Modified Hausdorff Fractal Dimension (MHFD)

TL;DR

This paper introduces a modified Hausdorff fractal dimension that improves robustness and noise resistance when estimating the complexity of non-fractal images, enhancing its practical applicability.

Contribution

A novel modification to the Hausdorff fractal dimension that reduces shape dependence and noise sensitivity for better complexity estimation of non-fractal images.

Findings

Demonstrated improved robustness on diverse images

Reduced impact of noise in complexity measurements

Promising performance in practical image analysis

Abstract

The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating complexity of non-fractal images. The modified Hausdorff fractal dimension stands on two features that weaken the requirement of presence of a shape and also reduce the impact of the noise possibly presented in the input image. The new algorithm has been evaluated on a set of images of different character with promising performance.