Tumor vasculature has a high degree of irregularity as compared to normal vasculature. The quantification of the morphometric complexity in tumor images can be useful in diagnosis. Also, it is desirable in several other medical applications to have an automated complexity analysis to aid in diagnosis and prognosis under treatment. e.g. in diabetic retinopathy and in arteriosclerosis. In addition, prior efforts at segmentation of the tumor vasculature using matched filtering, template matching and splines have been hampered by the irregularity of these vessels. We try to solve both problems by introducing a novel technique for vessel detection, followed by a tracing-independent complexity analysis based on a combination of ideas. First, the vessel cross-sectional profile is modeled using a continuous and everywhere differentiable family of super-Gaussian curves. This family generates rectangular profiles that can accurately localize the vessel boundaries in microvasculature images. Second, a robust non-linear regression algorithm based on M-estimators is used to estimate the parameters that optimally characterize the vessel’s shape. A framework for the quantitative analysis of the complexity of the vasculature based on the vessel detection is presented. A set of measures that quantify the complexity are proposed viz. Squared Error, Entropy-based and Minimum Description Length-based Shape Complexities. They are completely automatic and can deal with complexities of the entire vessel unlike existing tortuousity measures which deal only with vessel centerlines. The results are validated using carefully constructed phantom and real image data with ground truth information from an expert observer.