Pith. sign in

REVIEW 3 major objections 5 minor 59 references

CoE: Deep Coupled Embedding for Non-Rigid Point Cloud Correspondences

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A single network, trained with an unsupervised loss and no ground-truth correspondences, learns per-point embeddings that stay coupled across non-rigidly deformed point clouds, so dense correspondences reduce to nearest-neighbor search.

desk verdict Solid, well-engineered coupled-embedding method that delivers on its benchmarks, but the 'unsupervised / raw point cloud' claim is weaker than it looks because the whole pipeline assumes pre-alignment. read the letter →

arxiv 2412.05557 v2 pith:FQ4BG4PE submitted 2024-12-07 cs.CV

Huajian Zeng , Maolin Gao , Daniel Cremers This is my paper · ORCID
classification cs.CV
keywords non-rigidshapematchingpointcloudcorrespondencedeepcoupledembeddingLaplace-Beltramioperatornearestneighborretrievalweaklysupervisedlearningfunctionalmapssegmentation
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

This paper claims that dense correspondences between non-rigidly deformed point clouds can be obtained directly from a single learned per-point embedding, with no ground-truth point pairs required at training time and no second feature-extraction network at inference time. The embedding is trained to behave like the eigenbasis of the Laplace–Beltrami operator, while a cross-attention block and a contrastive loss keep the embeddings of the two shapes mutually consistent. Matching is then a nearest-neighbor search in this common embedding space. On FAUST, SCAPE, SHREC19, TOPKIDS, and DT4D-M the reported mean geodesic errors are lower than all compared supervised and weakly supervised baselines, and the same embedding transfers to partial matching and to segmentation by clustering. A sympathetic reader would care because the claim replaces cascaded feature-learning and functional-map stages with one representation that is simple enough to deploy directly.

What carries the argument

The load-bearing object is the predicted coupled embedding pair $\Psi_S,\Psi_T$, a per-point map from raw coordinates into a common $k$-dimensional space, with $k=50$ in the experiments. An ASAP DiffusionNet feature extractor produces intermediate per-point embeddings, and a full bipartite cross-attention block then lets every point of each shape attend to every point of the other, which is what couples the two embeddings instead of computing them independently. The loss in Eq. (7) ties these embeddings to the Laplace–Beltrami eigenbasis: $L_{\mathrm{off}}=\sum_i\|\Psi_i^\top L_i\Psi_i-\Lambda_i\|_F$ forces approximate diagonalization and a frequency ordering, $L_o=\sum_i\|\Psi_i^\top M_i\Psi_i-I\|_F$ enforces a soft basis constraint, and $L_c=\|D_S^\top M_S\Psi_S-D_T^\top M_T\Psi_T\|_F$ couples the two embeddings by matching the Fourier coefficients of descriptor functions. At inference the same network embeds two new shapes and dense correspondences are read off by nearest-neighbor search in this common space.

What would settle it

Run the released network on the same FAUST test pairs under two conditions: with the published pre-alignment, and after applying a random rotation in $\mathrm{SO}(3)$ to the target shape while keeping the source fixed. If correspondence accuracy in the rotated condition falls to the level of nearest-neighbor matching on raw HKS features, then the claimed coupling exists only inside the pre-aligned frame, confirming the paper's stated limitation rather than a pose-invariant embedding.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that a canonical coupled embedding of a deformable shape can be learned from raw point clouds by a single network with shared weights, and that this embedding is strong enough to make dense correspondence a trivial retrieval task. The network is trained by minimizing the total loss of Eq. (7), which combines an off-diagonal term forcing each predicted embedding to approximately diagonalize its own Laplacian, an orthogonality term enforcing a basis-like structure, and a contrastive term driving the Fourier coefficients of cheap input descriptors such as HKS to agree between the two shapes. This is a learned relaxation of the classical coupled-diagonalization problem of Eq. (1), without the ground-truth correspondences and manifold optimization that the classical formulation requires. The paper reports that nearest-neighbor search in the learned embedding achieves lower mean geodesic error than the compared supervised and weakly supervised methods on near-isometric, non-isometric, and topology-noisy benchmarks, and that the embeddings remain usable when shapes are noised or presented as partial scans.

