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REVIEW 3 major objections 4 minor 83 references

Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read A topology-adaptive deformation model can match 3D meshes with topological artifacts without any learned prior, and reports tighter 3D alignment than trained baselines on noisy benchmarks.

desk verdict The topology-adaptive deformation model is a genuine new contribution, but the paper's headline claim of beating trained methods rests on Chamfer distance alone, while the standard correspondence metric (MGE) shows the opposite. read the letter →

arxiv 2509.06862 v1 pith:5JUHXSV5 submitted 2025-09-08 cs.CV

Aymen Merrouche , Stefanie Wuhrer , Edmond Boyer This is my paper · ORCID
classification cs.CV
keywords 3Dshapematchingtopologicalartifactsas-rigid-as-possibledeformationneuralsigneddistancefieldbijectiveassociationssilhouettelossnon-rigidregistrationmeshtopologyadaptation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Non-rigid mesh matching usually assumes the deformation between two shapes is near-isometric or as-rigid-as-possible, but real scans from multi-view reconstruction often have topological artifacts—glued hands, closed ankles—that break both assumptions. The paper proposes a topology-adaptive deformation model that removes the assumption by allowing the template mesh itself to change topology while it is being deformed to match two shapes. In the proposed optimization, the template is represented twice: as a mesh for patch-wise ARAP deformations under bijective associations, and as a neural signed-distance field whose zero level set can be edited and re-meshed when alignment fails. The central claim is that this training-free strategy handles highly non-isometric shapes and noisy per-frame reconstructions, and reports tighter 3D alignment (lower Chamfer distance) than learning-based baselines on topological benchmarks, although its ground-truth correspondence error is higher on clean benchmarks.

What carries the argument

The central machinery is a dual representation of the template: a triangle mesh with a patch-wise rigid deformation model (ARAP, with rotations and translations per patch blended by distances), and a neural signed-distance field (a feature volume plus an MLP) whose zero level set is re-meshed after each topology update. The two are connected by differentiable iso-surface extraction, which converts vertex-level silhouette gradients into SDF parameter updates, so a topology edit is a gradient step in the space of implicit surfaces. Associations are kept bijective by representing them as a doubly stochastic patch-association matrix whose rows and columns sum to one, produced by a Sinkhorn proje

What would settle it

Take two meshes with known ground-truth correspondences where one has a glued hand, run the optimization with the template initialized as the glue-affected mesh, and check whether the accepted topology edits remove the glue and reduce geodesic error. If the edits reduce silhouette loss but leave geodesic error unchanged or worse, or if no edit is accepted, the claimed topology-adaptive mechanism is not what produces the alignment.

Watch

Extended reading notes

Core claim

The core claim is that topological differences between two shapes can be resolved during matching rather than repaired beforehand: the optimization grows, cuts, or reconnects regions of a template when the ARAP deformation under bijective associations cannot align them with the target. Topology edits are driven by a silhouette loss between the deformed template and the target; gradients with respect to template vertices are pushed through differentiable iso-surface extraction into the parameters of a neural signed-distance field, and the edited surface is extracted by marching cubes. An edit is accepted only when it lowers the total silhouette mismatch, which prevents the local patch-neighbo

Load-bearing premise

The load-bearing premise is that the silhouette loss points to the exact places where the template's topology is wrong, so editing the neural field along that gradient improves the true correspondences—and the greedy acceptance rule does not trap the search in a worse local topology.

Editorial extensions

If this is right

  • Mesh matching with topological artifacts no longer needs a separate preprocessing repair step; the optimiser can split or reattach regions when the ARAP deformation under bijective associations is infeasible.
  • Because no training data is used, the method is applicable to shape classes or acquisition settings for which no pre-trained correspondence model exists, such as per-frame multi-view reconstructions of moving people.
  • The template found by the optimization is itself an output: it shows which regions of the source had to be topologically edited to achieve the alignments, which can be read as a form of automatic artifact detection.
  • The method's 3D alignment quality on topological benchmarks is reported as better than learning-based baselines, while its geodesic error remains higher; this places the contribution in alignment quality rather than in semantic correspondence accuracy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: using a symmetry-aware or geodesic-consistency term to score topology edits could suppress the left-right flips the paper reports, since those flips lower Chamfer distance but greatly increase geodesic error.
  • Editorial inference: the greedy hill-climbing acceptance rule implies the result depends on the initial template and on the order of viewpoints; running the optimization with both input meshes as template and merging the two alignments could escape some local topology minima.
  • Editorial inference: the same topology-adaptive deformation model could be used beyond matching, for example to evolve a template through a sequence of per-frame reconstructions, which the authors name as future work.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper targets dense non-rigid mesh matching when the input meshes contain topological artifacts. It proposes a topology-adaptive deformation model that alternates between (i) finding bijective patch-level associations between a template and both input meshes, (ii) deforming the template with a patch-wise ARAP model, and (iii) editing the template's topology through its neural SDF representation using a silhouette-based objective. Correspondences are then extracted from the two deformed templates. The method is evaluated on FAUST, SCAPE, SMAL, a topologically corrupted subset of ExtFAUST, and 4DHumanOutfit, and compared with functional-map and deformation-guided baselines. The paper's central claim is that, without any data-driven prior, the method achieves better 3D alignment quality (measured by Chamfer distance) than learning-based methods, while being competitive on correspondence quality.

