The Isometric Log-Ratio Transform for Probabilistic Multi-Label Anatomical Shape Representation
Bibliographic record
Abstract
Sources of uncertainty in the boundaries of structures in medical images have motivated the use of probabilistic labels in segmentation applications. An important component in many medical image segmentation tasks is the use of a shape model, often generated by applying statistical techniques to training data. Standard statistical techniques (e.g., principal component analysis) often assume data lies in an unconstrained vector space, but probabilistic labels are constrained to the unit simplex. If these statistical techniques are used directly on probabilistic labels, relative uncertainty information can be sacrificed. A standard method for facilitating analysis of probabilistic labels is to map them to a vector space using the LogOdds transform. However, the LogOdds transform is asymmetric in one of the labels, which skews results in some applications. The isometric log-ratio (ILR) transform is a symmetrized version of the LogOdds transform, and is so named as it is an isometry between the Aitchison geometry, the inherent geometry of the simplex, and standard Euclidean geometry. We explore how to interpret the Aitchison geometry when applied to probabilistic labels in medical image segmentation applications. We demonstrate the differences when applying the LogOdds transform or the ILR transform to probabilistic labels prior to statistical analysis. Specifically, we show that statistical analysis of ILR transformed data better captures the variability of anatomical shapes in cases where multiple different foreground regions share boundaries (as opposed to foreground-background boundaries).
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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".