Load-bearing premise

The load-bearing premise is that every input shape is approximately rigidly pre-aligned to a common coordinate frame before training and inference, because the loss and the nearest-neighbor retrieval are not rotation- or translation-invariant.

Editorial extensions

If this is right

  • Dense correspondences for non-rigid point clouds reduce to one forward pass through a single network followed by nearest-neighbor search, removing the second feature network used in functional-map pipelines.
  • Because the loss needs only approximate rigid pre-alignment rather than ground-truth point pairs, the same model can be trained on one dataset and evaluated on others, including generalization from synthetic SURREAL shapes to FAUST, SCAPE, and SHREC19.
  • The learned embeddings keep their accuracy under additive Gaussian noise and topology changes, with the smallest performance degradation reported among the compared methods.
  • The same embedding supports other analysis tasks without retraining: $k$-means clustering of the per-point embeddings gives meaningful and cross-shape-consistent segmentation, and the adapted partial matching loss handles full-to-partial and partial-to-partial pairs.
  • Classical Laplace–Beltrami eigenbases suffer from sign flips and repeated-eigenvalue ambiguity; the learned embeddings are reported to be consistent across shapes where the eigenbases are not, which is what makes the direct retrieval possible.

Reading between the lines

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

  • The paper's pre-alignment assumption means the method currently does not provide pose-invariant embeddings; a direct extension is to feed the same loss through an SO(3)/SE(3)-equivariant backbone, which the paper itself names as future work, and then test whether the coupling survives random rotations of the input.
  • An implicit testable consequence of the geometry-awareness claim is that Euclidean distance in the learned embedding should track geodesic distance on the surface; measuring that correlation on held-out shapes would separate genuine geometric encoding from mere descriptor copying.
  • Since the contrastive term is written for any descriptor functions, the method should tolerate replacements of HKS by other cheap per-point features; stability of correspondence accuracy under such swaps would show that the coupling, not the specific descriptor, carries the result.
  • If nearest-neighbor retrieval in a shared embedding works across near-isometric and non-isometric human shapes, the same architecture is a candidate for other articulated object categories such as animals, hands, or clothing with no changes to the loss, although the paper reports experiments only on human shapes.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes CoE, a method that learns per-point high-dimensional embeddings for non-rigid point cloud correspondences using a single network. The architecture consists of an ASAP DiffusionNet feature extractor followed by a cross-attention block that couples the two input shapes. The unsupervised loss (Eq. 7) combines an off-diagonal term that encourages the embeddings to approximate LBO eigenbases, an orthogonality term, and a contrastive term that aligns Fourier coefficients of HKS descriptors. Dense correspondences are obtained by nearest-neighbor search in the embedding space. The method is evaluated on FAUST, SCAPE, SHREC19, TOPKIDS, DT4D-M, and SURREAL, with additional experiments on partial matching and segmentation. The paper reports state-of-the-art results among point-cloud-only methods and is released with code.

Significance. If the results hold, the method offers a simple and practical alternative to functional-map-based pipelines: it trains a single network without ground-truth correspondences and retrieves dense maps by nearest-neighbor search. The paper provides explicit loss equations, per-component ablations (Table 4), generalization and robustness experiments, and a public code release. These are clear strengths. The main significance caveat is that the method relies on precomputed spectral quantities (LBO eigenvalues/eigenvectors and HKS descriptors) and on pre-aligned input shapes, so the 'raw point cloud / unsupervised' framing is narrower than the abstract suggests. This makes the central claim conditional on an alignment assumption that is not part of the learned embedding itself.

