Comment on: "Extended Hough transform for linear feature detection"

Cha et al. [1] recently proposed an efficient extendedHough transform (EHT) method for line detection. The most distinctive advantage of their EHT method is the ability to detect any line segment with desired length. In their proposed EHT method, first the input gray image with size h×w is transferred into the edge map by using the edge detector, e.g. the Sobel operator. For each edge pixel, the voting process is performed in two 3-D Hough spaces, each Hough space is consisted of a set of 2-D Hough planes [2], to detect line segments. In the EHT method, each 2-D Hough plane is used to collect the evidence of the line segments which is passing through a specific column of the input image. Considering the first column of the edge map, the edge pixel is selected one by one in a top-down manner. For each selected edge pixel with location (x, y), 0 x w − 1 and 0 y h− 1, a slope-intercept equation =− x+ y is created, and then the voting process is performed in the first Hough plane of the first Hough space for −1 < 1 corresponding to the angle range (−45◦, 45◦]; after rotating x and y axes by 90◦, i.e. mapping the edge pixels with location (x, y) into the one with location (−y, x), the voting process is performed in the first Hough plane of the second Hough space. Note that each edge pixel in the first column of the edge map must perform two voting processes for the first and second Hough spaces. By the same arguments, for the second column of the edge map, the above two voting processes are applied to the second Hough plane of the first Hough space and the second Hough space, and so on. After finishing the voting processes for the last column of the edge map, we sum up the number of votes of each pair of and through all Hough planes of each Hough space. For each pair of and , if the number of total votes is lager than the specific threshold, it can be claimed that the input image has a line segment with the parameters and and its starting point and ending point can be determined by checking the number of votes of