Modeling sets of unordered points using highly eccentric ellipses
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Modeling sets of unordered points using highly eccentric ellipses Demetrios Gerogiannis* , Christophoros Nikou and Aristidis Likas
Abstract An algorithm for modeling a set of unordered two-dimensional points by line segments is presented. The points are modeled by highly eccentric ellipses, and line segments are extracted by the major axes of these elongated ellipses. At first, a single ellipse is fitted to points which is then iteratively split to a large number of highly eccentric ellipses to cover the set of points. Then, a merge process follows in order to combine neighboring ellipses with almost collinear major axes to reduce the complexity of the model. Experimental results on various databases show that the proposed scheme is an efficient technique for modeling unordered sets of points and shapes by line segments. A computer vision application of the method is also presented regarding the detection of retinal fundus image features, such as end-points, junctions, and crossovers. Keywords: Model fitting; Modeling by line segments; Line segment clustering; Ellipse eccentricity
1 Introduction In many computer vision applications, at a mid-level process, it is common to fit line segments in order to model a set of unordered points so as to summarize higher level features. For example, the detection of vanishing points [1], the vectorization of raster images [2], and the detection of road structures and parts [3] are among applications necessitating line segment description of image structures. In many of the aforementioned problems, the involved algorithms assume that they are provided with an ordered point set and standard polygonal approximation [4,5] is then applied. However, determining the ordering of point sets is not a trivial task, and in the method described herein, we relax this assumption by making no prior hypothesis about the ordering of the points. In the above context, the Hough transform (HT) is a widely used method for line fitting, and many variants have been proposed to improve its efficiency [6,7]. One of these variants is the randomized Hough transform (RHT) [8,9] which randomly selects a number of pixels from the input image and maps them into one point in the parameter space which was shown to be less complex, compared to the original algorithm, as far as time and *Correspondence: [email protected] Department of Computer Science and Engineering, University of Ioannina, Ioannina 45110, Greece
storage issues are concerned. In [10], the probabilistic HT was proposed whose basic idea is to apply a random sampling of edge points to reduce computational complexity and execution time. Further improvements were introduced in [11]. A similar concept was proposed in [12], where an orientation-based strategy was adopted to filter out inappropriate edge pixels, before performing the standard HT line detection which improves the randomized detection process. Also, the idea of fuzziness is integrated in the main algorithm in [13] to model the uncertainty imposed to the contour
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