Spatially-variant anisotropic morphological filters driven by gradient fields

Abstract. This paper deals with the theory and applications of spatia-lly-variant mathematical morphology. We formalize the definition of spa-tially variant dilation/erosion and opening/closing for gray-level images using exclusively the structuring function, without resorting to comple-ment. This sound theoretical framework allows to build morphological operators whose structuring elements can locally adapt their orientation across the dominant direction of image structures. The orientation at each pixel is extracted by means of a diffusion process of the average square gradient field, which regularizes and extends the orientation in-formation from the edges of the objects to the homogeneous areas of the image. The proposed filters are used for enhancement of anisotropic images features such as coherent, flow-like structures.