major comments (3)
  1. [Sec. 6 and Sec. 4.1, Eq. (2)] The paper's own limitation section states that the method requires shapes to be pre-aligned, but the abstract and contributions do not qualify this condition. Since f_theta in Eq. (2) consumes raw Cartesian coordinates and no SO(3)/SE(3)-equivariant layer is used, a global rotation of the target point cloud changes the predicted embedding and breaks the coupling achieved by the cross-attention block and the losses in Eqs. (4)-(6). All evaluated benchmarks (FAUST, SCAPE, SHREC19, TOPKIDS, DT4D-M, SURREAL) are canonically oriented human shapes, so the reported state-of-the-art numbers are obtained under a favorable extrinsic alignment. This assumption is load-bearing for the central claim of 'raw point cloud' matching and should be stated prominently in the abstract and contribution list.
  2. [Abstract and Sec. 1 vs. Tables 2-3 and Sec. 9] The method is described as 'unsupervised' and 'directly from raw point clouds', but the pipeline requires precomputed LBO eigenvalues/eigenvectors, HKS descriptors, and procrustes alignment (Sec. 9). The tables label the method as weakly supervised (W), acknowledging that pre-alignment is a form of weak supervision. The contrastive loss (Eq. 6) uses HKS descriptors derived from the same LBO that the off-diagonal loss (Eq. 4) anchors the embedding to. This is not a logical circularity, but it means the learned embedding is strongly anchored to precomputed spectral information rather than learned purely from raw geometry. The paper should rephrase its claims as 'weakly supervised / pre-aligned spectral feature learning' to avoid overstating the unsupervised raw-point-cloud contribution.
  3. [Tables 2 and 3] All reported mean geodesic errors are single-run numbers without standard deviations, confidence intervals, or significance tests. Given the small test sets (e.g., 20 shapes for FAUST and SCAPE) and the small differences to the closest point-cloud baseline on some columns (e.g., Table 2, DT4D-M: Ours 13.1 vs. NIE 12.1 when trained on FAUST), it is difficult to assess whether the claimed improvements are statistically meaningful. The authors should provide multiple training runs, bootstrapped confidence intervals, or pairwise significance tests to support the state-of-the-art claim.
minor comments (5)
  1. [Sec. 5.2] The statement that the method is 'comparable (if not superior) to SSMSM' should be quantified with the actual numbers from Table 2: when trained on FAUST, SSMSM achieves lower mean geodesic error on FAUST (2.4 vs. 3.7), SCAPE (6.8 vs. 8.7), and SHREC19 (9.0 vs. 9.5), while CoE is better only on TOPKIDS and DT4D-M. This does not invalidate the point-cloud-only comparison, but the sentence should be more precise.
  2. [Sec. 4.2, Eq. (7)] The loss weights mu_off=1, mu_o=5e1, mu_c=1e3 are given only in the text, with no sensitivity analysis. The ablations in Table 4 remove entire loss terms but do not vary the weights. A short study of weight sensitivity would strengthen the claim that the proposed loss is robust.
  3. [Sec. 5.6 and Sec. 11 (supplementary)] The partial shape matching extension is presented as a proof-of-concept, but it uses deep features from SSMSM instead of HKS and applies test-time adaptation. This is not the same unsupervised pipeline as in the main experiments, and only qualitative results are provided. The text should make this dependency even clearer in the main paper.
  4. [Sec. 4.2, after Eq. (5)] There is a typo: 'shapeS' should be 'shape S'. Also, the sentence 'the optimal embedding to minimise both the orthogonal loss and the off-diagonal loss is the individual LBO eigenbasis of shapeS and T' would benefit from a citation or a brief proof sketch, as it is a key motivation for the loss design.
  5. [Abstract] The abstract says 'unsupervised' and 'raw point clouds'; for consistency with the method's dependence on precomputed HKS and pre-alignment, the abstract should use 'weakly supervised' and state the alignment condition. This would bring the paper's framing in line with the tables and the limitations section.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the learned embedding is trained with self-supervised LBO/HKS losses, but the reported correspondences are evaluated on held-out shapes and are not fitted to ground truth by construction.

full rationale

The derivation chain is: define an embedding extractor f_theta and cross-attention module h_phi, train them with the total loss of Eq. (7), which combines the off-diagonal loss (Eq. 4), the orthogonal loss (Eq. 5), and the contrastive loss (Eq. 6). The off-diagonal and orthogonal terms indeed anchor the predicted embedding to the input shape's LBO eigenbasis (the paper states the optimal solution is the individual LBO eigenbasis), and the contrastive term couples the embeddings by aligning the spectral coefficients of HKS descriptors. This is a self-supervised objective built from intrinsic quantities derived from the input point cloud; it does not use ground-truth correspondences during training. At inference, dense correspondences are obtained by nearest-neighbor search in the embedding space and are evaluated on held-out test shapes (FAUST/SCAPE splits, SHREC19, TOPKIDS, DT4D-M) and on cross-dataset generalization after training on SURREAL. Therefore, the reported performance is not forced by construction: the network must generalize to unseen shapes, and the results are not simply a renaming of the HKS descriptor or the LBO eigenbasis. The pre-alignment requirement conceded in Sec. 6 is an input assumption and a scope limitation, not a circular step. The citations to the authors' own prior work concern standard datasets (SHREC16, TOPKIDS) and classical geometry-processing references; no load-bearing argument reduces to a self-citation or to an imported uniqueness theorem. The design is self-referential in the benign sense that the supervision is derived from the same geometric operators used at inference, but this is a legitimate self-supervised learning setup rather than a case where the claimed prediction is identical to its input by construction.

