A robust algorithm for the fractal dimension of images and its applications to the classification of natural images and ultrasonic liver images

2010 ◽  
Vol 90 (6) ◽  
pp. 1894-1904 ◽  
Author(s):  
Wen-Li Lee ◽  
Kai-Sheng Hsieh
Keyword(s):  
Fractal Dimension ◽  
Natural Images ◽  
Robust Algorithm

Image Processing Applications Based on Texture and Fractal Analysis

2011 ◽  
pp. 226-250 ◽  
Author(s):  
Radu Dobrescu ◽  
Dan Popescu
Keyword(s):  
Fractal Dimension ◽  
Texture Classification ◽  
Malignant Tumour ◽  
Classification Performance ◽  
Textured Surfaces ◽  
Box Counting ◽  
Image Partition ◽  
Fractal Analyses ◽  
Occurrence Matrix

Texture analysis research attempts to solve two important kinds of problems: texture segmentation and texture classification. In some applications, textured image segmentation can be solved by classification of small regions obtained from image partition. Two classes of features are proposed in the decision theoretic recognition problem for textured image classification. The first class derives from the mean co-occurrence matrices: contrast, energy, entropy, homogeneity, and variance. The second class is based on fractal dimension and is derived from a box-counting algorithm. For the purpose of increasing texture classification performance, the notions “mean co-occurrence matrix” and “effective fractal dimension” are introduced and utilized. Some applications of the texture and fractal analyses are presented: road analysis for moving objective, defect detection in textured surfaces, malignant tumour detection, remote land classification, and content based image retrieval. The results confirm the efficiency of the proposed methods and algorithms.

DEFINITION AND CLASSIFICATION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION

Fractals ◽  
2017 ◽  
Vol 25 (05) ◽  
pp. 1750048 ◽  
Author(s):  
Y. S. LIANG
Keyword(s):  
Fractal Dimension ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
One Dimensional ◽  
Nondifferentiable Functions ◽  
Differentiable Functions ◽  
Closed Intervals ◽  
Bounded Variation Functions

The present paper mainly investigates the definition and classification of one-dimensional continuous functions on closed intervals. Continuous functions can be classified as differentiable functions and nondifferentiable functions. All differentiable functions are of bounded variation. Nondifferentiable functions are composed of bounded variation functions and unbounded variation functions. Fractal dimension of all bounded variation continuous functions is 1. One-dimensional unbounded variation continuous functions may have finite unbounded variation points or infinite unbounded variation points. Number of unbounded variation points of one-dimensional unbounded variation continuous functions maybe infinite and countable or uncountable. Certain examples of different one-dimensional continuous functions have been given in this paper. Thus, one-dimensional continuous functions are composed of differentiable functions, nondifferentiable continuous functions of bounded variation, continuous functions with finite unbounded variation points, continuous functions with infinite but countable unbounded variation points and continuous functions with uncountable unbounded variation points. In the end of the paper, we give an example of one-dimensional continuous function which is of unbounded variation everywhere.

Fractal dimension and classification of music

2000 ◽  
Vol 11 (14) ◽  
pp. 2179-2192 ◽  
Author(s):  
M. Bigerelle ◽  
A. Iost
Keyword(s):  
Fractal Dimension

Analysis and classification of speech signals by generalized fractal dimension features

2009 ◽  
Vol 51 (12) ◽  
pp. 1206-1223 ◽  
Author(s):  
Vassilis Pitsikalis ◽  
Petros Maragos
Keyword(s):  
Fractal Dimension ◽  
Speech Signals

scholarly journals Hydrophobicity classification of polymeric materials based on fractal dimension

2008 ◽  
Vol 11 (4) ◽  
pp. 415-419 ◽  
Author(s):  
Daniel Thomazini ◽  
Maria Virginia Gelfuso ◽  
Ruy Alberto Corrêa Altafim
Keyword(s):  
Fractal Dimension ◽  
Polymeric Materials

scholarly journals Classification of texture using random box counting and binarization methods

2021 ◽  
Vol 10 (1) ◽  
pp. 533-540
Author(s):  
Wijdan Jaber AL-kubaisy ◽  
Maha Mahmood
Keyword(s):  
Image Processing ◽  
Fractal Dimension ◽  
Blood Cells ◽  
Multifractal Analysis ◽  
Vision System ◽  
White Blood Cells ◽  
Real Life ◽  
Self Similarity ◽  
Box Counting

The heterogeneous texture classifications with the complexity of structures provide variety of possibilities in image processing, as an example of the multifractal analysis features. The task of texture analysis is a highly significant field of study in the field of machine vision. Most of the real-life surfaces exhibit textures and an efficiently modelled vision system must have the ability to deal with this variety of surfaces. A considerable number of surfaces maintain a self-similarity quality as well as statistical roughness at different scales. Fractals could provide a great deal of advantages; also, they are popular in the process of modelling these properties in the tasks related to the field of image processing. With two distinct methods, this paper presents classification of texture using random box counting and binarization methods calculate the estimation measures of the fractal dimension BCM. There methods are the banalization and random selecting boxes. The classification of the white blood cells is presented in this paper based on the texture if it is normal or abnormal with the use of a number of various methods.

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