An Efficient Differential Box-Counting Approach to Compute Fractal Dimension of Image

  title={An Efficient Differential Box-Counting Approach to Compute Fractal Dimension of Image},
  author={Nirupam Sarkar and Bidyut Baran Chaudhuri},
  journal={IEEE Trans. Syst. Man Cybern. Syst.},
Fractal dimension is an interesting feature proposed to characterize roughness and self-similarity in a picture. This feature has been used in texture segmentation and classification, shape analysis and other problems. An efficient differential box-counting approach to estimate fractal dimension is proposed in this note. By comparison with four other methods, it has been shown that the authors, method is both efficient and accurate. Practical results on artificial and natural textured images… 

Figures and Tables from this paper

Efficient fractal method for texture classification

The discriminating capacity and the time efficiency of EFD are evaluated in comparison with fractal dimension (FD) computed by box counting both theoretically and empirically and revealed that EFD is better than FD for texture identification and classification.

Fractal dimension estimation for texture images: A parallel approach

A New Box-Counting Method for Estimation of Image Fractal Dimension

The computation results of fractal dimension of simulated images and Brodatz texture images demonstrate the new box-counting method is effective and produces a wider range in fractal Dimension than the original DBC method.

An Improve Differential Box Counting Method to Estimate Fractal Dimension

This paper proposes a new method based on the aggregate gray level values in the image to estimate the dimension of gray scale image, and shows an improvement over the traditional DBC method.

An improved box-counting method for image fractal dimension estimation

Analysing Fractal Dimension of Color Images

Fractal Dimension (FD) is an important feature of fractal geometry that finds the significant application in different fields including texture segmentation, shape classification and image analysis.

A new box-counting method for image fractal dimension estimation

A new method based on the idea of dilation is proposed, which is simple and understandable, and has the same desired counting accuracy in x, y, and z directions and can outperform other existing methods in estimation accuracy and robustness.

An Improved Differential Box-Counting Approach to Compute Fractal Dimension of Gray-Level Image

  • Song-tao Liu
  • Computer Science
    2008 International Symposium on Information Science and Engineering
  • 2008
The results show that the proposed approach not only has more precise estimated value of fractal dimension, but also consumes less computational time.

A practical method for estimating fractal dimension

Relative improved differential box-counting approach to compute fractal dimension of grayscale images

Various methods used to calculate the FD of gray scale images are emphasized and key problems involved in the computation of Differential box count method are presented.

Random Fractals: characterization and measurement

Mandelbrot’s fractal geometry provides both a description and a mathematical model for many of the seemingly complex shapes found in nature. Such shapes often possess a remarkable invariance under

Fractal-Based Description of Natural Scenes

  • A. Pentland
  • Environmental Science
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 1984
The3-D fractal model provides a characterization of 3-D surfaces and their images for which the appropriateness of the model is verifiable and this characterization is stable over transformations of scale and linear transforms of intensity.

Multiple Resolution Texture Analysis and Classification

Textures are classified based on the change in their properties with changing resolution, and the relation of a texture picture to its negative, and directional properties are discussed.

Fractals: not just another pretty picture

The reduction of imagery to a set of fractals as a way to achieve greatly improved image compression is examined and the performance and the extent of its applicability are discussed.

The use of the fractal dimension to quantify the morphology of irregular‐shaped particles

For several decades, sedimentologists have had difficulty in obtaining an efficient index of particle form that can be used to specify adequately irregular morphology of sedimentary particles.

Automated image segmentation by mathematical morphology and fractal geometry

  • Jean Paul Rigaut
  • Materials Science
  • 1988
A new method for automated image segmentation is presented. It makes use of a combination of principles derived from mathematical morphology and fractal geometry.

Shading into Texture

Fractal Geometry of Nature

This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.