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

The central method is a learned spectral embedding: the free parameters are the hand-tuned loss weights and embedding/descriptor dimensions, and the axioms are the availability of a point cloud Laplacian, approximate pre-alignment, and HKS as a coupling descriptor. No new physical entities are introduced. The approach is an extension of classical coupled diagonalization [16,22] to learned point cloud embeddings.

free parameters (5)
  • Loss weight mu_off = 1
    Hand-chosen in Eq. (7) to balance the off-diagonal loss.
  • Loss weight mu_o = 5e1 (50)
    Hand-chosen weight for the orthogonality loss.
  • Loss weight mu_c = 1e3 (1000)
    Hand-chosen weight for the contrastive coupling loss.
  • Embedding dimension k = 50
    Dimension of the per-point embedding; ablation shows robustness for k between 30 and 80.
  • HKS feature dimension d = 512
    Descriptor dimension used as input to the network.
assumptions (5)
  • domain assumption Shapes are intrinsically 2D compact manifolds sampled as point clouds with a well-defined cotangent Laplacian.
    Sec. 3 and Sec. 8 define the LBO and assume the point cloud Laplacian from [44] is reliable.
  • domain assumption Approximate rigid pre-alignment of input shapes is available.
    Sec. 2.3 states 'We make use of the weak supervision same as in [43]', and Sec. 6 lists 'it requires shapes to be pre-aligned' as a limitation.
  • domain assumption HKS descriptors of corresponding points provide a usable coupling signal across non-rigid deformations.
    HKS is used in the contrastive loss Lc (Eq. 6); the paper replaces HKS with SSMSM features for partial shapes, indicating HKS is not always sufficient.
  • standard math The LBO eigenvalues Lambda used in the off-diagonal loss are meaningful targets for the learned embedding.
    Eq. (4) penalizes deviation of Psi^T L Psi from Lambda, assuming the spectrum is informative and computable.
  • ad hoc to paper Cross-attention between the two shapes is necessary and sufficient to couple embeddings.
    Architectural choice in Sec. 4.1; ablation shows it helps but no theoretical guarantee is provided.

how reviews work

0 comments
Cite this review

Pith. "Pith review of CoE: Deep Coupled Embedding for Non-Rigid Point Cloud Correspondences." pith.science (2026). https://pith.science/paper/FQ4BG4PE

@misc{pith2026241205557,
  author       = {Pith},
  title        = {Pith review of: CoE: Deep Coupled Embedding for Non-Rigid Point Cloud Correspondences},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FQ4BG4PE}},
  note         = {Machine review of arXiv:2412.05557}
}
read the original abstract

The interest in matching non-rigidly deformed shapes represented as raw point clouds is rising due to the proliferation of low-cost 3D sensors. Yet, the task is challenging since point clouds are irregular and there is a lack of intrinsic shape information. We propose to tackle these challenges by learning a new shape representation -- a per-point high dimensional embedding, in an embedding space where semantically similar points share similar embeddings. The learned embedding has multiple beneficial properties: it is aware of the underlying shape geometry and is robust to shape deformations and various shape artefacts, such as noise and partiality. Consequently, this embedding can be directly employed to retrieve high-quality dense correspondences through a simple nearest neighbor search in the embedding space. Extensive experiments demonstrate new state-of-the-art results and robustness in numerous challenging non-rigid shape matching benchmarks and show its great potential in other shape analysis tasks, such as segmentation.

Figures

Figures reproduced from arXiv: 2412.05557 by the authors.

