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An Alternating Diffusion-Clustering Framework for Image Segmentation: Stability and Convergence |
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PP: 1103-1115 |
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doi:10.18576/amis/200419
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Author(s) |
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Ali Abou El Qassime,
Youness El Ansari,
Mehdi Abou El Qassime,
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Abstract |
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| We introduce a coupled mathematical model for image segmentation that relies on a bidirectional interaction between nonlinear diffusion and a discrete clustering operator. Rather than treating diffusion and segmentation separately, we couple them through a feedback mechanism: a Perona–Malik-type equation with a segmentation-dependent conductance interacts with a clustering step that is continuously regularized by the diffusion process. The resulting system defines a joint evolution where each component influences the other at every iteration. On the theoretical side, we prove existence and uniqueness for a linearized and regularized version of the diffusion subproblem with fixed segmentation. We also derive stability conditions for the explicit numerical scheme under a CFL-type constraint and study the convergence behavior of the iterative fixed-point algorithm. The model yields an unsupervised segmentation approach that preserves edges while enforcing spatial regularity, without requiring annotated data. Experiments on dermoscopic images achieve a Dice coefficient of 0.8672, a Jaccard index of 0.7714, and an overall accuracy of 0.9221, with particularly high specificity (0.9908) and precision (0.9808). These results demonstrate that the proposed coupled PDE-discrete system yields competitive performance while providing mathematical interpretability, offering a rigorous alternative to purely data-driven segmentation methods. |
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