I.J. Image, Graphics and Signal Processing, 2016, 9, 26-30
Published Online September 2016 in MECS (http://www.mecs-press.org/)
DOI: 10.5815/ijigsp.2016.09.04
Copyright © 2016 MECS I.J. Image, Graphics and Signal Processing, 2016, 9, 26-30
Comparison of Mamdani Fuzzy Inference System
for Multiple Membership Functions
Pushpa Mamoria
Department of Computer Science, Babasaheb Bhimrao Ambedkar University, Lucknow, India
Email: p.mat76@gmail.com
Deepa Raj
Department of Computer Science, Babasaheb Bhimrao Ambedkar University, Lucknow, India
Email: Deepa_raj200@yahoo.co.in
Abstract—Contrast enhancement is an emerging method
for image enhancement of specific application to analyze
the images clearer for interpretation and analysis in the
spatial domain. The goal of Contrast enhancement is to
serve an input image so that resultant image is more
suited to the particular application. Images with good
steps of grays between black and white are commonly
the best images for the aim of human perception, a novel
approach is proposed in this paper based on fuzzy logic.
Mamdani fuzzy inference system models are developed
to enhance the contrast of images based on different
membership functions (MFs).
Index Terms—Contrast enhancement; fuzzy logic; fuzzy
inference system; spatial domain; membership function.
I. INTRODUCTION
Image enhancement technique is a process that gives
an output image which is more suitable for analysis of a
specific application like Medical, Satellite images,
Military, Print Media. It is broadly classified in two
categorize, spatial domain and frequency domain. In
Frequency domain, image enhancement is mainly based
on Fourier transform and the Spatial domain is based on
pixels manipulation of an image. Due to fast computation,
efficiency, and less processing resources, spatial domain
technique is more suitable as equivalence to other
methods. Image enhancement has classified in the spatial
domain as brightness control, contrast enhancement,
noise reduction and edge enhancement. Apart from other
methods, contrast enhancement method is used to
remove noise and contrast improvement from given
image to enhance the image for faster interpretation and
analysis.
Image enhancement methods are also known as
Contrast enhancement methods, which is mainly used
three basic types of functions negative and identity
transformation, log and inverse-log transformation, and
nth power and nth root transformations. These functions
are used to remove noise, improve visibility and increase
contrast to enhance the image for proper analysis and
interpretation [5, 6].
In spite of these two domains, one more domain has
been described recently to enhance images in various
enhancement applications which are known a fuzzy
domain. A fuzzy domain is based on fuzzy sets of fuzzy
logic methods. Fuzzy logic methods able to handle vague
and unclear difficulties by using expert knowledge and
represent knowledge as a powerful tool to mimic human
reasoning. Fuzzy sets are used to make rules to make
machine just like as human perception [7, 8]. Fuzzy
contrast technique is used for better enhancement of
images without increasing the noise which is present in
input image [9]. This method is also applicable to low
contrast images [10]. This kind of fuzzy techniques
based on fuzzy rule-based model also known as IF-
THEN rules by using different membership functions
[11]. Enhancements of images are also effective and
flexible by using fuzzy sets in fuzzy rule-based
techniques [12].
Two types of fuzzy inference system (FIS) models are
presented to better determine the image contrast
enhancement of gray-scale image based on attributes
such as the number of IF-THEN rules, different
membership functions (MFs), fuzzy contrast factor [13,
14, 15].
In Fuzzy Theory, there are two types of available
fuzzy Rule-based models namely non-additive and
additive rule model. The non-additive rule based model
is also known as Mamdani fuzzy inference system
(Mamdani FIS) while additive rule based model is
known as Takagi-Sugeno fuzzy inference system
(Sugeno FIS) [2, 3, 4]. The main differences between
these two FIS are as follows. (i) Sugeno FIS requires less
number of rules as compared to Mamdani FIS, (ii) the
computation required for defuzzification would be less in
Sugeno FIS than Mamdani FIS because output
membership function is not used in Sugeno FIS during
defuzzification and the resultant output would be
weighted average.
Sugeno FIS uses simple IF-THEN rules and
incorporates these rules based on human reasoning rather
than a complex mathematical model. Thus, Mamdani FIS
is widely used due to intuitive nature of rule base.
Sugeno FIS is computationally efficient and well suited
to work with optimization and linear techniques. Crisp