Estimating the gradient in the Perona-Malik equation

An impressive and efficient improvement in the classical scale-space analysis was proposed by Perona and Malik (1990) where they describe the diffusion process known as the Perona-Malik (PM) equation. Despite the illposed nature of the PM equation, many of its applications could be carried with success in the signal processing field. On the other hand Weickert and Benamouda (1997) proved the regularization of the PM equation describing and analyzing a model on a semidiscrete system. In this article we present a regularized model of the PM diffusion equation for image segmentation. We start from the hypothesis of well-posedness in the discrete space and the stability conditions. We show two methods for automatic setting of the gradient threshold k, which is changed for each iteration of the partial differential equation (PDE) integration steps. Experimental segmentations are implemented for noise reduction of generic digital images and for segmentation of microcalcifications on X-ray biomedical images.