Significance. If the main claim holds, this is a useful contribution: it offers a purely optimization-based alternative to learning-based mesh matching that can explicitly adapt topology, which is relevant for real-world multi-view reconstructions. The paper is clearly written, the ablation study is informative, and the code is publicly announced. The idea of using neural SDF edits to resolve topological obstructions inside an ARAP alignment loop is original and worth publishing. However, the headline advantage over learned methods is metric-dependent and currently overstated: the Chamfer distance improvements are accompanied by worse mean geodesic error on the same benchmarks, and the topology-update acceptance rule is based on silhouette overlap, which the paper's own failure analysis shows can improve while correspondence quality degrades. The central mechanism is plausible but the evidence for the strongest claim needs to be rebalanced and quantified.

major comments (3)
  1. [Abstract; Table 2] The claim that the method 'even outperform[s] methods trained on large datasets in 3D alignment quality' rests entirely on Chamfer distance. On the same topology-corrupted benchmarks, the proposed method has worse MGE than Merrouche et al. (ExtFAUST: 8.74 vs. 7.32; 4DHumanOutfit: 13.31 vs. 6.15). MGE is the standard correspondence-quality metric, and Chamfer distance is not the objective being optimized. Please qualify the abstract/conclusion claim, report both metrics together, state the number of test pairs, and provide error bars or a significance test. It would also be informative to report the CD/MGE numbers after excluding left-right flip cases (Fig. 3), since those flips are acknowledged to lower CD while increasing MGE.
  2. [Sec. 3.1.3; Algorithm 1 (lines 24-35); Fig. 3; Fig. 12] Topology updates are accepted based solely on the silhouette loss. The paper's own examples show that this criterion can improve geometric overlap while degrading correspondences: Fig. 3 shows a left-right flip with smaller Chamfer distance and significantly larger MGE, and Fig. 12 documents accepted topology edits that create disconnected components or suboptimal cuts. Since the topology-adaptive deformation is the main novelty, the acceptance criterion should either incorporate a correspondence-aware or symmetry-aware term, or the paper should quantify how often such flips/failure cases occur in the reported averages and show that the CD advantage is not driven by them.
  3. [Sec. 3.2; Algorithm 1; Sec. 8.6] The text says the template is initialized as either M or N, but Algorithm 1 and Sec. 8.6 fix T0 = M, and topology updates use only l_topo(N, \tilde T_N^i). This asymmetry is not discussed or justified. Because the template choice and the one-sided topology editing can bias the extracted correspondences, the paper should either evaluate both initializations or explicitly justify the fixed choice. As written, the claim that the method is initialization-agnostic is not supported.
minor comments (4)
  1. [Sec. 3.1.3] Typo: 'neural filed representation' should be 'neural field representation'. Also, 'm-cubes' is used as a shorthand for marching cubes without defining it at first use.
  2. [Supplementary Fig. 6] The caption and surrounding text contain missing numbers ('with vertices', 'with vertices'), apparently due to a compilation issue. Please fix so the discretization experiment is readable.
  3. [Eq. (9)] The displayed equation for l_sil has a line break and extra parentheses that make it hard to parse. Please re-set it cleanly.
  4. [Sec. 4] The runtime (54 min per pair on ExtFAUST/4DHumanOutfit) is mentioned only in the supplementary. Since the method is optimization-based, a comparison of runtime with the learning-based baselines (including their test-time optimization) would help calibrate the practical contribution.

Circularity Check

0 steps flagged · score 0.0 of 10

No load-bearing circularity: the method is an iterative geometric optimization, and the reported CD/MGE metrics are measurements of its outputs, not quantities fitted by construction.

full rationale

The claimed contribution is an optimization procedure (Alg. 1) that alternates between association search (Eq. 2), ARAP-aware deformation (Eq. 8), and topology edits (Eq. 10). Each objective is a geometric loss over silhouette overlap, rigidity, bijectivity, and regularization; none of these losses is fit to the reported Chamfer distance or mean geodesic error and then renamed a prediction. Correspondences are extracted from the optimized template via nearest-neighbor projection (Alg. 1, line 43), so the output is directly produced by optimization rather than being equivalent to an input constant. The self-citations to Merrouche et al. [52] provide the patch-based GNN parametrization and the baseline/evaluation fittings on 4DHumanOutfit; these are supporting implementation or comparison details, not a derivation chain that forces the central claim. In fact, the paper's own Fig. 3 and ablation Table 3 show that CD can improve while MGE worsens, demonstrating that the CD advantage is not a metric optimized by construction and that evaluation validity, not circularity, is the relevant risk.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The method is an optimization with many hand-set hyperparameters (loss weights, patch count, iterations, viewpoints). The most consequential assumptions are that silhouette supervision can drive topology edits toward correct correspondences and that the GNN parameterizations remain stable enough under topology edits. The paper does not introduce new physical entities.

