Synthetic Data and Generative AI

Chapter 6: Shape classification and synthetization via explainable AI

Abstract

Here I define the mathematical concept of shape and shape signature in two dimensions, using parametric polar equations. The signature uniquely characterizes the shape, up to a translation or scale factor. In practical applications, the data set consists of points or pixels located on the shape, rather than the curve itself. If these points are not properly sampled – if they are not uniformly distributed on the curve – they need to be reweighted to compute a meaningful centroid of the shape, and to perform shape comparisons. I discuss the weights, and then introduce metrics to compare shapes (observed as sets of points or pixels in an image). These metrics are related ...