Box-Counting Method of 2D Neuronal Image: Method Modification and Quantitative Analysis Demonstrated on Images from the Monkey and Human Brain.

Nemanja Rajković,Bojana Krstonošić,Nebojša Milošević

doi:10.1155/2017/8967902

Nemanja Rajković, Bojana Krstonošić + Show 1 more

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https://doi.org/10.1155/2017/8967902

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Abstract

This study calls attention to the difference between traditional box-counting method and its modification. The appropriate scaling factor, influence on image size and resolution, and image rotation, as well as different image presentation, are showed on the sample of asymmetrical neurons from the monkey dentate nucleus. The standard BC method and its modification were evaluated on the sample of 2D neuronal images from the human neostriatum. In addition, three box dimensions (which estimate the space-filling property, the shape, complexity, and the irregularity of dendritic tree) were used to evaluate differences in the morphology of type III aspiny neurons between two parts of the neostriatum.

Highlights

The fractal analysis, a modern mathematical method of measuring complexity in nature [1], is initially derived from fractal geometry [2]
The concepts of fractal geometry are being used in diverse research areas [3] and are proven to be useful tool as quantitative methods for image analysis in medical science [2, 4]
There are several different methods which calculate fractal dimension (FD) of object in a plane, but all of them can be summarized in two basic approaches: length-related and mass-related methods [3]

Summary

Introduction

The fractal analysis, a modern mathematical method of measuring complexity in nature [1], is initially derived from fractal geometry [2]. There are several different methods which calculate FD of object in a plane, but all of them can be summarized in two basic approaches: length-related and mass-related methods [3]. One of them is traditional boxcounting method (BC method) which is based on concept of “covering” the image with rectangular coordinate grid [2]. This method is not suitable for measuring length, as well as other features of patterns, it is the best technique for estimating the FD. For that reason BC method is commonly used among other fractal techniques [2, 4, 5]

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