Edge contours using multiple scales

Abstract

An algorithm for finding a single good path through the set of edge points detected by gradient of Gaussian operator is discussed. First, an algorithm for finding contours at one scale is presented, then an extension of that algorithm which uses multiple scales to produce improved detection of weak edges is presented. The set of possible edge points is placed on a priority queue with the edge point having largest magnitude at the top. The strongest edge point that is not already on a contour is retrieved from the queue. The point in the computed direction is examined first, then in those in the adjacent directions on either side of it. Each branch is followed to the end and a weight assigned at each point based on four factors: a measure of noisiness, a measure of curvature, contour length, and the gradient magnitude. The point with the largest average weight is chosen. After searching from the initial point in one direction, a similar search is conducted in the oppositedirection unless a closed contour has been formed. In the algorithm for multiple scales the search for a contour proceeds as for the single scale, using the largest scale, until a best partial contour at that scale has been found. Then the next finer scale is chosen and the neighborhood around the end points of the contour are examined to determine possible edge points in a direction similar to the end point of the contour. The original algorithm is then followed for each of the points satisfying the above condition, and the best is chosen as an extension to the original edge. Further, in order to determine the size neighborhood that should be searched when attempting to pick up an edge at a smaller scale, a theoretical analysis of the movement of idealized edges is performed. This analysis examines two adjacent step edges having the same parity (a staircase) and opposite parity (a pulse). It is determined that maximum movement for both cases is σ, where σ is the standard deviation of the Gaussian used. This maximum movement occurs for the staircase when the two nearby edges have the same step size and are at a distance of 2σ apart. However, for edges closer or farther away, maximum movement decreases rapidly. For a pulse, maximum movement occurs when the two edges have the same step size and are very close together. Again the movement decreases rapidly as the edges become farther apart. Movement also decreases in both cases when the relative strengths of the two edges are not equal.