We propose an object-based interpolation that utilizes the core, a multiscale representation of object shape, as the basis for determining an interpolated object's position and intensities. The core calculations are made directly from image intensities, with no intermediate location of object boundaries. The core of the interpolated object is first determined by an interpolation of the cores of the corresponding objects. The intensity at each of the positions in the object specified by the interpolated core is then determined by interpolating intensities from the equivalent positions in the corresponding objects; positions with equivalent distances along and from the core are chosen via the algorithm described in the paper. This object-based geography has produced promising results for simple, single-core interobject interpolations, and research continues in determining an interpolation method for multifigure objects as well as the background positions in realistic medical images.