Morphological conditional estimates of image complexity and information content

Abstract

We propose new morphological conditional estimates of image complexity and information content as well as morphological mutual information. These morphological estimates take into account both the number and the shape of image tessellation (mosaic) regions. We provide such a region shape account via joint use of mosaic image shape models based on the morphological image analysis (MIA) proposed by Yu. Pyt’ev and morphological thickness maps from the mathematical morphology (MM) introduced by J. Serra. Mathematical properties of morphological thickness maps are explored w.r.t. properties of structured elements, and corresponding properties of the proposed morphological image complexity and information content are proved. Some experimental results on image shape comparison in terms of shape complexity and information are reported. Open access images from a Kimia99 database  are utilized for these experiments.