Multifractal analysis of mammographic images

Abstract

The study targets improving early breast-tumor detection via computer analysis of mammograms. It highlights limitations of conventional mammography, tissue density, imaging artifacts, and interpretive subjectivity, underscoring the need for objective decision-support algorithms. We propose a methodology that combines multifractal analysis with modern segmentation and visualizes local structural differences as fractal-dimension heatmaps. Сlient-server prototype is described: Python on the server handles computation and image processing; the client (HTML/CSS/JavaScript) manages interaction and data. Preprocessing applies median and Gaussian filtering followed by Otsu thresholding to obtain stable breast masks with few small artifacts. For segmentation, a U-Net trained on MIAS and DDSM is used; combining its mask with the Otsu mask improves ROI completeness and contour stability. A key element is constructing local fractal-dimension maps with a sliding window. Local fractal-dimension estimates in overlapping windows form a continuous map capturing spatial deviations in tissue structure. Pathological regions show D differences relative to adjacent parenchyma, enhancing interpretability and suitability for semi-automatic detection. We outline limitations of classical box-counting for grayscale images and motivate differential box-counting, which operates in intensity space, reduces dependence on binarization, and increases sensitivity to subtle texture variations. Preliminary MIAS/DDSM experiments indicate viability: heatmaps align with tissue structure and support quantitative “inside–outside” analysis (ROI vs surroundings), local fractal-dimension profiles across lesion boundaries, and aggregated metrics. Future work includes DICOM integration, automated ROI detection, optimization of slidingwindow and DBC quantization parameters, and extended validation on clinical datasets.