An Affine moment invariant for multi-component shapes

We introduce an image based algorithmic tool for analyzing multi-component shapes here. Due to the generic concept of multi-component shapes, our method can be applied to the analysis of a wide spectrum of applications where real objects are analyzed based on their shapes - i.e. on their corresponded black and white images. The method allocates a number to a shape, herein called a multi-component shapes measure. This number/measure is invariant with respect to affine transformations and is established based on the theoretical frame developed in this paper. In addition, the method is easy to implement and is robust (e.g. with respect to noise). We provide two small but illustrative examples related to aerial image analysis and galaxy image analysis. Also, we provide some synthetic examples for a better understanding of the measure behavior.