Convergence index filter for vector fields

This paper proposes a unique filter called an iris filter, which evaluates the degree of convergence of the gradient vectors within its region of support toward a pixel of interest. The degree of convergence is related to the distribution of the directions of the gradient vectors and not to their magnitudes. The convergence index of a gradient vector at a given pixel is defined as the cosine of its orientation with respect to the line connecting the pixel and the pixel of interest. The output of the iris filter is the average of the convergence indices within its region of support and lies within the range [-1, 1]. The region of support of the iris filter changes so that the degree of convergence of the gradient vectors in it becomes a maximum, i.e., the size and shape of the region of support at each pixel of interest changes adaptively according to the distribution pattern of the gradient vectors around it. Theoretical analysis using models of a rounded convex region and a semicylindrical one is given. These show that rounded convex regions are generally enhanced, even if the contrast to their background is weak and also that elongated objects are suppressed. The filter output is 1/pi at the boundaries of rounded convex regions and semicylindrical ones, This value does not depend on the contrast to their background, This indicates that boundaries of rounded or slender objects, with weak contrast to their background, are enhanced by the iris filter and that the absolute value of 1/pi can be used to detect the boundaries of these objects. These theoretical characteristics are confirmed by the experiments using artificial and real X-ray images.