Efficient vertex detection algorithms using the Hough transform

A recurring problem in computer image processing is the detection of curves and straight lines in a digital image. The Hough transform technique has been widely used in the field of machine vision for detecting straight lines and curves in an image. Typically, the parameters of the normal form of a straight line (p, theta) are used for detecting straight lines in the image plane. In order to detect a straight line, the Hough transform method requires an extensive search on the p, theta-space by varying the values of theta from 0 to pi. In the present paper, three algorithms have been proposed to reduce the search on the parametric theta-axis of the parameter space for determining the vertices of a polygonal part. Prior to the application of these algorithms, the pixels belonging to each of the edges of the polygonal part are identified using a rule-base. In the first algorithm, the approximate theta-value for each of the edges is determined using regression analysis and the Hough transform is performed over a small range on either side of this angle value. In the second algorithm, a binary search on the parametric plane for each of the edges is performed. This eliminates the need to compute the p values for every increment of theta. The third algorithm improves on the binary search method by restricting the search to a small range of a values. The proposed algorithms are valid for identifying vertices of convex, as well as non-convex, pat polygonal parts. Such a system can act as a preprocessor for inspection, feature recognition and reverse engineering of flat polygonal parts.