A new tool for shape decomposition is presented. It is a function defined on the shape domain and computed using a linear system of equations. It is demonstrated that the level curves of the new function provide a hierarchical partitioning of the shape domain into visual parts, without requiring any features to be estimated. The new tool is an unconventional distance transform where the minimum distance to the union of the shape boundary and an unknown critical curve is computed. This curve divides the shape domain into two parts, one corresponding to the coarse scale structure and the other one corresponding to the fine scale structure.