free parameters (9)
  • Patch count L = 200
    Chosen by hand; controls granularity of associations and deformations (Sec. 8.2).
  • Neural field fitting weights lambda_1..lambda_4 = 1, 1e-1, 5e4, 1e-4
    Hand-set weights in Eq. 1 (Sec. 8.1).
  • Association loss weights gamma_1, gamma_2 = 1e4, 5e3
    Hand-set weights in Eq. 2 (Sec. 8.3).
  • Deformation loss weights beta_1, beta_2, beta_3 = 1e4, 5e2, 1e6
    Hand-set weights in Eq. 8 (Sec. 8.4).
  • Topology loss weights alpha_1..alpha_4 = 1, 5e2, 2, 5e4
    Hand-set weights in Eq. 10 (Sec. 8.5).
  • Tolerance tau in l_min = 2e-4
    Hand-set in Sec. 8.5; bounds template deviation from original.
  • Number of viewpoints |Omega| = 50
    Hand-set for silhouette supervision (Sec. 8.4).
  • Optimization schedule n, n_top, K, n1, n2, n3 = 500/2000, 300, 10, 1, 10, 5
    Hand-set in Sec. 8.6; controls iteration counts and topology update frequency.
  • SDF feature volume resolution and feature size = 128x128x128, feature size 8
    Hand-set in Sec. 8.1.
assumptions (5)
  • domain assumption Input shapes are 2D manifolds embedded in 3D, discretized as triangle meshes.
    Assumed in Sec. 3; the method operates on triangle meshes.
  • domain assumption The deformation induced by ground-truth correspondences is approximately ARAP except where topology impedes alignment.
    Motivates the ARAP deformation model and its limitations; stated in Sec. 1.
  • domain assumption Silhouette loss is a sufficient surrogate for 3D alignment to guide both deformation and topology edits.
    Used in Eqs. 8-10; the paper's failure cases and left-right flip cast doubt on this assumption.
  • domain assumption Editing the neural SDF and re-extracting the mesh with marching cubes yields a valid 2D manifold discretization, and gradients through MeshSDF are usable.
    Invoked in Sec. 3.1.3 and via MeshSDF [58] in Sec. 8.6.
  • domain assumption The GNN parametrization of associations and deformations remains sufficiently robust under topology changes for the greedy hill-climbing optimization to work.
    The paper states topology changes affect receptive fields (Sec. 3.1.3) and relies on the greedy acceptance rule to mitigate this.

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Pith. "Pith review of Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach." pith.science (2026). https://pith.science/paper/5JUHXSV5

@misc{pith2026250906862,
  author       = {Pith},
  title        = {Pith review of: Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5JUHXSV5}},
  note         = {Machine review of arXiv:2509.06862}
}
read the original abstract

Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps assume the deformation induced by the ground truth correspondences to be near-isometric, ARAP-like deformation-guided approaches assume the latter to be ARAP. Neither assumption holds in certain topological configurations of the input shapes. We are motivated by real-world scenarios such as per-frame multi-view reconstructions, often suffering from topological artefacts. To this end, we propose a topology-adaptive deformation model allowing changes in shape topology to align shape pairs under ARAP and bijective association constraints. Using this model, we jointly optimise for a template mesh with adequate topology and for its alignment with the shapes to be matched to extract correspondences. We show that, while not relying on any data-driven prior, our approach applies to highly non-isometric shapes and shapes with topological artefacts, including noisy per-frame multi-view reconstructions, even outperforming methods trained on large datasets in 3D alignment quality.

Figures

Figures reproduced from arXiv: 2509.06862 by the authors.

Figure 1
Figure 1. To match two meshes M and N with topological arte￾facts (see red boxes), we jointly optimise for a template T , ini￾tialised as either M or N , and its alignments T˜M and T˜N with Mand N using a novel topology adaptive deformation model (see green box) under ARAP and bijective associations constraints. We are motivated by real-world scenarios such as per￾frame multi-view reconstructions, which, despite achieving str… view at source ↗
Figure 2
Figure 2. Given M and N with topological artefacts (glued hands in M), we optimise for a template T and its alignments T˜M and T˜N with M, N . With T initialised as M or N , we alternate between: 1. Finding associations Π T ,M , Π T ,N between T and M, N as small matrices under a bijectivity constraint (red block), 2. Finding the best ARAP alignments T˜M, T˜N between T and M, N under these associations (blue block), 3. Editin… view at source ↗
Figure 3
Figure 3. When a plausible alignment is possible, our approach [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (9 more)
Figure 5
Figure 5. Figure 5: Qualitative ablation results on an example from [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 7
Figure 7. Figure 7: Correspondences and deformation results on examples [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Correspondences and deformation results on examples [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Correspondences and deformation results on examples [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 11
Figure 11. Figure 11: Correspondence results on 4DHumanOutfit (top and [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 14
Figure 14. Figure 14: , it uses the graph convolution operator from [72]. The individual loss term weights in Eq. 2 are fixed to γ1 = 1e4, γ2 = 5e3. ReLU Conv(32,64) ReLU Conv(6,32) Patch-Wise Max Pool [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]
Figure 12
Figure 12. Figure 12: Examples where the topology optimisation strategy [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]
Figure 13
Figure 13. Figure 13: SΣ’s architecture. 8.2. Patch Decomposition To obtain the surface patches (Pk)1≤k≤L, we employ a fur￾thest point sampling like strategy using geodesic distances, similarly to [52]. In all our experiments, we use L = 200 surface patches. 8.3. Association Model The asso…
Figure 16
Figure 16. Figure 16: Periodic weighting scheme wK(i). As shown in [PITH_FULL_IMAGE:figures/full_fig_p016_16.png]

