IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 17, NO. 2, APRIL 1998 263 A Fuzzy Vessel Tracking Algorithm for Retinal Images Based on Fuzzy Clustering Yannis A. Tolias, Student, IEEE, and Stavros M. Panas,* Member, IEEE Abstract—In this paper we present a new unsupervised fuzzy algorithm for vessel tracking that is applied to the detection of the ocular fundus vessels. The proposed method overcomes the problems of initialization and vessel profile modeling that are encountered in the literature and automatically tracks fundus vessels using linguistic descriptions like “vessel” and “nonvessel.” The main tool for determining vessel and nonvessel regions along a vessel profile is the fuzzy C-means clustering algorithm that is fed with properly preprocessed data. Additional procedures for checking the validity of the detected vessels and handling junctions and forks are also presented. The application of the proposed algorithm to fundus images and simulated vessels re- sulted in very good overall performance and consistent estimation of vessel parameters. Index Terms— Fuzzy clustering, fuzzy techniques, retinal im- ages, vessel tracking. I. INTRODUCTION T HE accurate and automated analysis of vessel mor- phology is a valuable tool in medical imaging since it is applicable to many diagnostic processes, i.e., retinal fluorescein angiography and cineangiography. In general, the algorithms that have been presented in the literature can be divided in two major categories: those that use an edge detection approach—Sobel edge detectors, gradient operators and morphological edge detectors—and those that use matched filtering and thresholding in order to detect the existence of vessels in the image. Pappas and Lim [1] have tried to estimate the vessel diameter by assuming an elliptical vessel profile and a second order model for the background. Each profile is considered independently, so the continuity information of the vessel is not used at all. Eichel et al. [2] proposed an algorithm based on a sequential search that assigns belief values to edges and paths, according to a probabilistic model called the path metric. The path metric Manuscript received July 2, 1997; revised January 12, 1998. This work was supported by the General Secretariat for Research and Development, Ministry of Development, Greece under the PENED94 Programme, Grant 339. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was W. E. Higgins. Asterisk indicates corresponding author. Y. A. Tolias is with the the Telecommunications Laboratory, Signal Processing and Biomedical Technology Unit, Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki GR- 54006, Greece. *S. M. Panas is with the the Telecommunications Laboratory, Signal Processing and Biomedical Technology Unit, Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki GR- 54006, Greece (e-mail: panas@psyche.ee.auth.gr). Publisher Item Identifier S 0278-0062(98)04996-9. was designed in a manner that it’s value increases when the followed path is member of a vessel edge. However, there exist cases when false paths are tracked because the algorithm cannot resolve if a path is a true vessel edge or not. Another problem associated with Eichel’s method is that it tracks edges instead of vessels; in cases of junctions or forks the edge is still being followed even if it does not belong to the same vessel. Chaudhuri et al. [3] presented an algorithm that is based on directional two-dimensional (2-D) matched filters that assume a Gaussian vessel profile and small vessel radius variations. The primary advantage of this method is that it is completely unsupervised and may result in a good initial estimate of the vessels in the image. However, the detected vessels may not be continuous, junction points are not always detected, small vessels are missed and the validity of the detected vessels is not checked. Liu and Sun [4] presented an adaptive tracking algorithm using a three-stage recursive procedure. First, given a starting position and direction, a segment in the vascular network is identified. Then, by filling it with the surrounding back- ground pixel values, the detected segment is deleted from the angiogram. The detection-deletion scheme is employed to prevent the problem of tracking-path reentry in those areas where vessels overlap. Finally, all branch points are detected by use of matched filtering along both edges of the vessel. The detected branch points are used as the starting points in the next recursion. The recursive procedure terminates when no new branch point is found. The algorithm performs well when applied to angiograms of coronary and radial arteries. To provide a quantitative evaluation, vascular networks identified by the algorithm are compared to those identified by a human. The algorithm results in some false-negative errors, but very few false-positive errors. Miles and Nutall [5] proposed an algorithm that calculates the vessel position and diameter by minimizing the difference between the vessel profile and a predefined set of model profiles. The start and finish points, as well as the initial vessel direction, are entered by the user. Zhou et al. [6] presented an algorithm that relies on a matched filtering approach coupled with a priori knowledge about retinal vessel properties to automatically detect the vessel boundaries, track the midline of the vessel, and extract useful parameters of clinical interest. By modeling the vessel profile using Gaussian functions, improved estimates of vessel diameters over previous algorithms are obtained. An adaptive densitometric tracking technique based on local neighborhood information is also used to improve computational perfor- mance in regions where the vessel is relatively straight. The 0278–0062/98$10.00  1998 IEEE