Fractional Active Contour Model with Adaptive Hessian Weighting for Mammogram Segmentation.

Background: Accurate segmentation of breast masses in mammographic images is a crucial step in computer-aided diagnosis (CAD) systems. However, mammograms are often affected by noise, low contrast, weak boundaries, and intensity inhomogeneity, which significantly challenge reliable segmentation. Methods: In this study, a novel variational active contour model is proposed by integrating spatially adaptive fractional-order enhancement with Hessian-based curvature weighting. A spatially varying fractional-order map is first derived from the image gradient to selectively enhance texture details and weak edges. Based on the enhanced image, second-order structural information is extracted through the Hessian matrix, whose eigenvalues are employed to construct an adaptive edge-stopping function sensitive to local curvature. To further address intensity inhomogeneity, a local region-fitting energy term inspired by the region-scalable fitting model is incorporated into the formulation. The proposed model is implemented within a level-set framework, ensuring numerical stability and topological flexibility. Results: The proposed method was evaluated on two publicly available mammogram datasets, namely INbreast and CBIS-DDSM. Quantitative comparisons using the Dice Similarity Coefficient (DSC) and Hausdorff Distance demonstrate that the proposed approach consistently outperforms classical active contour models and achieves competitive performance compared to learning-based methods, particularly in challenging cases involving low contrast and irregular lesion boundaries. Conclusions: The proposed fractional active contour model provides a robust, fully unsupervised, and interpretable solution for mammographic mass segmentation. By jointly exploiting adaptive fractional enhancement, Hessian-based curvature information, and local intensity fitting, the method effectively addresses key challenges inherent to mammogram images, making it a promising tool for assisting breast cancer detection in CAD systems.