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Reference graph

Works this paper leans on

83 extracted references · 77 canonical work pages

  1. [1]

    Zero-shot 3d shape correspon- dence

    Ahmed Abdelreheem, Abdelrahman Eldesokey, Maks Ovs- janikov, and Peter Wonka. Zero-shot 3d shape correspon- dence. InSIGGRAPH Asia, 2023. 3

    2023

  2. [2]

    Skeleton- aware networks for deep motion retargeting.ACM Transac- tions on Graphics (ToG), 2020

    Kfir Aberman, Peizh Uo Li, Dani Lischinski, Olga Sorkine- Hornung, Daniel Cohen-Or, and Baoquan Chen. Skeleton- aware networks for deep motion retargeting.ACM Transac- tions on Graphics (ToG), 2020. 1

    2020

  3. [3]

    Ranking via sinkhorn propagation.arXiv preprint arXiv:1106.1925,

    Ryan Prescott Adams and Richard S Zemel. Ranking via sinkhorn propagation.arXiv preprint arXiv:1106.1925,

    arXiv 1925

  4. [4]

    Optimal step nonrigid icp algorithms for surface registration

    Brian Amberg, Sami Romdhani, and Thomas Vetter. Optimal step nonrigid icp algorithms for surface registration. InCon- ference on Computer Vision and Pattern Recognition, 2007. 2

    2007

  5. [5]

    Scape: Shape completion and animation of people.ACM Transactions on Graphics (TOG), 2005

    Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Se- bastian Thrun, Jim Rodgers, and James Davis. Scape: Shape completion and animation of people.ACM Transactions on Graphics (TOG), 2005. 7, 2

    work page 2005

  6. [6]

    4dhumanoutfit: a multi-subject 4d dataset of human motion sequences in varying outfits exhibiting large displacements.Computer Vision and Image Understanding,

    Matthieu Armando, Laurence Boissieux, Edmond Boyer, Jean-S´ebastien Franco, Martin Humenberger, Christophe Legras, Vincent Leroy, Mathieu Marsot, Julien Pansiot, Sergi Pujades, et al. 4dhumanoutfit: a multi-subject 4d dataset of human motion sequences in varying outfits exhibiting large displacements.Computer Vision and Image Understanding,

    work page

  7. [7]

    The wave kernel signature: A quantum mechanical approach to shape analysis

    Mathieu Aubry, Ulrich Schlickewei, and Daniel Cremers. The wave kernel signature: A quantum mechanical approach to shape analysis. InInternational Conference on Computer Vision, 2011. 2

    work page 2011

  8. [8]

    Neural human deformation transfer

    Jean Basset, Adnane Boukhayma, Stefanie Wuhrer, Franck Multon, and Edmond Boyer. Neural human deformation transfer. InInternational Conference on 3D Vision, 2021. 1, 7, 2

    work page 2021

Show all 83 references
  1. [9]

    Hybrid functional maps for crease-aware non- isometric shape matching

    Lennart Bastian, Yizheng Xie, Nassir Navab, and Zorah L¨ahner. Hybrid functional maps for crease-aware non- isometric shape matching. InConference on Computer Vi- sion and Pattern Recognition, 2024. 3, 7, 8, 2

    2024

  2. [10]

    Besl and Neil D

    Paul J. Besl and Neil D. McKay. A method for registration of 3-d shapes.IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992. 2

    1992

  3. [11]

    Biasotti, A

    S. Biasotti, A. Cerri, A. Bronstein, and M. Bronstein. Recent trends, applications, and perspectives in 3d shape similarity assessment.Computer Graphics Forum, 2016. 2

    2016

  4. [12]

    Federica Bogo, Javier Romero, Matthew Loper, and Michael J. Black. FAUST: Dataset and evaluation for 3D mesh registration. InConference on Computer Vision and Pattern Recognition, 2014. 7, 2

    2014

  5. [13]

    Boscaini, J

    D. Boscaini, J. Masci, E. Rodol `a, M. M. Bronstein, and D. Cremers. Anisotropic diffusion descriptors.Computer Graphics Forum, 2016. 2

    2016

  6. [14]

    Learning shape correspondence with anisotropic convolutional neural networks

    Davide Boscaini, Jonathan Masci, Emanuele Rodol `a, and Michael Bronstein. Learning shape correspondence with anisotropic convolutional neural networks. InAdvances in Neural Information Processing Systems, 2016. 2

    2016

  7. [15]

    Bronstein, Michael M

    Alexander M. Bronstein, Michael M. Bronstein, and Ron Kimmel. Generalized multidimensional scaling: A frame- work for isometry-invariant partial matching.Proceedings of the National Academy of Sciences of the United States of America, 2006. 2

    2006

  8. [16]

    Bronstein, Michael M

    Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel, Mona Mahmoudi, and Guillermo Sapiro. A gromov-hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching.Interna- tional Journal of Computer Vision, 2010. 2

    2010

  9. [17]

