Maximum Likelihood Estimation of Depth Maps Using Photometric Stereo
Bibliographic record
Abstract
Photometric stereo and depth-map estimation provide a way to construct a depth map from images of an object under one viewpoint but with varying illumination directions. While estimating surface normals using the Lambertian model of reflectance is well established, depth-map estimation is an ongoing field of research and dealing with image noise is an active topic. Using the zero-mean Gaussian model of image noise, this paper introduces a method for maximum likelihood depth-map estimation that accounts for the propagation of noise through all steps of the estimation process. Solving for maximum likelihood depth-map estimates involves an independent sequence of nonlinear regression estimates, one for each pixel, followed by a single large and sparse linear regression estimate. The linear system employs anisotropic weights, which arise naturally and differ in value to related work. The new depth-map estimation method remains efficient and fast, making it practical for realistic image sizes. Experiments using synthetic images demonstrate the method's ability to robustly estimate depth maps under the noise model. Practical benefits of the method on challenging imaging scenarios are illustrated by experiments using the Extended Yale Face Database B and an extensive data set of 500 reflected light microscopy image sequences.
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How this classification was reachedexpand
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 | 0.001 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".