Fractal dimension and object eccentricity trends in natural and synthetic images
We characterize the fractal dimension of images of overlapping ellipses for varying eccentricity values. Using the Box-Counting Method, we calculated the fractal dimensions of a synthetic (images of overlapping ellipses) and natural data set (images of green peas). A non-linear relation between the number of ellipses and the fractal dimension was found for all eccentricity values. Upon normalization with the area fraction, the best fit curve was found to be N−α where 0.5 ≤ α ≤ 0.57. A similar trend between the fractal dimension and number of objects was also observed for the natural data.