Requirements for a good shape representation lead to descriptors that are object centered and that have the notion of scale. These representations usually take the form of shape skeletons at multiple detail levels. Classical tool for skeleton extraction is the grassfire equation, in which the process is lossless and the equation can be run backwards in order to obtain shape boundary from the shape skeleton. Many complicated strategies have been devised to assign significance to skeletal points in order to arrive at the skeleton scale space. A recent alternative approach is to introduce regularization directly to the skeleton extraction process, by combining diffusion with grassfire. Very recently, techniques, similar in spirit, which combine nonlinear smoothing of the shape boundary with the grassfire, in order to extract an axis based description, are presented independently. When diffusion is introduced into the formulation, inverse equation is no longer stable. This is the issue we will be addressing in the context of the method presented by Tari and Shah for extraction of nested symmetries from arbitrary images in arbitrary dimension. The basic tool used in the method is a specific distance function which is the steady-state solution of an elliptic boundary value problem. We present an inverse equation and show how one may obtain the whole distance surface from a sparse representation, providing a means for determining the shape boundary from the shape skeleton. The presented technique can be used for feature-preserving compression.