Scale Adaptive Complexity Measure of 2D Shapes

In this paper, we describe a complexity (or irregularity) measure of 2D shapes. Three properties are first calculated to separately describe the complexity of the boundary, the global structure, and the symmetry of the shape. Then, a model consisting of the above parameters are developed to describe the entire complexity of the shape. This model further incorporates the scale information into the boundary complexity definition and also into the determination of weights associated with different properties. Finally, we test our complexity model on a synthetic dataset, and demonstrate its application on screening shapes extracted from noisy shoeprint images