    Free- form mesh tracking: a patch-based approach

    Cedric Cagniart, Edmond Boyer, and Slobodan Ilic. Free- form mesh tracking: a patch-based approach. InConference on Computer Vision and Pattern Recognition, 2010. 3, 5

    2010

  10. [18]

    Unsupervised deep multi-shape matching

    Dongliang Cao and Florian Bernard. Unsupervised deep multi-shape matching. InLecture Notes in Computer Sci- ence (including subseries Lecture Notes in Artificial Intelli- gence and Lecture Notes in Bioinformatics), 2022. 3, 5, 7

    2022

  11. [19]

    Self-supervised learn- ing for multimodal non-rigid 3d shape matching

    Dongliang Cao and Florian Bernard. Self-supervised learn- ing for multimodal non-rigid 3d shape matching. InConfer- ence on Computer Vision and Pattern Recognition, 2023. 3, 5

    2023

  12. [20]

    Spectral meets spatial: Harmonising 3d shape matching and interpolation

    Dongliang Cao, Marvin Eisenberger, Nafie El Amrani, Daniel Cremers, and Florian Bernard. Spectral meets spatial: Harmonising 3d shape matching and interpolation. InCon- ference on Computer Vision and Pattern Recognition, 2024. 1, 3, 7, 8, 2

    2024

  13. [21]

    Unsu- pervised learning of robust spectral shape matching.ACM Transactions on Graphics (ToG), 2023

    Dongliang Cao, Paul Roetzer, and Florian Bernard. Unsu- pervised learning of robust spectral shape matching.ACM Transactions on Graphics (ToG), 2023. 3, 7, 8, 2

    2023

  14. [22]

    R. R. Coifman, S. Lafon, A. B. Lee, M. Maggioni, B. Nadler, F. Warner, and S. W. Zucker. Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffu- sion maps.Proceedings of the National Academy of Sciences of the United States of America, 2005. 2

    2005

  15. [23]

    Dyke, and Juyong Zhang

    Bailin Deng, Yuxin Yao, Roberto M. Dyke, and Juyong Zhang. A survey of non-rigid 3d registration.Computer Graphics Forum, 2022. 2

    2022

  16. [24]

    Learning elemen- tary structures for 3d shape generation and matching

    Theo Deprelle, Thibault Groueix, Matthew Fisher, Vladimir Kim, Bryan Russell, and Mathieu Aubry. Learning elemen- tary structures for 3d shape generation and matching. InAd- vances in Neural Information Processing Systems, 2019. 2

    2019

  17. [25]

    Deep orientation-aware functional maps: Tackling symme- try issues in shape matching

    Nicolas Donati, Etienne Corman, and Maks Ovsjanikov. Deep orientation-aware functional maps: Tackling symme- try issues in shape matching. InConference on Computer Vision and Pattern Recognition, 2022. 3, 7, 2

    2022

  18. [26]

    Deep geometric functional maps: Robust feature learning for shape correspondence

    Nicolas Donati, Abhishek Sharma, and Maks Ovsjanikov. Deep geometric functional maps: Robust feature learning for shape correspondence. InConference on Computer Vision and Pattern Recognition, 2020. 3

    2020

  19. [27]

    Spectral teacher for a spatial student: Spectrum-aware real-time dense shape correspondence

    Omri Efroni, Dvir Ginzburg, and Dan Raviv. Spectral teacher for a spatial student: Spectrum-aware real-time dense shape correspondence. InInternational Conference on 3D Vision,

  20. [28]

    Eisenberger, D

    M. Eisenberger, D. Novotny, G. Kerchenbaum, P. Labatut, N. Neverova, D. Cremers, and A. Vedaldi. Neuromorph: Unsupervised shape interpolation and correspondence in one go. InConference on Computer Vision and Pattern Recogni- tion, 2021. 1, 2, 3, 7

    2021

  21. [29]

    Smooth shells: Multi-scale shape registration with functional maps

    Marvin Eisenberger, Zorah Lahner, and Daniel Cremers. Smooth shells: Multi-scale shape registration with functional maps. InConference on Computer Vision and Pattern Recog- nition, 2020. 3, 7

    2020

  22. [30]

    Deep shells: Unsupervised shape corre- spondence with optimal transport

    Marvin Eisenberger, Aysim Toker, Laura Leal-Taix ´e, and Daniel Cremers. Deep shells: Unsupervised shape corre- spondence with optimal transport. InAdvances in Neural information processing systems, 2020. 1, 3, 7

    2020

  23. [31]

    On bending invariant sig- natures for surfaces.Transactions on Pattern Analysis and Machine Intelligence, 2003

    Asi Elad Elbaz and Ron Kimmel. On bending invariant sig- natures for surfaces.Transactions on Pattern Analysis and Machine Intelligence, 2003. 2

    2003

  24. [32]

    Cyclic functional mapping: Self-supervised correspondence between non-isometric de- formable shapes

    Dvir Ginzburg and Dan Raviv. Cyclic functional mapping: Self-supervised correspondence between non-isometric de- formable shapes. InEuropean Conference on Computer Vi- sion, 2020. 3

    2020

  25. [33]

    3d-coded: 3d cor- respondences by deep deformation

    Thibault Groueix, Matthew Fisher, Vladimir G Kim, Bryan C Russell, and Mathieu Aubry. 3d-coded: 3d cor- respondences by deep deformation. InEuropean Conference on Computer Vision, 2018. 2

