Shape-based interpolation as applied to binary images causes the interpolation process to be influenced by the shape of the object. It accomplishes this by first applying a distance transform to the data. This results in the creation of a gray-level data set in which the value at each point represents the minimum distance from that point to the surface of the object. (By convention, points inside the object are assigned positive values; points outside are assigned negative values.) This distance transformed data set is then interpolated using linear or higher order interpolation and is then thresholded at a distance value of 0 to produce the interpolated binary data set. In this paper, we describe a new method that extends shape-based interpolation to gray-level input data sets. This generalization consist of first lifting the n-dimensional image data to represent it as a surface, or equivalently as a binary image, in an (n plus 1)- dimensional space. The binary shape-based method is then applied to this image to create an (n plus 1)-dimensional binary interpolated image. Finally, this image is collapsed (inverse of lifting) to create the n-dimensional interpolated gray-level data set. We have conducted several evaluation studies involving patient CT and MR data as well mathematical phantoms. They all indicate that the new method produces more accurate results than conventional gray-level interpolation methods, although at the cost of increased computation.