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Automated fundus image analysis plays an important role in the computer aided diagnosis of ophthalmologic disorders. A lot of eye disorders, as well as cardiovascular disorders, are known to be related with retinal vasculature changes. Many studies has been done to explore these relationships. However, most of the studies are based on limited data obtained using manual or semi-automated methods due to the lack of automated techniques in the measurement and analysis of retinal vasculature. In this thesis, a fully automated retinal vessel width measurement technique is proposed. This novel method models the accurate vessel boundary delineation problem in two-dimension into an optimal surface segmentation problem in threedimension. Then the optimal surface segmentation problem is transformed into finding a minimum-cost closed set problem in a vertex-weighted geometric graph. The problem is modeled differently for straight vessel and for branch point because of the different conditions in straight vessel and in branch point. Furthermore, many of the retinal image analysis needs the location of the optic disc and fovea as a prerequisite information, for example, in the analysis of the relationship between vessel width and the distance to the optic disc. Hence, a simultaneous optic disc and fovea detection method is presented, which includes a two-step classification of three classes. The major contributions of this thesis include: 1) developing a fully automated vessel width measurement technique for retinal blood vessels, 2) developing a simultaneous optic disc and fovea detection method, 3) validating the methods using multiple datasets, and 4) applying the proposed methods in multiple retinal vasculature analysis studies.