Figure 1
Figure 1. We propose a novel way to learn coupled embeddings of non-rigidly deformable shapes that are geometry-aware, robust and [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Examples of LBO eigenbases and our learned coupled [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Pipeline overview. Given a pair of shapes [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Qualitative result on DT4D-M. Ours produces the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 6
Figure 6. Figure 6: Robustness against topological changes (the left shoul [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 8
Figure 8. Figure 8: Our runtime vs. input point clouds size, ranging from [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 7
Figure 7. Figure 7: Visualisation of a challenging pair with crossed legs. We [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 10
Figure 10. Figure 10: Illustration of mean geodesic error under different spec [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: Qualitative result on SHREC16 HOLES. Ours per [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: Visual comparison of our learned coupled embeddings vs. the LBO eigenbases. The first ten are shown. It can be seen that [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 13
Figure 13. Figure 13: Failure cases on FAUST. All three failure examples relate to the touching hands, where the points of two hands are locally [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]
Figure 14
Figure 14. Figure 14: Qualitative results on SCAPE. Leftmost is the reference shape. Accurate correspondences are consistently obtained by our [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]
Figure 15
Figure 15. Figure 15: Qualitative results on TOPKIDS. Leftmost is the reference shape. Although our method can handle topological noise ( [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]
Figure 16
Figure 16. Figure 16: Qualitative results on DT4D-M. More qualitative non-isometric matching results ( [PITH_FULL_IMAGE:figures/full_fig_p015_16.png]
Figure 17
Figure 17. Figure 17: Robustness against additive noise. Ours produces stable correspondences under this noise compared to the baselines (errors [PITH_FULL_IMAGE:figures/full_fig_p016_17.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

59 extracted references · 55 canonical work pages

  1. [15]

    G-msm: Unsupervised multi-shape match- ing with graph-based affinity priors

    Marvin Eisenberger, Aysim Toker, Laura Leal-Taix ´e, and Daniel Cremers. G-msm: Unsupervised multi-shape match- ing with graph-based affinity priors. In CVPR, 2023. 3

    work page 2023

  2. [1]

    Scape: shape completion and animation of people

    Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Se- bastian Thrun, Jim Rodgers, and James Davis. Scape: shape completion and animation of people. In ACM SIGGRAPH 2005 Papers, pages 408–416. 2005. 6

    work page 2005

  3. [2]

    Understanding and improving features learned in deep functional maps

    Souhaib Attaiki and Maks Ovsjanikov. Understanding and improving features learned in deep functional maps. In CVPR, 2023. 1, 4, 5

    work page 2023

  4. [3]

    DPFM: Deep Partial Functional Maps

    Souhaib Attaiki, Gautam Pai, and Maks Ovsjanikov. DPFM: Deep Partial Functional Maps. In 3DV, 2021. 5, 1

    work page 2021

  5. [4]

    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. In ICCV workshops, pages 1626–1633,

    work page

  6. [5]

    Federica Bogo, Javier Romero, Matthew Loper, and Michael J. Black. FAUST: Dataset and evaluation for 3D mesh registration. In Proceedings IEEE Conf. on Com- puter Vision and Pattern Recognition (CVPR) , Piscataway, NJ, USA, 2014. IEEE. 3

    work page 2014

  7. [6]

    Faust: Dataset and evaluation for 3d mesh registration

    Federica Bogo, Javier Romero, Matthew Loper, and Michael J Black. Faust: Dataset and evaluation for 3d mesh registration. In CVPR, 2014. 6

    2014

  8. [7]

    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. In CVPR,

Show all 59 references
  1. [8]

    Unsu- pervised learning of robust spectral shape matching

    Dongliang Cao, Paul Roetzer, and Florian Bernard. Unsu- pervised learning of robust spectral shape matching. ACM Transactions on Graphics (TOG), 2023. 1, 3

    2023

  2. [9]

    Geometric diffusions as a tool for harmonic anal- ysis and structure definition of data: Diffusion maps

    Ronald R Coifman, Stephane Lafon, Ann B Lee, Mauro Maggioni, Boaz Nadler, Frederick Warner, and Steven W Zucker. Geometric diffusions as a tool for harmonic anal- ysis and structure definition of data: Diffusion maps. Pro- ceedings of the national academy of sciences, 102(21):...

