Efficient Shape Modeling: ⋮-Entropy, Adaptive Coding, and Boundary Curves -vs- Blum’s Medial Axis

Abstract

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 ⋮-entropy of two compact classes of curves. We then construct two adaptive encodings for non-compact 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. Finally, we apply our results to databases of naturally occurring shapes, determining whether the boundary or medial axis is more efficient. Along the way we construct explicit near-optimal boundary-based approximations for compact classes of shapes, construct an explicit compression scheme for non-compact classes of shapes based on the medial axis, and derive some new results about the medial axis.