Applications of the Information Dimension in Detecting Border Perturbations

Abstract

This study utilizes the concept of information dimension based on Shannon and Tsallis' entropy to analyze the contours of flat objects. Our objective is to employ the information dimension for detecting perturbations in borders. We create examples of squares with slight border perturbations, possessing the same mass and sharing identical box-counting dimensions yet exhibiting distinct information dimensions. This construction was devised with the understanding that entropy is responsive to the image frequency within each box. Consequently, the information dimension provides a more precise index of fractal shapes when compared to the box-counting dimension.