Recognition of Partial Circular Shapes from Segmented Contours

method gives satisfactory results. Finding peaks is a more difficult task in the radius histogram in the two-stage This paper presents a circle-finding method to deal with partially occluded circles using segmented contours. Contours Hough transform [3, 4], which is sensitive to inaccuracy in are segmented using a criterion based on the derivative of the the first stage. A particular deficiency of the Gerig Hough curvature. Constant curvature segments are primitives inputted transform method [5] is that it cannot find concentric circles into a clustering algorithm which brings out the relationships in its simplest implementation. Other versions of the among contour segments which are likely to represent the same Hough transform method [6] can perform quickly, but only circles. A minimization criterion is used to find the circle paramto estimate the centers of the circles, and suffer from impreeters, providing an accurate parameter estimation. The method cision in estimating the center when the missing parts of allows recovery of the contour segments used to estimate circle a contour are significant. parameters, providing useful information in some practical apOn the other hand, the accuracy of parameter estimation plications.  1996 Academic Press, Inc. for the Hough transform methods depends on the quantization of the accumulator space. Applications which require more accuracy in parameter estimation usually use INTRODUCTION an initial estimation of the circle parameters by a Hough Circular contour recognition has received much attentransform technique and subsequently perform a leasttion since the earliest days in image analysis research, squares fit on points which fall in a template around the mainly because a wide range of round and circular objects initial estimated circle [7]. Alternatively, robust estimators are present in many machine vision applications in indusare used in an iterative way starting from this initial estimatrial and other environments. In these applications, the tion to avoid the sensitivity to outliers [8]. location of circular or round objects allows automatic maIn the work presented here, the problem of circle finding nipulation or automatic inspection for grading or sorting. is dealt with from another direction. The motivation was In particular, the work we are presenting here has been to deal with the problems of circular contours in several aimed at some applications in the agricultural and food degrees of partial occlusion, bringing out their circle paindustries to locate fruits more accurately for robotic harrameters in an accurate way and also to identify the proporvesting and for sorting of food products. tion of missing (or present) circular contours of each object. The classical approach to recognizing geometrical patKnowing the proportion of missing circular contour allows terns has been the Hough transform [1] which, due to its one, for example, to reject broken items in a grading simple but exhaustive approach in calculating the three process. parameters that define a circular arc (center coordinates Our approach was to look at the problem with a more and radius), leads to a heavy computational burden in time structured representation. Instead of using points as primiand memory. In order to reduce this complexity, later tives to find the relations among them without taking into approaches to the original Hough transform have been account other close-by feature points, curve segments were developed to recognize circular patterns. A comparative used as initial inputs, and their relationships were used to study of these techniques was made by Yuen et al. [2]. look for segments which define or belong to the same Even the most memory efficient method requires twice the circle. Once curves have been segmented into constant image storage (the two-stage Hough transform [3, 4]) to curvature segments, an interpretation process looks for achieve at least one pixel accuracy in the calculation of relationships between the curve segments and groups them the parameters. into different sets. Segments in the same set are likely to Some problems in Hough transform techniques are the represent a single circle whose parameters (radius and choice of a threshold and finding peaks in the accumulator center coordinates) and proportion of contour may be subsequently found. space, although for finding peaks, the Gerig and Klein [5]