Moment invariants for multi-component shapes with applications to leaf classification

Abstract

In this paper we introduce seven new invariants for multi-component shapes, and apply them to the leaf classification problem. One of the new invariants is an area based analogue of the already known boundary based anisotropy measure, defined for the multi-component shapes (Rosin and Žunić, 2011). The other six invariants are completely new. They are derived following the concept of the geometric interpretation (Xu and Li, 2008) of the first two Hu moment invariants (Hu, 1961). All the invariants introduced are computable from geometric moments corresponding to the shape components. This enables an easy and straightforward computation of translation, rotation, and scaling invariants. Also, being area based, the new invariants are robust to noise and mild deformations. Several desirable properties of the new invariants are discussed and evaluated experimentally on a number of synthetic examples. The usefulness of the new multi-component shape invariants, in the shape based object analysis tasks, is demonstrated on a well-known leaf data set.