SRE-FMaps: A Sinkhorn-Regularized Elastic Functional Map Framework for Non-Isometric 3D Shape Matching
Bibliographic record
Abstract
Precise 3D shape correspondence is a fundamental prerequisite for critical applications ranging from medical anatomical modeling to visual recognition. However, non-isometric 3D shape matching remains a challenging task due to the limited sensitivity of traditional Laplace-Beltrami (LB) bases to local geometric deformations such as stretching and bending. To address these limitations, this paper proposes a Sinkhorn-Regularized Elastic Functional Map framework (SRE-FMaps) that integrates entropy-regularized optimal transport with an elastic thin-shell energy basis. First, a sparse Sinkhorn transport plan is adopted to initialize a bijective correspondence with linear computational complexity. Then, a non-orthogonal elastic basis, derived from the Hessian of thin-shell deformation energy, is introduced to enhance high-frequency feature perception. Finally, correspondence stability is quantified through a cosine-based elastic distance metric, enabling retrieval and classification. Experiments on the SHREC2015, McGill, and Face datasets demonstrate that SRE-FMaps reduces the correspondence error by a maximum of 32% and achieves an average of 92.3% classification accuracy (with a peak of 94.74% on the Face dataset). Moreover, the framework exhibits superior robustness, yielding a recall of up to 91.67% and an F1-score of 0.94, effectively handling bending, stretching, and folding deformations compared with conventional LB-based functional map pipelines. The proposed framework provides a scalable solution for non-isometric shape correspondence in medical modeling, 3D reconstruction, and visual recognition.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".