For accurate determination of thickness-profile in vessel quantification, it is important to find appropriate vessel cross-sections. To obtain vessel cross-sections, a centerline-based approach has been widely used, but it has several inherent problems causing improper cross-sections. First, this approach cannot define cross-sections in a unique way. Second, cross-sections are sensitive to the degree of smoothness of a detected vessel centerline. Third, a small variation in a centerline causes a considerable change in the resultant cross-sections and this phenomenon brings about improper cross-sections in the abnormal vessel of asymmetric structure. Finally, wrong cross-sections may be detected due to the intersection with the other cross-sections in a region of high curvature. In this paper, instead of a centerline, we propose and adopt a complementary geodesic distance field. Then, we detect a sequence of equidistant lines by using the proposed distance field. Finally, we determine cross-sections by refining the obtained equidistant lines. Due to the prospective properties of the proposed distance field, we can alleviate all of the conventional problems and obtain the cross-sections more proper for vessel quantification. Through the intensive simulation using various 2-D synthesized images, we prove that the proposed method provides non-intersecting cross-sections which are insensitive to local variation of geometrical shapes in abnormal vessels.