    2018

  26. [34]

    Kim, Bryan C

    Thibault Groueix, Matthew Fisher, Vladimir G. Kim, Bryan C. Russell, and Mathieu Aubry. A papier-mache ap- proach to learning 3d surface generation. InConference on Computer Vision and Pattern Recognition, 2018. 2

    2018

  27. [35]

    Unsupervised cycle- consistent deformation for shape matching.Computer Graphics Forum, 2019

    Thibault Groueix, Matthew Fisher, Vladimir G Kim, Bryan C Russell, and Mathieu Aubry. Unsupervised cycle- consistent deformation for shape matching.Computer Graphics Forum, 2019. 2

    2019

  28. [36]

    Unsupervised learning of dense shape correspondence

    Oshri Halimi, Or Litany, Emanuele Rodola, Alex M Bron- stein, and Ron Kimmel. Unsupervised learning of dense shape correspondence. InConference on Computer Vision and Pattern Recognition, 2019. 3

    2019

  29. [37]

    Arc-flow: Articulated, resolution-agnostic, correspondence-free matching and interpolation of 3d shapes under flow fields

    Adam Hartshorne, Allen Paul, Tony Shardlow, and Neill DF Campbell. Arc-flow: Articulated, resolution-agnostic, correspondence-free matching and interpolation of 3d shapes under flow fields. InInternational Conference on 3D Vision,

  30. [38]

    Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980,

    Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980,

    arXiv

  31. [39]

    Modular primitives for high-performance differentiable rendering.ACM Transac- tions on Graphics (ToG), 2020

    Samuli Laine, Janne Hellsten, Tero Karras, Yeongho Seol, Jaakko Lehtinen, and Timo Aila. Modular primitives for high-performance differentiable rendering.ACM Transac- tions on Graphics (ToG), 2020. 5

    2020

  32. [40]

    Dpc: Unsupervised deep point correspondence via cross and self construction

    Itai Lang, Dvir Ginzburg, Shai Avidan, and Dan Raviv. Dpc: Unsupervised deep point correspondence via cross and self construction. InInternational Conference on 3D Vision,

  33. [41]

    Learning multi-resolution functional maps with spectral attention for robust shape matching

    Lei Li, Nicolas Donati, and Maks Ovsjanikov. Learning multi-resolution functional maps with spectral attention for robust shape matching. InAdvances in Neural Information Processing Systems, 2022. 1, 3, 7

    2022

  34. [42]

    Pmnet: Learning of disentangled pose and movement for unsuper- vised motion retargeting

    Jongin Lim, Hyung Jin Chang, and Jin Young Choi. Pmnet: Learning of disentangled pose and movement for unsuper- vised motion retargeting. InBritish Machine Vision Confer- ence, 2020. 1

    2020

  35. [43]

    Deep functional maps: Structured prediction for dense shape correspondence

    Or Litany, Tal Remez, Emanuele Rodola, Alex Bronstein, and Michael Bronstein. Deep functional maps: Structured prediction for dense shape correspondence. InInternational Conference on Computer Vision, 2017. 1, 3

    2017

  36. [44]

    Bronstein, and Michael M

    Roee Litman, Alexander M. Bronstein, and Michael M. Bronstein. Diffusion-geometric maximally stable compo- nent detection in deformable shapes. InComputers and Graphics (Pergamon), 2011. 2

    2011

  37. [45]

    Smpl: A skinned multi- person linear model.ACM Transactions on Graphics (ToG),

    Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll, and Michael J Black. Smpl: A skinned multi- person linear model.ACM Transactions on Graphics (ToG),

  38. [46]

    Lorensen and Harvey E

    William E. Lorensen and Harvey E. Cline. Marching cubes: A high resolution 3d surface construction algorithm.ACM SIGGRAPH Computer Graphics, 1987. 3, 4, 6

    1987

  39. [47]

    Memory-scalable and simplified functional map learning

    Robin Magnet and Maks Ovsjanikov. Memory-scalable and simplified functional map learning. InConference on Com- puter Vision and Pattern Recognition, 2024. 3, 7

    2024

  40. [48]

    Nicp: neural icp for 3d human registration at scale

    Riccardo Marin, Enric Corona, and Gerard Pons-Moll. Nicp: neural icp for 3d human registration at scale. InEuropean Conference on Computer Vision, 2024. 2

    2024

  41. [49]

    Bronstein, and Pierre Vandergheynst

    Jonathan Masci, Davide Boscaini, Michael M. Bronstein, and Pierre Vandergheynst. Geodesic convolutional neural networks on riemannian manifolds. InInternational Con- ference on Computer Vision, 2016. 2

    2016

  42. [50]

    Zoomout: Spectral upsampling for efficient shape correspondence

    Simone Melzi, Jing Ren, Emanuele Rodol `a, Abhishek Sharma, Peter Wonka, and Maks Ovsjanikov. Zoomout: Spectral upsampling for efficient shape correspondence. ACM Transactions on Graphics (ToG), 2019. 3, 7

    2019

  43. [51]

    Learning latent permutations with gumbel- sinkhorn networks

    Gonzalo Mena, David Belanger, Scott Linderman, and Jasper Snoek. Learning latent permutations with gumbel- sinkhorn networks. InInternational Conference on Learning Representations, 2018. 5

