Continuous and orientation-preserving correspondences via functional maps
Why this work is in the frame
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Bibliographic record
Abstract
We propose a method for efficiently computing orientation-preserving and approximately continuous correspondences between non-rigid shapes, using the functional maps framework. We first show how orientation preservation can be formulated directly in the functional (spectral) domain without using landmark or region correspondences and without relying on external symmetry information. This allows us to obtain functional maps that promote orientation preservation, even when using descriptors, that are invariant to orientation changes. We then show how higher quality, approximately continuous and bijective pointwise correspondences can be obtained from initial functional maps by introducing a novel refinement technique that aims to simultaneously improve the maps both in the spectral and spatial domains. This leads to a general pipeline for computing correspondences between shapes that results in high-quality maps, while admitting an efficient optimization scheme. We show through extensive evaluation that our approach improves upon state-of-the-art results on challenging isometric and non-isometric correspondence benchmarks according to both measures of continuity and coverage as well as producing semantically meaningful correspondences as measured by the distance to ground truth maps.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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