The given document discusses various aspects of complexity in different fields such as computer science, biology, etc. It emphasizes the importance of quantitative evaluation of complexity and its potential value in various fields. It also highlights the relationship between complexity and concepts like entropy and randomness.
Although this research focuses on images, it suggests that the theoretical framework can be applied to anything that can be represented as histograms or other types of sequences.
The method used in this research involves creating grayscale histograms at various positions (ranges) in black and white images and calculating the average variance of these histograms. This approach is similar to the concept of a kernel. Since the average variance depends on the range of the histogram, the researchers try different resolutions (i.e., different relative kernel sizes) to account for this variation.
The term “typical scale” is used, which can be thought of as the length at which complexity becomes visible. Additionally, a complexity index that considers all aspects is defined, which could also be useful.
The document includes two images that illustrate the concepts discussed.