Anisotropic Morphological Filters With Spatially-Variant Structuring Elements Based on Image-Dependent Gradient Fields

Abstract

This paper deals with the theory and applications of spatially-variant discrete mathematical morphology. We review and formalize the definition of spatially variant dilation/erosion and opening/closing for binary and gray-level images using exclusively the structuring function, without resorting to complement. This theoretical framework allows to build morphological operators whose structuring elements can locally adapt their shape and orientation across the dominant direction of the structures in the image. The shape and orientation of the structuring element at each pixel are extracted from the image under study: the orientation is given by means of a diffusion process of the average square gradient field, which regularizes and extends the orientation information from the edges of the objects to the homogeneous areas of the image; and the shape of the orientated structuring elements can be linear or it can be given by the distance to relevant edges of the objects. The proposed filters are used on binary and gray-level images for enhancement of anisotropic features such as coherent, flow-like structures. Results of spatially-variant erosions/dilations and openings/closings-based filters prove the validity of this theoretical sound and novel approach.

Multiscale Image Analysis Based on Robust and Adaptive Morphological Scale-Spaces

“…-local orientations, including typically anisotropic gradient-driven operators (Verdú-Monedero et al, 2011).…”

An Approach to Adaptive Quadratic Structuring Functions Based on the Local Structure Tensor

“…Some methods of this type work in multiple scales in order to adapt the size of the structuring element to the local scale of structures in the image [2,18]. Other methods address structure by considering local orientation only [17], or by combining local orientation with other factors such as distances to edges [21] or degree of anisotropy [12]. It should be noted, however, that one can always find an orientation even though it may very well be completely irrelevant (i.e.…”

“…Some methods for adaptive morphology, such as the line-shaped or rectangular structuring elements presented by Verdú-Monedero et al [21] or the continuous PDE-based morphology presented by Breuß et al [6], use the LST components implicitly or explicitly, but without using the anisotropy information it contains. Only the Elliptical Adaptive Structuring Elements (EASE) method [11,12] takes advantage of this property of the LST.…”

Spatially and Intensity Adaptive Morphology

“…Adaptive morphology can be classified in two main approaches: spatially adaptive morphology and intensity adaptive morphology. The first class defines morphological operators [3]- [13] where the size and/or shape of the structuring element depends on the local spatial structures present in the image. The second class proposes operators [14]- [18] that process the image level sets differently (i.e.…”