    2005

  3. [10]

    Shrec’16: Partial matching of deformable shapes

    Luca Cosmo, Emanuele Rodola, Michael M Bronstein, An- drea Torsello, Daniel Cremers, Y Sahillioˇglu, et al. Shrec’16: Partial matching of deformable shapes. In Eurographics Workshop on 3D Object Retrieval, EG 3DOR, pages 61–67. Eurographics Association, 2016. 8, 2, 3

    2016

  4. [11]

    Dyke, and Juyong Zhang

    Bailin Deng, Yuxin Yao, Roberto M. Dyke, and Juyong Zhang. A Survey of Non-Rigid 3D Registration.CGF, 2022. 2

    2022

  5. [12]

    Vector neurons: a general framework for so(3)-equivariant networks

    Congyue Deng, Or Litany, Yueqi Duan, Adrien Poulenard, Andrea Tagliasacchi, and Leonidas Guibas. Vector neurons: a general framework for so(3)-equivariant networks. arXiv preprint arXiv:2104.12229, 2021. 8

    2021 arXiv

  6. [13]

    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. In CVPR, 2020. 6, 7

    2020

  7. [14]

    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. In CVPR, 2020. 3, 6

    2020

  8. [16]

    Bronstein, Klaus Glashoff, and Alexander M

    Davide Eynard, Artiom Kovnatsky, Michael M. Bronstein, Klaus Glashoff, and Alexander M. Bronstein. Multimodal manifold analysis by simultaneous diagonalization of lapla- cians. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015. 2, 3, 4, 5

    2015

  9. [17]

    Deciphering interaction fingerprints from protein molecular surfaces using geometric deep learning

    Pablo Gainza, Freyr Sverrisson, Frederico Monti, Emanuele Rodola, Davide Boscaini, Michael M Bronstein, and Bruno E Correia. Deciphering interaction fingerprints from protein molecular surfaces using geometric deep learning. Nature Methods, 17(2):184–192, 2020. 1

    2020

  10. [18]

    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. In ECCV, 2018. 3

    2018

  11. [19]

    Denoising diffu- sion probabilistic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffu- sion probabilistic models. In Neurips, 2020. 4

    2020

  12. [20]

    Guibas, and Shi-Min Hu

    Jiahui Huang, Tolga Birdal, Zan Gojcic, Leonidas J. Guibas, and Shi-Min Hu. Multiway Non-rigid Point Cloud Regis- tration via Learned Functional Map Synchronization. IEEE Transactions on Pattern Analysis and Machine Intelligence, pages 1–1, 2022. 3, 6

    2022

  13. [21]

    Neural intrinsic embedding for non-rigid point cloud matching

    Puhua Jiang, Mingze Sun, and Ruqi Huang. Neural intrinsic embedding for non-rigid point cloud matching. In CVPR, pages 21835–21845, 2023. 1, 2, 6, 7

    2023

  14. [22]

    Bronstein, Alexander M

    Artiom Kovnatsky, Michael M. Bronstein, Alexander M. Bronstein, Klaus Glashoff, and Ron Kimmel. Coupled Quasi-harmonic Bases. CGF, 2013. 2, 3, 4, 5, 6

    2013

  15. [23]

    Shrec’16: Matching of deformable shapes with topological noise

    Zorah L ¨ahner, Emanuele Rodol `a, Michael M Bronstein, Daniel Cremers, Oliver Burghard, Luca Cosmo, Alexander Dieckmann, Reinhard Klein, Y Sahillio ˇglu, et al. Shrec’16: Matching of deformable shapes with topological noise. In Eurographics Workshop on 3D Object Retrieval, EG...

