Improvement of 2-Partition Entropy Approach Using Type-2 Fuzzy Sets for Image Thresholding

Improvement of 2-Partition Entropy Approach Using Type-2 Fuzzy Sets for Image Thresholding

Ouarda Assas (Department of Computer Science, University of M'sila, M'sila, Algeria)
Copyright: © 2015 |Pages: 16
DOI: 10.4018/IJAEC.2015070103
OnDemand PDF Download:
No Current Special Offers


Thresholding is a fundamental task and a challenge for many image analysis and pre-processing process. However, the automatic selection of an optimum threshold has remained a challenge in image segmentation. The fuzzy 2-partition entropy approach for threshold selection is one of the best image thresholding techniques. In this work, an improvement of the later method using type-2 fuzzy sets is proposed to represent the imprecision or lack of knowledge of the expert in the choice of the membership function associated with the image. Two databases are used to evaluate its effectiveness: dataset of standard grayscale test images and MR Brain images. Experiment results show that the type-2 Fuzzy 2-partition entropy algorithm performs equally well in terms of the quality of image segmentation and leads to a good visual result.
Article Preview

2. Fuzzy 2-Partition Entropy Technique

In the fuzzy 2-partition entropy approach proposed in (Cheng, 1998), an image is modelled by 2 fuzzy sets which have membership functions and there is no sharp boundary between these sets (Assas, 2012). An image is modelled by two fuzzy sets dark and bright, whose membership functions are defined as follows:


Where x is the independent variable and a and c are parameters determining the shape of the above two membership functions.

We assume that the images have 256 gray levels ranging from 0 to 255. Then, an exhaustive search is used to find the pair aopt and copt which forms a fuzzy 2-partition that has the maximum entropy as follows:For a = 0 to254 For c = (a+1) to255

  • 1.

    For given a and c. new membership functions µd(i) and µb(i) are computed, for i =0, ...,255.

  • 2.

    Probabilities of the two fuzzy events dark and bright are defined as:


where P(i)is the probability of the occurrence of the gray level i =0, ...,255.
  • 3.

    The entropy of this fuzzy 2-partition is given by:


  • 4.

    The selected threshold value Topt which is the mid- point of aopt and copt has to satisfy the following criterion function:



Complete Article List

Search this Journal:
Open Access Articles: Forthcoming
Volume 13: 4 Issues (2022): 1 Released, 3 Forthcoming
Volume 12: 4 Issues (2021)
Volume 11: 4 Issues (2020)
Volume 10: 4 Issues (2019)
Volume 9: 4 Issues (2018)
Volume 8: 4 Issues (2017)
Volume 7: 4 Issues (2016)
Volume 6: 4 Issues (2015)
Volume 5: 4 Issues (2014)
Volume 4: 4 Issues (2013)
Volume 3: 4 Issues (2012)
Volume 2: 4 Issues (2011)
Volume 1: 4 Issues (2010)
View Complete Journal Contents Listing