A Riemannian Elastic Metric for Shape-Based Plant Leaf Classification

The shapes of plant leaves are of great importance to plant biologists and botanists, as they can help to distinguish plant species and measure their health. In this paper, we study the performance of the Squared Root Velocity Function (SRVF) representation of closed planar curves in the analysis of plant-leaf shapes. We show that it provides a joint framework for computing geodesics (registration) and similarities between plant leaves, which we use for their automatic classification. We evaluate its performance using standard databases and show that it outperforms significantly the state-of-the-art descriptor-based techniques. Additionally, we show that it enables the computation of shape statistics, such as the average shape of a leaf population and its principal directions of variation, suggesting that the representation is suitable for building generative models of plant- leaf shapes.