We propose an approach to the problem of reconstruction of 3D surfaces from magnetic resonance (MR) images. We use shape-based contour interpolation and extrapolation algorithms implemented based on the active contour technique; our idea is to use distance mapping of feature points in order to model the active contour dynamics. We establish differential equations describing the active contour dynamics and set up an iterative procedure for numerical solution. The efficiency of approach is demonstrated on contours of liver and liver tumors in MR images.