    2018

  44. [52]

    Deformation-guided unsuper- vised non-rigid shape matching

    Aymen Merrouche, Joao Pedro Cova Regateiro, Stefanie Wuhrer, and Edmond Boyer. Deformation-guided unsuper- vised non-rigid shape matching. InBritish Machine Vision Conference, 2023. 1, 2, 4, 5, 7, 8, 3

    2023

  45. [53]

    Discrete differential-geometry operators for triangu- lated 2-manifolds

    Mark Meyer, Mathieu Desbrun, Peter Schr ¨oder, and Alan H Barr. Discrete differential-geometry operators for triangu- lated 2-manifolds. InVisualization and mathematics III. Springer, 2003. 2

    2003

  46. [54]

    Bronstein

    Federico Monti, Davide Boscaini, Jonathan Masci, Emanuele Rodol`a, Jan Svoboda, and Michael M. Bronstein. Geometric deep learning on graphs and manifolds using mixture model cnns. InConference on Computer Vision and Pattern Recognition, 2017. 2

    2017

  47. [55]

    Functional maps: a flexible representation of maps between shapes.ACM Transactions on Graphics (ToG), 2012

    Maks Ovsjanikov, Mirela Ben-Chen, Justin Solomon, Adrian Butscher, and Leonidas Guibas. Functional maps: a flexible representation of maps between shapes.ACM Transactions on Graphics (ToG), 2012. 2

    2012

  48. [56]

    Computing discrete min- imal surfaces and their conjugates.Experimental Mathemat- ics, 1993

    Ulrich Pinkall and Konrad Polthier. Computing discrete min- imal surfaces and their conjugates.Experimental Mathemat- ics, 1993. 2

    1993

  49. [57]

    Building statistical shape spaces for 3d human modeling.Pattern Recognition, 2017

    Leonid Pishchulin, Stefanie Wuhrer, Thomas Helten, Chris- tian Theobalt, and Bernt Schiele. Building statistical shape spaces for 3d human modeling.Pattern Recognition, 2017. 1

    2017

  50. [58]

    Meshsdf: Differentiable iso-surface extraction

    Edoardo Remelli, Artem Lukoianov, Stephan Richter, Benoit Guillard, Timur Bagautdinov, Pierre Baque, and Pascal Fua. Meshsdf: Differentiable iso-surface extraction. InAdvances in Neural Information Processing Systems, 2020. 6, 5

    2020

  51. [59]

    Discrete optimization for shape matching.Com- puter Graphics Forum, 2021

    Jing Ren, Simone Melzi, Peter Wonka, and Maks Ovs- janikov. Discrete optimization for shape matching.Com- puter Graphics Forum, 2021. 3, 7

    2021

  52. [60]

    Continuous and orientation-preserving correspon- dences via functional maps.ACM Transactions on Graphics (ToG), 2018

    Jing Ren, Adrien Poulenard, Peter Wonka, and Maks Ovs- janikov. Continuous and orientation-preserving correspon- dences via functional maps.ACM Transactions on Graphics (ToG), 2018. 3, 7, 2

    2018

  53. [61]

    Dense non-rigid shape correspondence using random forests

    Emanuele Rodol `a, Samuel Rota Bul `o, Thomas Windheuser, Matthias Vestner, and Daniel Cremers. Dense non-rigid shape correspondence using random forests. InConference on Computer Vision and Pattern Recognition, 2014. 2

    2014

  54. [62]

    Unsupervised deep learning for structured shape matching

    Jean-Michel Roufosse, Abhishek Sharma, and Maks Ovs- janikov. Unsupervised deep learning for structured shape matching. InInternational Conference on Computer Vision,

  55. [63]

    Shot: Unique signatures of histograms for surface and tex- ture description.Computer Vision and Image Understand- ing, 2014

    Samuele Salti, Federico Tombari, and Luigi Di Stefano. Shot: Unique signatures of histograms for surface and tex- ture description.Computer Vision and Image Understand- ing, 2014. 2

    2014

  56. [64]

    Weakly supervised deep functional maps for shape matching

    Abhishek Sharma and Maks Ovsjanikov. Weakly supervised deep functional maps for shape matching. InAdvances in Neural Information Processing Systems, 2020. 3

    2020

  57. [65]

    As-rigid-as-possible surface modeling

    Olga Sorkine and Marc Alexa. As-rigid-as-possible surface modeling. InSymposium on Geometry processing, 2007. 1, 2

    2007

  58. [66]

    A concise and provably informative multi-scale signature based on heat diffusion.Computer Graphics Forum, 2009

    Jian Sun, Maks Ovsjanikov, and Leonidas Guibas. A concise and provably informative multi-scale signature based on heat diffusion.Computer Graphics Forum, 2009. 2

    2009

  59. [67]

    Spatially and spectrally consistent deep functional maps

    Mingze Sun, Shiwei Mao, Puhua Jiang, Maks Ovsjanikov, and Ruqi Huang. Spatially and spectrally consistent deep functional maps. InInternational Conference on Computer Vision, 2023. 3, 7

    2023

  60. [68]

