Recent research suggests that retinal vessel caliber (or cross-sectional width) measured from retinal photographs is an important feature for predicting cardiovascular diseases (CVDs). One of the most utilized measures is to quantify retinal arteriolar and venular caliber as the Central Retinal Artery Equivalent (CRAE) and Central Retinal Vein Equivalent (CRVE). However, current computer tools utilize manual or semi-automatic grading methods to estimate CRAE and CRVE. These methods involve a significant amount of grader's time and can add a significant level of inaccuracy due to repetitive nature of grading and intragrader distances. An automatic and time efficient grading of the vessel caliber with highly repeatable measurement is essential, but is technically challenging due to a substantial variation of the retinal blood vessels' properties. In this paper, we propose a new technique to measure the retinal vessel caliber, which is an "edge-based" vessel tracking method. We measured CRAE and CRVE from each of the vessel types. We achieve very high accuracy (average 96.23%) for each of the cross-sectional width measurement compared to manually graded width. For overall vessel caliber measurement accuracy of CRAE and CRVE, we compared the results with an existing semi-automatic method which showed high correlation of 0.85 and 0.92, respectively. The intra-grader reproducibility of our method was high, with the correlation coefficient of 0.881 for CRAE and 0.875 for CRVE.