Morphological Features-Oriented Fusion Extraction Method for Quantification of Tubules and Non-Tubules in Breast Carcinoma

Siet, Joseph Jiun Wen (2026) Morphological Features-Oriented Fusion Extraction Method for Quantification of Tubules and Non-Tubules in Breast Carcinoma. Doctoral thesis, Tunku Abdul Rahman University of Management and Technology.

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Abstract

Breast cancer remains the most prevalent malignancy among women worldwide, with 2.31 million new cases and approximately 665,684 deaths reported in 2022, posing a significant challenge to achieving Sustainable Development Goal 3 (SDG3) on health and well-being. Accurate histopathological grading plays a critical role in diagnosis, prognosis, and therapeutic planning, with the Nottingham Histopathology Grading (NHG) system serving as the clinical standard. Among its three key criteria—tubule formation, nuclear pleomorphism, and mitotic count—tubule formation assessment is highly subjective and prone to inter- and intra-observer variability, leading to inconsistent grading outcomes. This necessitates the development of an objective, quantitative, and reproducible approach for tubule identification and differentiation. This research introduces a three-phase “rule-based tubular-differentiation selection/ decision framework” for rule-based quantitative modelling of tubule formation from breast histopathology images, incorporating image processing and mathematical modelling techniques. Phase 1 involves region of interest identification through cluster-based image registration. Forty-eight H&E-stained whole-slide image patches were processed using Macenko’s stain normalisation, followed by stain unmixing to extract H- and E-channels. K-means clustering was applied to segment nuclei and central lumen candidates, which were combined via image registration to form candidate structures (250 tubules and 250 non-tubules). Phase 2 introduces a multi-layered rule-based selection system comprising three Premier Criteria: (1) Premier Criterion 1 applies fractal analysis based on Galton’s distribution and a novel Galton’s Distance Heuristic derived using Lambert W function, enabling threshold-based differentiation between fractal-like tubules and non-fractals; (2) Premier Criterion 2 utilises Topological Data Analysis (TDA) with persistent homology to capture topological invariants of tubule structures, employing layer-2 barcode patterns to identify epistemic symmetry; (3) Premier Criterion 3 performs fine-granular extremity analysis on persistent homology intervals using Extreme Value Theory principles, introducing Ratio-T thresholds for delineating fractals from non-fractals. This integrated approach formalises the SimpFracHom-Conjecture, correlating fractal geometry and simplicial homology for robust tubule modelling. Phase 3 validates the delineation outcomes using a Confusion Matrix (Accuracy, Precision, Sensitivity, Specificity, and F1-score) and cross-verifies with state-of-the-art classifiers (SVM, Decision Tree, and KNN) using default parameters. The proposed framework achieved strong performance, with Phase 2 rules yielding Accuracy: 86.64%, Precision: 88.16%, Sensitivity: 83.66%, F1-score: 85.39%, and Specificity: 87.53% for the training set, and Accuracy: 88.73%, Precision: 87.03%, Sensitivity: 91.47%, F1-score: 88.91%, and Specificity: 85.40% for the test set. Additional validation using SVM and Decision Tree classifiers demonstrated generalised metrics between 80% and 90%, whereas KNN achieved outcomes between 75% and 80%, despite no parameter optimisation. These findings confirm the feasibility of integrating fractal and topological analyses for objective tubule quantification and differentiation. In conclusion, this research establishes a mathematically interpretable and reproducible framework that reduces subjectivity in tubule assessment while adhering to NHG standards. The integration of fractal geometry and TDA introduces a novel paradigm for histopathology image analysis, fostering automation in breast cancer grading systems and contributing towards precision pathology for improved clinical decision-making.