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New clinical studies suggest that narrowing of the retinal blood vessels may be an early indicator of cardiovascular diseases. One measure to quantify the severity of retinal arteriolar narrowing is the arteriolar-to-venular diameter ratio (AVR). The manual computation of AVR is a tedious process involving repeated measurements of the diameters of all arterioles and venules in the retinal images by human graders. Consistency and reproducibility are concerns. To facilitate large-scale clinical use in the general population, it is essential to have a precise, efficient and automatic system to compute this AVR. This paper describes a new approach to obtain AVR. The starting points of vessels are detected using a matched Gaussian filter. The detected vessels are traced with the help of a combined Kalman filter and Gaussian filter. A modified Gaussian model that takes into account the central light reflection of arterioles is proposed to describe the vessel profile. The width of a vessel is obtained by data fitting. Experimental results indicate a 97.1% success rate in the identification of vessel starting points, and a 99.2% success rate in the tracking of retinal vessels. The accuracy of the AVR computation is well within the acceptable range of deviation among the human graders, with a mean relative AVR error of 4.4%. The system has interested clinical research groups worldwide and will be tested in clinical studies.