Order of points on a line segment

Abstract

The Hough transform is a method for the detection of many lines on a plane [1,2,3,4]. This method achieves line detection by converting the line fitting problem on an imaging plane to a peak search problem in an accumulator space using the voting procedure. Although the Hough transform provides a method for line detection, this transform can not detect line segments. For the detection of line segments, it is necessary to detect both endpoints of each line segment. The detection of pairs of endpoints of line segments is mainly performed using the point following procedure by local window operation along each line; that is, assuming the connectivity of digitized points, the algorithm follows a series of sample points which should lie on a line. The method is, however, equivalent to a whole area search in the worst case, because it is necessary to investigate the connectivity of all sample points in the region of interest, point by point.