Evaluation and assessment of homogeneity in images. Part 1: Unique homogeneity percentage for binary images

•Assessment of an absolute homogeneity value on images.•Full parametrization of the macro-pixel curve defining homogeneity.•Developed for binary images in this first part.•Homogeneity calculated only with the self-information of an image.

Texture features analysis is one of the most important approaches for the assessment of homogeneity on images. However, all of them are either relative to the comparison with a standardized set of images, or further multivariate models are strongly required to predict or classify the images according to their features. In this first work, we propose an alternative and novel methodology to calculate a percentage of homogeneity by only using the self-information contained on the image. This methodology is based on the macropixel analysis theory and the generation of what is called the “homogeneity curve”. The homogeneity curve is deeply explored and the knowledge to what it could be considered the most homogeneous and inhomogeneous distribution for every case is spanned. This first work postulates the theory and demonstrates its usefulness with several examples applied to binary images. This will provide a theoretical framework to fully understand the homogeneity curve, postulating a mathematical model to parametrize homogeneity and its plausible deviations.

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