Local Editing of Cross-Surface Mappings with Iterative Least Squares Conformal Maps
Bibliographic record
Abstract
In this paper, we propose a novel approach to improve a given surface mapping through local refinement. The approach receives an established mapping between two surfaces and follows four phases: (i) inspection of the mapping and creation of a sparse set of landmarks in mismatching regions; (ii) segmentation with a low-distortion region-growing process based on flattening the segmented parts; (iii) optimization of the deformation of segmented parts to align the landmarks in the planar parameterization domain; and (iv) aggregation of the mappings from segments to update the surface mapping. In addition, we propose a new approach to deform the mesh in order to meet constraints (in our case, the landmark alignment of phase (iii)). We incrementally adjust the cotangent weights for the constraints and apply the deformation in a fashion that guarantees that the deformed mesh will be free of flipped faces and will have low conformal distortion. Our new deformation approach, Iterative Least Squares Conformal Mapping (ILSCM), outperforms other low-distortion deformation methods. The approach is general, and we tested it by improving the mappings from different existing surface mapping methods. We also tested its effectiveness by editing the mappings for a variety of 3D objects.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| 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 | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".