3D surface parameterization using manifold learning for medial shape representation
Bibliographic record
Abstract
The choice of 3D shape representation for anatomical structures determines the effectiveness with which segmentation, visualization, deformation, and shape statistics are performed. Medial axis-based shape representations have attracted considerable attention due to their inherent ability to encode information about the natural geometry of parts of the anatomy. In this paper, we propose a novel approach, based on nonlinear manifold learning, to the parameterization of medial sheets and object surfaces based on the results of skeletonization. For each single-sheet figure in an anatomical structure, we skeletonize the figure, and classify its surface points according to whether they lie on the upper or lower surface, based on their relationship to the skeleton points. We then perform nonlinear dimensionality reduction on the skeleton, upper, and lower surface points, to find the intrinsic 2D coordinate system of each. We then center a planar mesh over each of the low-dimensional representations of the points, and map the meshes back to 3D using the mappings obtained by manifold learning. Correspondence between mesh vertices, established in their intrinsic 2D coordinate spaces, is used in order to compute the thickness vectors emanating from the medial sheet. We show results of our algorithm on real brain and musculoskeletal structures extracted from MRI, as well as an artificial multi-sheet example. The main advantages to this method are its relative simplicity and noniterative nature, and its ability to correctly compute nonintersecting thickness vectors for a medial sheet regardless of both the amount of coincident bending and thickness in the object, and of the incidence of local concavities and convexities in the object's surface.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".