International Journal of Computer Applications in Engineering Sciences [VOL I, ISSUE II, JUNE 2011] [ISSN: 2231-4946] 100 | Page Application of Hough Transform for finding Parametric Curves Love Jain # , Devesh Mahor * # Institute of Engineering and Technology, J K Lakshmipat University, Jaipur * M.M.E.C., M. M. University, Mullana, Ambala # lovejain.eck@gmail.com * mahor.devesh@gmail.com Abstract — The Hough Transform has been used to characterize analytic features. It was first applied to the recognition of straight lines, and later extended to circles, ellipses and arbitrary shaped objects. The Hough Transform (HT) has long been recognized as a technique of almost unique promise for shape and motion analysis in images containing noisy, missing and extraneous data. Its main disadvantage is the computational and storage requirements increase as a power of the dimensionality of the curve. It is not difficult to implement Circular Hough Transform (CHT) algorithm on modern personal computer. The initial work is done on line detection and then this work is generalized for detection of circle in gray level images. The Hough transform gives better result in case of noisy images. In this paper, the algorithms for line and circle detection are proposed and the results are demonstrated. Keywords— Hough Transform, CHT, Binary image, image processing, image space. I. INTRODUCTION Hough transform is a technique to detect straight line segments in a given binary image. To achieve this, for the first time in 1962, Hough proposed a method which provided a robust technique to identify the parameters of straight line edges in an image space [1]. The Hough transform is a technique which can be used to isolate features of a particular shape within an image. It is used to detect straight lines within a two dimensional binary image. By Hough Transform It is possible to find all kind of shapes that can be mathematical expressed, for instance lines, circles and ellipses, but only straight lines will be considered here. II. HOUGH TRANSFORM FOR LINE The problem of determining the location and orientation of straight lines in images arises in many diverse areas of image processing and computer vision, Since straight lines occur in various natural and man- made objects and many complex objects can often be identified by their distinct combination of linear features [5]. The expression for any straight line in which „m‟ is the slope and ‟ c” is where the line intersects the y-axis can be set as: y = m x + c (1) Now if we reverse our variables and look instead at the values of (m, c) as a function of the image point coordinates (x, y), then Equation 1 becomes: c = y - m x (2) Now, consider two pixels P1 and P2, which lie on the same line in the (x, y) space. For each pixel, we can represent all the possible lines through it by a single line in the (m, c) space. Thus a line in the (x, y) space that passes through both pixels must lie on the intersection of the two lines in the (m, c) space, which represent the two pixels. This means that all pixels which lie on the same line in the (x, y) space are represented by lines which all pass through a single point in the (m, c) space, see Fig. 1 and Fig. 2. The problem by represent a line as a point in the (m, c) parameter-space is that both m and c goes toward infinity when the line becomes more and more vertical, and thereby the parameter space becomes infinity large. Fig. 2 The mapping of P1 and P2 from cartesian space to the (m, c) space [5] Fig. 1 Points on the same line [5]