    Implicit field supervision for robust non-rigid shape match- ing

    Ramana Sundararaman, Gautam Pai, and Maks Ovsjanikov. Implicit field supervision for robust non-rigid shape match- ing. InEuropean Conference on Computer Vision, 2022. 2

    2022

  61. [69]

    Shape registration in the time of transformers

    Giovanni Trappolini, Luca Cosmo, Luca Moschella, Ric- cardo Marin, Simone Melzi, and Emanuele Rodol `a. Shape registration in the time of transformers. InAdvances in Neu- ral Information Processing Systems, 2021. 2

    2021

  62. [70]

    A survey on shape correspondence

    Oliver van Kaick, Hao Zhang, Ghassan Hamarneh, and Daniel Cohen-Or. A survey on shape correspondence. In Eurographics Symposium on Geometry Processing, 2011. 2

    2011

  63. [71]

    Gomez, Łukasz Kaiser, and Illia Polosukhin

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszko- reit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. InAdvances in Neural Information Processing Systems, 2017. 2

    2017

  64. [72]

    Feast- net: Feature-steered graph convolutions for 3d shape analy- sis

    Nitika Verma, Edmond Boyer, and Jakob Verbeek. Feast- net: Feature-steered graph convolutions for 3d shape analy- sis. InConference on Computer Vision and Pattern Recogni- tion, 2018. 4

    2018

  65. [73]

    Efficient deformable shape correspondence via kernel matching

    Matthias Vestner, Zorah Lahner, Amit Boyarski, Or Litany, Ron Slossberg, Tal Remez, Emanuele Rodola, Alex Bron- stein, Michael Bronstein, Ron Kimmel, and Daniel Cre- mers. Efficient deformable shape correspondence via kernel matching. InInternational Conference on 3D Vision, 2018. 2

    2018

  66. [74]

    Product manifold filter: Non-rigid shape correspondence via kernel density estima- tion in the product space

    Matthias Vestner, Roee Litman, Emanuele Rodol `a, Alex Bronstein, and Daniel Cremers. Product manifold filter: Non-rigid shape correspondence via kernel density estima- tion in the product space. InConference on Computer Vision and Pattern Recognition, 2017. 2

    2017

  67. [75]

    Topology-adaptive mesh deformation for surface evolution, morphing, and multiview reconstruction.IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010

    Andrei Zaharescu, Edmond Boyer, and Radu Horaud. Topology-adaptive mesh deformation for surface evolution, morphing, and multiview reconstruction.IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010. 3

    2010

  68. [76]

    Surface feature detection and description with ap- plications to mesh matching

    Andrei Zaharescu, Edmond Boyer, Kiran Varanasi, and Radu Horaud. Surface feature detection and description with ap- plications to mesh matching. InConference on Computer Vision and Pattern Recognition, 2009. 2

    2009

  69. [77]

    Corrnet3d: Unsupervised end-to-end learning of dense correspondence for 3d point clouds

    Yiming Zeng, Yue Qian, Zhiyu Zhu, Junhui Hou, Hui Yuan, and Ying He. Corrnet3d: Unsupervised end-to-end learning of dense correspondence for 3d point clouds. InConference on Computer Vision and Pattern Recognition, 2021. 1, 2, 3

    2021

  70. [78]

    On the continuity of rotation representations in neural networks

    Yi Zhou, Connelly Barnes, Jingwan Lu, Jimei Yang, and Hao Li. On the continuity of rotation representations in neural networks. InConference on Computer Vision and Pattern Recognition, 2019. 4

    2019

  71. [79]

    Denoising functional maps: Diffusion models for shape cor- respondence

    Aleksei Zhuravlev, Zorah L ¨ahner, and Vladislav Golyanik. Denoising functional maps: Diffusion models for shape cor- respondence. InConference on Computer Vision and Pattern Recognition, 2025. 3, 7

    2025

  72. [80]

    3d menagerie: Modeling the 3d shape and pose of animals

    Silvia Zuffi, Angjoo Kanazawa, David W Jacobs, and Michael J Black. 3d menagerie: Modeling the 3d shape and pose of animals. InConference on Computer Vision and Pat- tern Recognition, 2017. 7, 2 Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided...

    2017

  73. [81]

    Additional Results 7.1. Ablation Studies We assess with ablations the added benefit of our approach’s core components: the bijective associations assumption, the as-rigid-as-possible deformation assumption and the adap- tive topology strategy. To ablate the bijective associati...

  74. [82]

    Neural Field Fitting The individual loss terms in the neural field fitting objective (Eq

    Implementation Details 8.1. Neural Field Fitting The individual loss terms in the neural field fitting objective (Eq. 1) are implemented as follows: lSDF (F,Σ) = 1 S SX j=1 (|SΣ(tri(F, xj ))−gt sd f(xj )|)(14) Target ULRSSM SmS Bastian et al. Merrouche et al. Ours Ours Merrouc...

  75. [83]

    Neural field fitting takes approximately4mnon an NVIDIA RTX A6000 GPU

    The neural field is optimised using Adam [38] for1500 iterations; the learning rate starts at 1e-3 and is halved at epochs 300, 600, 900, and 1200. Neural field fitting takes approximately4mnon an NVIDIA RTX A6000 GPU. Figure 12. Examples where the topology optimisation strate...

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.