Learning shape metrics with Monte Carlo optimization

Quantifying and modeling shape variation within a population, identifying morphological contrasts across groups, and categorizing individuals or objects according to morphological similarity are central problems in numerous domains of science and applications. In this paper, we present an approach to optimal shape categorization through a new family of metrics for shapes presented as a finite collection of labeled landmark points. We develop a technique to learn metrics that optimally differentiate and categorize shapes using Monte Carlo optimization methods. We discuss the theory and the practice of the methods and apply them to the analysis of synthetic data and the classification of multiple species of fruit flies based on the shape of their wings.