My research falls under a general theme of model selection for structures in 2D images based on efficiency of representation, which means the 'best' model is the one that requires the fewest bits. I work primarily with models of two-dimensional shape, though recent work with students has explored models of texture.

My previous work compares efficiency of two shape models: the Blum medial axis, which is a skeletal shape model, and the boundary curve. Results are presented in three papers, in which we compute the epsilon-entropy of classes of plane curves, compare adaptive approximation using the two shape models including an application of results to a large shape databse, and compare uniform encoding using the two shape models.

1. Epsilon entropy and adaptive encoding. Aimed at the CS crowd; applies results to shape database.
      K. Leonard, An efficiency criterion for 2D shape model selection, IEEE CVPR Proc., 1, 2006, 1289 - 1296.

2. Proofs and formal statements of CVPR paper.
     K. Leonard, Efficient shape modeling: epsilon-entropy, adaptive coding, and Blum's medial axis versus the
      boundary curve, Int. J. Comp. Vis., 74, 2007, 183 - 199.

3. Comparison for uniform encoding.
     K. Leonard. Efficient representation in spaces of plane curves. Rend. Linc. Mat. e Appl., 20(1), 2009, 69-93.

My current work aims to construct results similar to those presented in the above papers using a more general medial structure developed by Damon and Pizer.