An Efficiency Criterion for 2D Shape Model Selection.

We propose efficiency of representation as a criterion for evaluating shape models, then apply this criterion to compare the boundary curve representation with the medial axis. We estimate the å-entropy of two compact classes of curves. We then construct two adaptive encodings for noncompact classes of shapes, one using the boundary curve and the other using the medial axis, and determine precise conditions for when the medial axis is more efficient. Along the way we construct explicit near-optimal boundarybased approximations for compact classes of shapes and an explicit compression scheme for non-compact classes of shapes based on the medial axis. We end with an application of the criterion to shape data.