Calculating Fractal Dimension of Images Using Box-Counting Method

The fractal box-counting dimension is a method used to calculate the fractal dimension of images. This technique was implemented as part of my graduate-level programming assignment. In this assignment, I developed a program to compute the fractal box-counting dimension for given images. The box-counting dimension serves as a metric to quantify image complexity, revealing self-similarity characteristics and structural patterns within the image data. The algorithm implementation typically involves dividing the image into progressively smaller grid boxes and counting how many boxes contain image pixels at each scale. Through fractal dimension calculation, we can gain deeper insights into image morphology and content characteristics, with applications spanning image processing, pattern recognition, and computer vision. The core implementation requires logarithmic regression analysis of box counts versus box sizes to determine the dimension slope. This assignment presented both challenges and learning opportunities. By researching and coding this algorithm, I gained comprehensive understanding of fractal theory principles and their practical implementation. The program structure includes image preprocessing, multi-scale box counting, and dimension calculation modules. Completion of this project enhanced my expertise in both image processing techniques and fractal mathematics.