On the Incorporation of Time-delay Regularization into Curvature-based Diffusion

A new anisotropic nonlinear diffusion model incorporating time-delay regularization into curvature-based diffusion is proposed for image restoration and edge detection. A detailed mathematical analysis of the proposed model in the form of the proof of existence, uniqueness and stability of the viscosity solution of the model is presented. Furthermore, implementation issues and computational methods for the proposed model are also discussed in detail. The results obtained from testing our denoising and edge detection algorithm on several synthetic and real images showed the effectiveness of the proposed model in prserving sharp edges and fine structures while removing noise.