Applications of Vector Fields to Image Processing

Abstract

We use rotational and curvature properties of vector fields to identify critical features of an image. Using vector analysis and dif-ferential geometry, we establish the properties needed, and then use these properties in three ways. First, our results make it theoretically possible to identify extremal edges of an intensity function f(x, y) of two variables by considering the gradient vector field V = ∇f. There is also enough information in ∇f to find regions of high curvature (i.e., high curvature of the level paths of f). For color images, we use the vector field V = (I, Q). In application, the image is partitioned into a grid of squares. On the boundary of each square, V/|V| is sampled, and these unit vectors are used as the tangents of a curve α. The rotation number (or topological degree) η(α) and the average curvature ∫|κα| are computed for each square. Analysis of these numbers yields infor-mation on edges and curvature. Experimental results from both simu-lated and real data are described.