A theory of refractive and specular 3D shape by light-path triangulation
Bibliographic record
Abstract
We investigate the feasibility of reconstructing an arbitrarily-shaped specular scene (refractive or mirror-like) from one or more viewpoints. By reducing shape recovery to the problem of reconstructing individual 3D light paths that cross the image plane, we obtain three key results. First, we show how to compute the depth map of a specular scene from a single viewpoint, when the scene redirects incoming light just once. Second, for scenes where incoming light undergoes two refractions or reflections, we show that three viewpoints are sufficient to enable reconstruction in the general case. Third, we show that it is impossible to reconstruct individual light paths when light is redirected more than twice. Our analysis assumes that, for every point on the image plane, we know at least one 3D point on its light path. This leads to reconstruction algorithms that rely on an "environment matting" procedure to establish pixel-to-point correspondences along a light path. Preliminary results for a variety of scenes (mirror, glass, etc) are also presented.
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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 | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".