SRE-FMaps: A Sinkhorn-Regularized Elastic Functional Map Framework for Non-Isometric 3D Shape Matching
Why this work is in the frame
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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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it