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 ¿. The rotation number (or topological degree) ¿(¿) and the average curvature f|¿¿| 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.

Edge detection in the presence of noise is a well-known problem. This paper examines an applications-motivated approach for solving the problem using novel techniques and presents a method developed by the authors that performs well on a large class of targets. ROC curves are used to compare this method with other well-known edge detection operators, with favorable results. A theoretical argument is presented that favors LMMSE filtering over median filtering in extremely noisy scenes. Simulated results of the research are presented.