Shape Analysis of Breast Masses in Mammograms via the Fractal Dimension
Bibliographic record
Abstract
Masses due to benign breast diseases and tumors due to breast cancer present significantly different shapes on mammograms. In general, malignant tumors appear with rough and complex boundaries or contours, whereas benign masses present smooth, round, or oval contours. Fractal analysis may be used to derive shape features to perform pattern classification of breast masses and tumors. Several procedures have been proposed to compute the fractal dimension of various types of objects or regions of interest in biomedical images, among which the box-counting and ruler methods are popular. In this study, we applied the two methods mentioned above to compute the fractal dimension of both the two-dimensional (2D) contours of breast masses and tumors, as well as their one-dimensional (1D) signatures. A comparative analysis was performed to assess the performance of the two methods of computing the fractal dimension and the two methods of representing the boundaries of masses. It was observed that analysis of the 2D contour representation with the ruler method resulted in the highest classification accuracy of up to 0.946, as indicated by the area under the receiver operating characteristics (ROC) curve. The results indicate that the fractal dimension can serve as a good shape feature for the benign-versus-malignant classification of breast masses in mammograms.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".