A Hierarchical Statistical Modeling Approach for the Unsupervised 3-D Biplanar Reconstruction of the Scoliotic Spine
Bibliographic record
Abstract
This paper presents a new and accurate three-dimensional (3-D) reconstruction technique for the scoliotic spine from a pair of planar and conventional (postero-anterior with normal incidence and lateral) calibrated radiographic images. The proposed model uses a priori hierarchical global knowledge, both on the geometric structure of the whole spine and of each vertebra. More precisely, it relies on the specification of two 3-D statistical templates. The first, a rough geometric template on which rigid admissible deformations are defined, is used to ensure a crude registration of the whole spine. An accurate 3-D reconstruction is then performed for each vertebra by a second template on which nonlinear admissible global, as well as local deformations, are defined. Global deformations are modeled using a statistical modal analysis of the pathological deformations observed on a representative scoliotic vertebra population. Local deformations are represented by a first-order Markov process. This unsupervised coarse-to-fine 3-D reconstruction procedure leads to two separate minimization procedures efficiently solved in our application with evolutionary stochastic optimization algorithms. In this context, we compare the results obtained with a classical genetic algorithm (GA) and a recent Exploration Selection (ES) technique. This latter optimization method with the proposed 3-D reconstruction model, is tested on several pairs of biplanar radiographic images with scoliotic deformities. The experiments reported in this paper demonstrate that the discussed method is comparable in terms of accuracy with the classical computed-tomography-scan technique while being unsupervised and while requiring only two radiographic images and a lower amount of radiation for the patient.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".