272127.3275040

[6]

O.Litany T.Remez E.Rodola A.Bronstein andM.Bronstein “Deep Functional Maps: Structured Prediction for Dense Shape Correspondence ” inProceedings of the IEEE International Conference on Computer Vision (ICCV) (IEEE 2017) 5660–5668. 10.1109/iccv.2017.603

[7]

Bronstein A. (2008) 10.1007/978-0-387-73301-2_12

[8]

S.Zuffi A.Kanazawa D. W.Jacobs andM. J.Black “3D Menagerie: Modeling the 3D Shape and Pose of Animals ” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition (arXiv 2017) 6365–6373. 10.1109/cvpr.2017.586

[9]

X.Liu W.Jin andZ.Han “DT4D: A Large‐scale 4D Dataset for Dynamic Topology and Deformation ” preprint arXiv:2305.12345 May 19 2023.

[10]

Girouard A. "The Dirichlet‐to‐Neumann Map, the Boundary Laplacian, and Hörmander's Rediscovered Manuscript" Journal of Spectral Theory (2022) 10.4171/jst/399

[11]

Ezuz D. "Reversible Harmonic Maps Between Discrete Surfaces" ACM Transactions on Graphics (TOG) (2019) 10.1145/3202660

[12]

10.1111/cgf.12702

[13]

N.Donati A.Sharma andM.Ovsjanikov “Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence ” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (arXiv 2020) 8592–8601. 10.1109/cvpr42600.2020.00862

[14]

D.CaoandF.Bernard “Self‐supervised Learning for Multimodal Non‐rigid 3d Shape Matching ” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (arXiv 2023) 17735–17744. 10.1109/cvpr52729.2023.01701

[15]

Sharma A. "Weakly Supervised Deep Functional Maps for Shape Matching" Advances in Neural Information Processing Systems (2020)

[16]

S.Attaiki G.Pai andM.Ovsjanikov “DPFM: Deep Partial Functional Maps ” inProceedings of the2021 International Conference on 3D Vision (3DV) (IEEE 2021) 175–185. 10.1109/3dv53792.2021.00040

[17]

J.‐M.Roufosse A.Sharma andM.Ovsjanikov “Unsupervised Deep Learning for Structured Shape Matching ” inProceedings of the IEEE/CVF International Conference on Computer Vision (arXiv 2019) 1617–1627. 10.1109/iccv.2019.00170

[18]

D.CaoandF.Bernard “Unsupervised Deep Multi‐shape Matching ” inProceedings of theEuropean Conference on Computer Vision (Springer 2022) 55–71. 10.1007/978-3-031-20062-5_4

[19]

Sharp N. "Diffusionnet: Discretization Agnostic Learning on Surfaces" ACM Transactions on Graphics (TOG) (2022) 10.1145/3507905

[20]

Raganato A. "Attention and Positional Encoding Are (almost) All You Need for Shape Matching" Computer Graphics Forum (2023) 10.1111/cgf.14912

[21]

H.Huang S.Yuan C.Wen Y.Hao andY.Fang “3d‐trans: 3d Hierarchical Transformer for Shape Correspondence Learning ” inProceedings of the2024 10th International Conference on Automation Robotics and Applications (ICARA) (IEEE 2024) 536–540. 10.1109/icara60736.2024.10552931

[22]

F.LuoQ.LiL.Hu et al. “Deep Frequency‐Aware Functional Maps for Robust Shape Matching ” preprint arXiv:2402.03904 June 25 2024.

[23]

Li L. "Learning Multi‐resolution Functional Maps With Spectral Attention for Robust Shape Matching" Advances in Neural Information Processing Systems (2022)

[24]

Attaiki S. "Shape Non‐rigid Kinematics (SNK): A Zero‐shot Method for Non‐rigid Shape Matching via Unsupervised Functional Map Regularized Reconstruction" Advances in Neural Information Processing Systems (2023) 10.52202/075280-3068

[25]

D.Cao Z.Lähner andF.Bernard “Synchronous Diffusion for Unsupervised Smooth Non‐rigid 3d Shape Matching ” inProceedings of theEuropean Conference on Computer Vision (Springer 2024) 262–281. 10.1007/978-3-031-72652-1_16

[26]

Viganò G. "NAM: Neural Adjoint Maps for Refining Shape Correspondences" ACM Transactions on Graphics (TOG) (2025) 10.1145/3730943

