PCDAF: Phase-congruency driven dual adaptive fractional-order model for robust image segmentation

Robust medical image segmentation under strong noise and intensity inhomogeneity remains challenging, especially in modalities such as ultrasound and brain MRI. We propose a phase-congruency driven dual adaptive fractional-order (PCDAF) model that integrates phase congruency into a local region-based level set framework and introduces two spatially varying fractional orders in the data and edge terms. Phase congruency provides a contrast-invariant structural confidence map that modulates the order of a Riesz fractional operator for adaptive regional fitting and edge regularization. A frequency-domain analysis guides the admissible order ranges and PC-to-order mappings, enabling spatially adaptive control of texture enhancement, bias-field suppression, and noise attenuation. Extensive experiments on BUSI breast ultrasound and IBSR18 brain MRI demonstrate that PCDAF achieves substantial improvements over several classical variational models and competitive performance relative to strong deep learning baselines, although the gains over the strongest competitors are modest. Comprehensive ablation, parameter sensitivity, robustness (noise, bias, and initialization), and runtime analyses further characterize the stability, interpretability, and computational behavior of the proposed framework. These results indicate that PCDAF provides a transparent and robust alternative for medical image segmentation under severe noise and intensity inhomogeneity.