An affine moment invariant for multi-component shapes

We introduce an image based algorithmic tool for analyzing multi-component shapes. The method allocates a number to a shape, herein called a multi-component shape measure. This number/measure is invariant with respect to affine transformations and is established based on the theoretical framework developed here. In addition, the method is easy to implement and fast to compute. We provide two small but illustrative examples related to the analysis of both aerial and celestial galaxy imagery. We also provide some synthetic examples for a better understanding of the behavior of the measure.