This paper proposes a new morphology-based approach for the interslice interpolation of current transformer (CT) and MRI datasets composed of parallel slices. Our approach is object based and accepts as input data binary slices belonging to the same anatomical structure. Such slices may contain one or more regions, since topological changes between two adjacent slices may occur. Our approach handles explicitly interslice topology changes by decomposing a many-to-many correspondence into three fundamental cases: one-to-one, one-to-many, and zero-to-one correspondences. The proposed interpolation process is iterative. One iteration of this process computes a transition sequence between a pair of corresponding input slices, and selects the element located at equal distance from the input slices. This algorithmic design yields a gradual, smooth change of shape between the input slices. Therefore, the main contribution of our approach is its ability to interpolate between two anatomic shapes by creating a smooth, gradual change of shape, and without generating over-smoothed interpolated shapes.