International Journal Of Engineering Research And Development e-ISSN: 2278-067X, p-ISSN: 2278-800X, www.ijerd.com Volume 13, Issue 11 (November 2017), PP.01-07 1 An Improved Hough Transform for Circle Detection Nitin Bhatia Department of Computer Science, DAV College, Jalandhar 144008, India Corresponding Author:Nitin Bhatia Abstract:-Digital image processing relies heavily on detection of various objects. Detection of geometric objects like lines and circles helps image understanding. In this paper, an improved version of Hough transform for circle detection in digital images is presented. Hierarchical Hough transform has been modified to achieve better computational efficiency. An important property of square root of integers has been examined and applied to work in the favour of algorithm. The experimental analysis shows considerable improvement in speed of the algorithm without compromising the accuracy. Keywords:-Circle detection, Hough transform, hierarchical Hough transform, Automatic thresholding. --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 01-11-2017 Date of acceptance: 09-11-2017 --------------------------------------------------------------------------------------------------------------------------------------- I. INTRODUCTION Curve detection in digital images has a variety of applications. Line and circle detection are two of the many different geometrical objects that can be detected from images. Circular objects can be located in a digital image with the help of circle detection [1]-[4]. Most popular technique to detect circles from images is Hough transform [5]. In literature, many variations of Hough transform are available. Fast Hough transform or hierarchical Hough transform is one such variation [6]. Randomised Hough transform uses randomised image pixels to vote for Hough space cells or bins instead of using all pixels, thus reducing time required [7]. Fuzzy Hough transform uses fuzzy logic to decide the membership of an image pixel to a Hough bin [8]. Apart from techniques based on Hough transform, other techniques have also been proposed [9]-[12]. Mingzhu and Huanrong [9] give a simple method of choosing a pixel and then finding two other pixels, one in horizontal and other in vertical direction, and fit a circle to these three points. The efficiency of the method depends on the selection of initial pixel. Chen et al. [10] propose an algorithm in which edge image is divided into several sub-images by the properties of circle, and then the parameters of circles are calculated using the point pairs chosen from the sub-images followed by a data merging method to process the parameters. Ayala- Ramirez et al. [11] present a circle detection method based on genetic algorithms. The method does not work well while detecting small circles from digital images. Cuevas et al. [12] propose a method based on Electro- magnetism optimization, which is a nature inspired technique to detect circles. The technique requires a number of parameters to be set manually to detect circles. We propose a method based on hierarchical Hough transform. The main feature of this method is its speed. The proposed method shows its robustness to the presence of noise as well. We conduct experiments on a large number of images most of which are natural images and the accuracy of the method is observed to be the same as that of conventional Hough transform. The method shows very high efficiency in terms of time requirements. The comparisons are made with techniques given by [12] and [13]. II. HOUGH TRANSFORM Hough transform continues to be one of the landmark algorithm for curve detection in digital images. It works on the basis of voting in the Hough parameter space, a three dimensional space in case of circles. The local maxima is then selected as the bin which corresponds to circles in the image space. A. Classical Hough Transform Classical or standard Hough transform choses the simplistic approach of using equation of circle as (x − h) 2 −y − k 2 − r 2 =0 . Using all image points as (x, y) and voting for each bin as (h, k, r). This minimalistic approach is time consuming. B. HierarchicalHoughTransform The main drawback of circular Hough transform is its slow speed due to large number of computations. Speed inefficiency of CHT is dealt with using a hierarchical algorithm to work down the Hough space from coarser level to finer level [10], [11]. The Hough space used by the technique is dynamically quantized. It reduces the time taken as well as the memory needed to store the accumulated votes during the transform. The process starts with considering the whole HT space as a single accumulator cell which is assumed to attract number of votes equal to the number of edge pixels in the image space. Whenever, an accumulator cell is voted