  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.

Computer Vision and Pattern Recognition