    2016

  16. [24]

    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. In NeurIPS, 2022. 7

    2022

  17. [25]

    4dcomplete: Non-rigid motion esti- mation beyond the observable surface

    Yang Li, Hikari Takehara, Takafumi Taketomi, Bo Zheng, and Matthias Nießner. 4dcomplete: Non-rigid motion esti- mation beyond the observable surface. In ICCV, 2021. 7

    2021

  18. [26]

    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. In ICCV, 2017. 1

    2017

  19. [27]

    Smooth non-rigid shape matching via effective dirichlet energy optimization

    Robin Magnet, Jing Ren, Olga Sorkine-Hornung, and Maks Ovsjanikov. Smooth non-rigid shape matching via effective dirichlet energy optimization. In 3DV, 2022. 7

    2022

  20. [28]

    Correspondence learning via linearly- invariant embedding

    Riccardo Marin, Marie-Julie Rakotosaona, Simone Melzi, and Maks Ovsjanikov. Correspondence learning via linearly- invariant embedding. Neurips, 2020. 1, 2, 6, 7

    2020

  21. [29]

    Shrec 2019: Matching humans with dif- ferent connectivity

    Simone Melzi, Riccardo Marin, Emanuele Rodol `a, Umberto Castellani, Jing Ren, Adrien Poulenard, Peter Wonka, and Maks Ovsjanikov. Shrec 2019: Matching humans with dif- ferent connectivity. In Eurographics Workshop on 3D Object Retrieval, 2019. 6

    2019

  22. [30]

    Functional maps: a flexible representation of maps between shapes

    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), 31(4):1–11, 2012. 1, 3

    2012

  23. [31]

    Point cloud-based automatic assessment of 3d computer animation course- works

    Gianluca Paravati, Fabrizio Lamberti, Valentina Gatteschi, Claudio Demartini, and Paolo Montuschi. Point cloud-based automatic assessment of 3d computer animation course- works. IEEE Transactions on Learning Technologies, 2017. 1

    2017

  24. [32]

    Pytorch: An imperative style, high-performance deep learning library

    Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zem- ing Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. Neurips, 2019. 1

    2019

  25. [33]

    Pointnet: Deep learning on point sets for 3d classification and segmentation

    Charles Ruizhongtai Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. In CVPR, 2017. 3, 5

    2017

  26. [34]

    Pointnet++: Deep hierarchical feature learning on point sets in a metric space

    Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. Neurips, 2017. 3, 5

    2017

  27. [35]

    Continuous and orientation-preserving correspon- dences via functional maps

    Jing Ren, Adrien Poulenard, Peter Wonka, and Maks Ovs- janikov. Continuous and orientation-preserving correspon- dences via functional maps. ACM Transactions on Graphics (TOG), 37(6):1–16, 2018. 6

    2018

  28. [36]

    Hierarchical shape segmentation and registra- tion via topological features of laplace-beltrami eigenfunc- tions

    Martin Reuter. Hierarchical shape segmentation and registra- tion via topological features of laplace-beltrami eigenfunc- tions. Int. J. Comput. Vision, 2010. 2

    2010

  29. [37]

    Laplace-beltrami spectra as ’shape-dna’ of surfaces and solids

    Martin Reuter, Franz-Erich Wolter, and Niklas Peinecke. Laplace-beltrami spectra as ’shape-dna’ of surfaces and solids. Comput. Aided Des., 2006. 2

    2006

  30. [38]

    Partial functional corre- spondence

    Emanuele Rodol `a, Luca Cosmo, Michael M Bronstein, An- drea Torsello, and Daniel Cremers. Partial functional corre- spondence. In CGF, 2017. 3

    2017

  31. [39]

    Rustamov

    Raif M. Rustamov. Laplace-Beltrami Eigenfunctions for De- formation Invariant Shape Representation. InGeometry Pro- cessing. The Eurographics Association, 2007. 1, 2

    2007

  32. [40]

    Recent advances in shape correspon- dence

    Yusuf Sahillio ˘glu. Recent advances in shape correspon- dence. In The Visual Computer, 2020. 2

    2020

  33. [41]

    Shot: Unique signatures of histograms for surface and tex- ture description

    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, 125:251–264, 2014. 1

    2014

  34. [42]

    Global matching of point clouds for scan registration and loop detection

    Carlos S ´anchez-Belenguer, Simone Ceriani, Pierluigi Tad- dei, Erik Wolfart, and V ´ıtor Sequeira. Global matching of point clouds for scan registration and loop detection. Robot. Auton. Syst., 2020. 1

    2020

  35. [43]

    Weakly supervised deep functional maps for shape matching

    Abhishek Sharma and Maks Ovsjanikov. Weakly supervised deep functional maps for shape matching. In Neurips, 2020. 3, 6, 7

    2020

  36. [44]

