On a Fast Piece-Wise Linear Hough Transform PLHT and its Application

Replacing the Hough calculation of the trigonomeric functions, sine and cos0,by the piece-wise linear Hough function(PLH), the basic cost for the sine , cose and the multiplications is removed. The PLH function is directly introduced from the usual Hough function. The PLH function inherits the basic properties of the usual Hough function from the view point to extract the line patterns from the pattern space. The computing cost of the PLH transform was reduced to about 1/6 of that of the usual Hough transform. It was also investigated that an additional property of the PLH transform contributes to reduce the memory cost to about 70 % of the usual Hough transform. Hough transform is one of the important methods to extract line patterns from the noisy and unclustered points of the image. As the edge or line patterns are the essential features in several industrial vision systems, it is practically required to make the Hough transform efficient from the view point of the computing and memory costs. A new fast Hough transform algorithm is introduced and its application is shortly presented in this paper. From this point of view, it is important to reduce the computing cost to utilize the Hough transform in several application. One of the factors in order to realize this cost reduction is to reduce the number of Hough calculations with respect to the number of edge points and and resolution numbers of the parameter space. It is still expectative to decrease the computing cost for the core Hough calculation defined by eq.(l). x.cos 0 + y.sin 8 (1) * =€I : perpendicular angle from x-axis JJ : the length of the perpendicular line In this paper, replacing Hough calculation of the trigonometric functions by the piecewise linear Hough(PLH) function which is composed of m pieces of line segments, the basic cost for the sine , cose and multiplications can be removed. It is shown in section 3 that the PLH function inherits the basic properties of the usual Hough function from the view point of to extract line patterns from the pattern space, and a few modifications of the pattern behavior in pattern space are also presented. In section 4, an new algorithm of piece-wise linear Hough transform(PLHT) is introduced, and some experimental results of PLHT are presented to demonstrate the reduction of the computing cost using an image of industrial engine parts. 2. Piece-wise Linear Hough Function 2.