30-10-2012, 04:27 PM
Fuzzy Logic Based Digital Image Edge Detection
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Abstract
In this paper fuzzy based edge detection algorithm is
developed. In the proposed algorithm, edginess at each pixel of
a digital image is calculated using three (3) 3 3linear spatial
filters i.e. low-pass, high-pass and edge enhancement (Sobel)
filters through spatial convolution process. Edge strength
values derived from the three masks form three set of edges,
utilized as fuzzy system inputs. Based on the Gaussian
membership functions and fuzzy rules the fuzzy system decide
whether a pixel in focus belong to an edge or non-edge. The
final pixel classification of a given image is produced by
generating output pixel value using Mamdani defuzzifier
method. The robustness of the proposed method results for
different captured images are compared to those obtained with
Sobel and Prewitt operators. Experimental results show the
ability and high performance of proposed algorithm.
INTRODUCTION
n edge is defined as an abrupt variation in pixel
intensity within an image while the process of
detecting outlines of an object and boundaries between
objects and the background in the image is known as edge
detection. Edge detection is a very important tool widely
used in many computer vision and image processing
applications. Earlier edge detection methods, such as Sobel,
Prewitt, Kirsch and Robert are based on the calculation of
the intensity gradient magnitude at each image pixel. In
these algorithms, the gradient value is compared to the
threshold value and a pixel location is classified as an edge
if the value of the gradient is higher than a threshold.
Gradient-based edge detectors have a major drawback of
being very sensitive to noise.In order to counter noise
problems Canny proposed an approach to edge detection in
which the image is convolved with the first order derivatives
of Gaussian filter for smoothing in the local gradient
direction followed by edge detection and thresholding
[Canny 1986]. Extensions of Canny edge detector can be
found in [Laligant et al. 1994].
APPLICATION OF FUZZY LOGIC BASED EDGE
DETECTION
Fuzzy logic represents a powerful approach to decision making
[Zadeh 1965, Kaufmann 1975, Bezdek 1981]. Since the concept
of fuzzy logic was formulated in 1965 by Zadeh, many
researches have been carried out on its application in the various
areas of digital image processing such as image quality
assessment, edge detection, image segmentation, etc. Many
techniques have been suggested by researchers in the past for
fuzzy logic-based edge detection [Cheung and Chan 1995, Kuo,
et al. 1997, El-Khamy et al. 2000]. In [Zhao, et al. 2001], Zhao,
et al. proposed an edge detection technique based on probability
partition of the image into 3-fuzzy partitions (regions) and the
principle of maximum entropy for finding the parameters value
that result in the best compact edge representation of images. In
their proposed technique the necessary condition for the entropy
function to reach its maximum is derived. Based on this
condition an effective algorithm for three-level thresholding is
obtained. Several approaches on fuzzy logic based edge
detection have been reported based on fuzzy If-Then rules [Tao,
et al. 1993, Li 1997]. In most of these methods, adjacent points
of pixels are assumed in some classes and then fuzzy system
inference are implemented using appropriate membership
function, defined for each class [Mahani, et al. 2008].
EXPERIMENTAL RESULTS
The proposed fuzzy edge detection method was simulated
using MATLAB on different images, its performance are
compared to that of the Sobel and Kirsch operators. Samples
for a set of four test images are shown in Fig. 3(a). The edge
detection based on Sobel and Kirsch operators using the
image processing toolbox in MATLAB with threshold
automatically estimated from image‘s binary value is
illustrated in Fig. 3(b) and 3©. The sample output of the
proposed fuzzy technique is shown in Fig. 3(d). The
resulting images generated by the fuzzy method seem to be
much smoother with less noise and has an exhaustive set of
fuzzy conditions which helps to provide an efficient edge
representation for images with a very high efficiency than
the conventional gradient-based methods (Sobel and Kirsch
methods).
CONCLUSION
In this paper, effective fuzzy logic based edge detection has
been presented. This technique uses the edge strength
information derived using three (3) masks to avoid detection
of spurious edges corresponding to noise, which is often the
case with conventional gradient-based techniques. The three
edge strength values used as fuzzy system inputs were
fuzzified using Gaussian membership functions. Fuzzy ifthen
rules are applied to modify the membership to one of
low, medium, or high classes. Finally, Mamdani defuzzifier
method is applied to produce the final edge image.Through
the simulation results, it is shown that the proposed
algorithm is far less computationally expensive, its
application on the image improve the quality of edges as
much as possible compared to the Sobel and Kirsch
methods.This algorithm is suitable for applications in
various areas of digital image processing such as face
recognition, fingerprint identification, remote sensing and
medical imaging where boundaries of specific regions need
to be determined for further image analysis.