Segmentation on surfaces with the Closest Point Method
Why this work is in the frame
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Bibliographic record
Abstract
We propose a method to detect objects and patterns in textures on general surfaces. Our approach applies the Chan-Vese variational model for active contours without edges to the problem of segmentation of scalar surface data. This leads to gradient descent equations which are level set equations on surfaces. These equations are evolved using the Closest Point Method, which is a recent technique for solving partial differential equations (PDEs) on surfaces. The final algorithm has a particularly simple form: it merely alternates a time step of the usual Chan-Vese model in a small 3D neighborhood of the surface with an interpolation step. We remark that the method can treat very general surfaces since it uses a closest point function to represent the underlying surface. Various experimental results are presented, including segmentation on smooth surfaces, non-smooth surfaces, open surfaces, and general triangulated surfaces.
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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