This paper presents a new approach to 3-D shape metamorphosis. We express the interpolation of two shapes as a process where one shape deforms to maximize its similarity with another shape. The process incrementally optimizes an objective function while deforming an implicit surface model. We represent the deformable surface as a level set (iso-surface) of a densely sampled scalar function of 3 dimensions. Such level-set models have been shown to mimic conventional parametric deformable surface models by encoding surface movements as changes in the greyscale values of a volume dataset. Thus, a well-founded mathematical structure leads to a set of procedures that describes how voxel values can be manipulated to create deformations that are represented as a sequence of volumes. The result is a 3-D morphing method that offers several advantages over previous methods including minimal need for user input, no model parameterization, flexible topology, and sub-voxel accuracy.