Many three-dimensional (3-D) medical images have lower resolution in the z direction than in the x or y directions. Before extracting and displaying objects in such images, an interpolated 3-D gray-scale image is usually generated via a technique such as linear interpolation to fill in the missing slices. Unfortunately, when objects are extracted and displayed from the interpolated image, they often exhibit a blocky and generally unsatisfactory appearance, a problem that is particularly acute for thin treelike structures such as the coronary arteries. Two methods for shape-based interpolation that offer an improvement to linear interpolation are presented. In shape-based interpolation, the object of interest is first segmented (extracted) from the initial 3-D image to produce a low-z-resolution binary-valued image, and the segmented image is interpolated to produce a high-resolution binary-valued 3-D image. The first method incorporates geometrical constraints and takes as input a segmented version of the original 3-D image. The second method builds on the first in that it also uses the original gray-scale image as a second input. Tests with 3-D images of the coronary arterial tree demonstrate the efficacy of the methods.