Developability of heightfields via rank minimization
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
This work concerns the computation and approximation of developable surfaces --- surfaces that are locally isometric to the two-dimensional plane. These surfaces are heavily studied in differential geometry, and are also of great interest to fabrication, architecture and fashion. We focus specifically on developability of heightfields. Our main observation is that developability can be cast as a rank constraint, which can then be plugged into theoretically-grounded rank-minimization techniques from the field of compressed sensing. This leads to a convex semidefinite optimization problem, which receives an input heightfield and recovers a similar heightfield which is developable. Due to the sparsifying nature of compressed sensing, the recovered surface is piecewise developable, with creases emerging between connected developable pieces. The convex program includes one user-specified parameter, balancing adherence to the original surface with developability and number of patches. We moreover show, that in contrast to previous techniques, our discretization does not introduce a bias and the same results are achieved across resolutions and orientations, and with no limit on the number of creases and patches. We solve this convex semidefinite optimization problem efficiently, by devising a tailor-made ADMM solver which leverages matrix-projection observations unique to our problem. We employ our method on a plethora of experiments, from denoising 3D scans of developable geometry such as documents and buildings, through approximating general heightfields with developable ones, and up to interpolating sparse annotations with a developable heightfield.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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