A curve evolution-based variational approach to simultaneous image restoration and segmentation

In this paper, we introduce a novel approach for simultaneous restoration and segmentation of blurred noisy images by approaching a variant of the Mumford-Shah functional from a curve evolution perspective. In particular, by viewing the active contour as the set of discontinuities in the image, we derive a gradient flow to minimize an extended Mumford-Shah functional where the known blurring function is incorporated as part of the data fidelity term. Each gradient step involves solving a discrete approximation of the corresponding partial differential equation to obtain a smooth and deblurred estimate of the observed image without blurring across the curve. The experimental results based on both synthetic and real images demonstrate that the proposed method segments and restores the blurred images effectively. We conclude that our work is an edge-preserving image restoration technique that couples segmentation, denoising, and deblurring within a single framework. In addition, this framework provides an intellectual connection between regularization theory (used to solve the deblurring inverse problem) and the theory of curve evolution.