Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors
Bibliographic record
Abstract
This paper describes methods for recovering time-varying shape and motion of non-rigid 3D objects from uncalibrated 2D point tracks. For example, given a video recording of a talking person, we would like to estimate the 3D shape of the face at each instant, and learn a model of facial deformation. Time-varying shape is modeled as a rigid transformation combined with a non-rigid deformation. Reconstruction is ill-posed if arbitrary deformations are allowed, and thus additional assumptions about deformations are required. We first suggest restricting shapes to lie within a low-dimensional subspace, and describe estimation algorithms. However, this restriction alone is insufficient to constrain reconstruction. To address these problems, we propose a reconstruction method using a Probabilistic Principal Components Analysis (PPCA) shape model, and an estimation algorithm that simultaneously estimates 3D shape and motion for each instant, learns the PPCA model parameters, and robustly fills-in missing data points. We then extend the model to model temporal dynamics in object shape, allowing the algorithm to robustly handle severe cases of missing data.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".