Fractal and Multi-Scale Fractal Dimension analysis: a comparative study of Bouligand-Minkowski method

TL;DR

This paper compares Fractal Dimension and Multi-Scale Fractal Dimension methods for shape analysis, evaluating their effectiveness and parameter configurations on a classified shape database.

Contribution

It provides a systematic comparison of two fractal-based shape complexity measures, highlighting their differences and practical considerations in shape analysis.

Findings

Multi-Scale Fractal Dimension offers more detailed shape complexity insights.

Parameter settings significantly influence the performance of both methods.

The comparative analysis guides better method selection for shape characterization.

Abstract

Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape analysis is the complexity, and Fractal Dimension and Multi-Scale Fractal Dimension are both well-known methodologies to estimate it. This papers presents a comparative study between Fractal Dimension and Multi-Scale Fractal Dimension in a shape analysis context. Through experimental comparison using a shape database previously classified, both methods are compared. Different parameters configuration of each method are considered and a discussion about the results of each method is also presented.