[27]

A shortest augmenting path algorithm for dense and sparse linear assignment problems

R. Jonker, A. Volgenant

Computing 1987 10.1007/bf02278710

[28]

Botsch M. (2010) 10.1201/b10688

[29]

Bunge A. "Polygon laplacian Made Simple" Computer Graphics Forum (2020) 10.1111/cgf.13931

[30]

Sauter S. A. (2010) 10.1007/978-3-540-68093-2_4

[31]

Guilemin V. (2010) 10.1090/chel/370

[32]

Y.Chen B.Fernando H.Bilen T.Mensink andE.Gavves “Neural Feature Matching in Implicit 3d Representations ” inProceedings of theThirty‐Eighth International Conference on Machine Learning (PMLR 2021) 1582–1593.

[33]

Su J. "Roformer: Enhanced Transformer With Rotary Position Embedding" Neurocomputing (2024) 10.1016/j.neucom.2023.127063

[34]

Li Y. "Learnable Fourier Features for Multi‐dimensional Spatial Positional Encoding" Advances in Neural Information Processing Systems (2021)

[35]

P.Wang “Bidirectional Cross Attention ”Github Repository https://github.com/lucidrains/bidirectional‐cross‐attention.

[36]

Schuster T. "Confident Adaptive Language Modeling" Advances in Neural Information Processing Systems (2022)

[37]

M.Elbayad J.Gu E.Grave andM.Auli “Depth‐Adaptive Transformer ” preprint arXiv:1910.10073 October 22 2019.

[38]

S.Teerapittayanon B.McDanel andH.‐T.Kung “Branchynet: Fast Inference via Early Exiting From Deep Neural Networks ” inProceedings of the2016 23rd International Conference on Pattern Recognition (ICPR) (IEEE 2016) 2464–2469. 10.1109/icpr.2016.7900006

[39]

Z.Liu Z.Xu H.‐J.Wang T.Darrell andE.Shelhamer “Anytime Dense Prediction With Confidence Adaptivity ” preprint arXiv:2104.00749 April 1 2021.

[40]

J.Wubben J. M.Cecilia C. T.Calafate J.‐C.Cano andP.Manzoni “Evaluating the Effectiveness of Takeoff Assignment Strategies Under Irregular Configurations ” inProceedings of the2021 IEEE/ACM 25th International Symposium on Distributed Simulation and Real Time Applications (DS‐RT) (IEEE 2021) 1–7. 10.1109/ds-rt52167.2021.9576125

[41]

Kim V. G. "Blended Intrinsic Maps" ACM Transactions on Graphics (TOG) (2011) 10.1145/2010324.1964974

[42]

Dao T. "Flashattention: Fast and Memory‐Efficient Exact Attention With IO‐awareness" Advances in Neural Information Processing Systems (2022) 10.52202/068431-1189

[43]

Deep Residual Learning for Image Recognition

Kaiming He, Xiangyu Zhang, Shaoqing Ren et al.

2016 IEEE Conference on Computer Vision and Patter... 10.1109/cvpr.2016.90

[44]

A.Vaswani G.Shazeer N.Parmar et al. “Attention Is All You Need ” inProceedings of the Advances in Neural Information Processing Systems 30 eds.I.Guyon U. V.Luxburg S.Bengio et al. 5998–6008.Curran Associates Inc. 2017.

[45]

Approximation capabilities of multilayer feedforward networks

Kurt Hornik

Neural Networks 1991 10.1016/0893-6080(91)90009-t

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Details

Published: Jan 01, 2026
Vol/Issue: 20(1)
License: View

Authors

A

Amirreza Amirfathiyan

Computer Vision Research Laboratory, Faculty of Electrical and Computer Engineering Tabriz (Sahand) University of Technology Tabriz Iran

H

Hossein Ebrahimnezhad

Computer Vision Research Laboratory, Faculty of Electrical and Computer Engineering Tabriz (Sahand) University of Technology Tabriz Iran

Cite This Article

Amirreza Amirfathiyan, Hossein Ebrahimnezhad (2026). TransLAP: Non‐Isometric Shape Matching Using Transformer Based Linear Assignment Problem. IET Image Processing, 20(1). https://doi.org/10.1049/ipr2.70333

TransLAP: Non‐Isometric Shape Matching Using Transformer Based Linear Assignment Problem

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