In diagnosing diseases and planning surgeries the structure and length of blood vessels is of great importance. In this research we develop a novel method for the segmentation of 2-D and 3-D images with an application to blood vessel length measurements in 3-D abdominal MRI images. Our approach is robust to noise and does not require contrast-enhanced images for segmentation. We use an effective algorithm for skeletonization, graph construction and shortest path estimation to measure the length of blood vessels of interest.