When analysing digital images in metric spaces, several parameters based on image content and/or image structure can be used. Among these, a parameter that can be easily measured in practice for measuring self-similar images/image details is the fractal dimension or the fractal dimension-based quantities derived from it. All this makes it possible to perform measurements on individual or mass images or image details. However, the interpretation of the data obtained in this way raises several problems. The aim of this work is to describe the mathematical foundations of fractal dimension measurement characteristic of spectral content in digital images, by presenting it through practical examples. We also describe a possible solution regarding how the application of spectral image structure in practice can improve the interpretation and reliability of the measured results of box counting algorithms. We also examine the mathematical possibility of how the concept of spectral self-similar image structure and the entropy of the Second Law of Thermodynamics can help in the interpretation of image data obtained during living or inanimate natural science processes. By re-examining previous results and using new measurement results, we illustrate the role of geometry resolution in spectral fractal structure-based studies. Considering the entire Universe as a single sensor, we provide the main parameters of this sensor, including values characteristic of its spectral fractal structure.
József Berke (Thu,) studied this question.