Edge detection has been an essential step in image processing, and there has been much work undertaken to date. This paper inspects a fuzzy mathematical morphology in order to reach a higher-level of edge-image processing. The proposed scheme uses a fuzzy morphological gradient to detect object boundaries, when the boundaries are roughly defined as a curve or a surface separating homogeneous regions. The automatic edge detection algorithm consists of two major steps. First, a new version of anisotropic diffusion is proposed for edge detection and image restoration. All improvements of the new version use fuzzy mathematical morphology to preserve the edge accuracy and to restore the images to homogeneity. Second, the fuzzy morphological gradient operation detects the step edges between the homogeneous regions as object boundaries. This operation uses geometrical characteristics contained in the structuring element in order to extract the edge features in the set of edgeness, a set consisting of the quality values of the edge pixels. This set is prepared with fuzzy logic for decision and selection of authentic edge pixels. For experimental results, the proposed method has been tested successfully with both synthetic and real pictures.

A method of visualization of multimodal images by one monochromatic image is presented on the basis of the projection pursuit approach of the inverse process of the anisotropic diffusion which is a method of image restoration enhancing contrasts at edges. The extension of the projection from a linear one to nonlinear sigmoidal functions enhances the contrast further. The deterministic annealing technique is also incorporated into the optimization process for improving the contrast enhancement ability of the projection. An application of this method to a pair of MRI images of brains reveals its promising performance of superior visualization of tissues.