Significant Paths for 2D Shapes Using Measures on the Blum Medial Axis

We examine properties of the Blum Medial Axis (BMA) to improve its effectiveness for automated shape understanding. The BMA has been used to represent objects since the 1960s. Here we examine measurements on the BMA including shape tubularity (ST), erosion thickness (ET), and the extended distance function (EDF). We make connections between the three and use the EDF to find significant paths in 2D shapes. Three shapes are used: a whale tail with only one significant path, a symmetrical flower with a few identical significant paths, and a chicken shape with a few distinct significant paths. We analyze values of the EDF in order to automatically determine the significant directions within a shape. We also establish a relationship between the ST and ET measures that aid in shape identification in future work.