    A Laplacian for Non- manifold Triangle Meshes

    Nicholas Sharp and Keenan Crane. A Laplacian for Non- manifold Triangle Meshes. CGF, 2020. 1

    2020

  37. [45]

    Diffusionnet: Discretization agnostic learning on surfaces

    Nicholas Sharp, Souhaib Attaiki, Keenan Crane, and Maks Ovsjanikov. Diffusionnet: Discretization agnostic learning on surfaces. ACM Trans. Graph., 2022. 3, 4, 5

    2022

  38. [46]

    Score-based generative modeling through stochastic differential equa- tions

    Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Ab- hishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equa- tions. In ICLR, 2021. 4

    2021

  39. [47]

    A brief introduction to statistical shape analysis

    Mikkel B Stegmann and David Delgado Gomez. A brief introduction to statistical shape analysis. Informatics and mathematical modelling, Technical University of Denmark, DTU, 15(11), 2002. 1

    2002

  40. [48]

    A concise and provably informative multi-scale signature based on heat diffusion

    Jian Sun, Maks Ovsjanikov, and Leonidas Guibas. A concise and provably informative multi-scale signature based on heat diffusion. In CGF, 2009. 1, 4, 6, 3

    2009

  41. [49]

    Multidimensional scaling: I

    Warren S Torgerson. Multidimensional scaling: I. theory and method. Psychometrika, 17(4):401–419, 1952. 2

    1952

  42. [50]

    Learning from synthetic humans

    Gul Varol, Javier Romero, Xavier Martin, Naureen Mah- mood, Michael J Black, Ivan Laptev, and Cordelia Schmid. Learning from synthetic humans. In CVPR, 2017. 7

    2017

  43. [51]

    Attention is all you need

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszko- reit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. Neurips, 2017. 5

    2017

  44. [52]

    Fan Wang, Qixing Huang, and Leonidas J. Guibas. Image co-segmentation via consistent functional maps. In ICCV,

  45. [53]

    Sarma, Michael M

    Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E. Sarma, Michael M. Bronstein, and Justin M. Solomon. Dynamic graph cnn for learning on point clouds. ACM Trans. Graph.,

  46. [54]

    Geodesicembedding (ge): A high-dimensional embedding approach for fast geodesic distance queries

    Qianwei Xia, Juyong Zhang, Zheng Fang, Jin Li, Mingyue Zhang, Bailin Deng, and Ying He. Geodesicembedding (ge): A high-dimensional embedding approach for fast geodesic distance queries. IEEE Transactions on Visualization and Computer Graphics, 2022. 2 CoE: Deep Coupled Embeddi...

    2022

  47. [55]

    This property leads to its widespread application in compu- tational geometry and computer graphics, especially when dealing with curved surfaces or manifolds

    Laplace-Beltrami Operator For a given function u defined on a Riemannian manifold M, the Laplace-Beltrami Operator ∆u measures how the function deviates from its average value within each lo- cal neighborhood, taking into account the geometry of M. This property leads to its w...

  48. [56]

    The embed- ding extractor is based on the ASAP DiffusionNet with the default configuration published in [2] and the cross atten- tion block is based on the implementation in [3]

    Implementation Details Our network is implemented in PyTorch [32]. The embed- ding extractor is based on the ASAP DiffusionNet with the default configuration published in [2] and the cross atten- tion block is based on the implementation in [3]. We em- ploy HKS [48] as descrip...

  49. [57]

    frequency-aligned

    Ablation Study 10.1. Architecture and Loss In this section, we first explain the difference between Dif- fusionNet and our ASAP variant.Then we evaluate our pro- posed loss terms Loff, Lo and Lc. We discard Loff and Lo together, and then Lo, Lc respectively, since Loff and Lo ...

  50. [58]

    Partial Shape Matching As a proof-of-concept, we extend our method to the chal- lenging task to match partial shapes. We take a full-partial pair (from the same shape category in SHREC16 [10]) dur- ing the training, and once the network is trained, we can directly match two pa...

  51. [59]

    See figure captions for explanation

    More Qualitative Results In this section, we present additional qualitative results in- cluding failure cases. See figure captions for explanation. Figure 12. Visual comparison of our learned coupled embeddings vs. the LBO eigenbases. The first ten are shown. It can be seen th...

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.