This document summarizes a research paper that proposes a novel fuzzy logic based edge detection technique for digital images. The technique uses three linear spatial filters to generate edge strength values for each pixel, which are then used as inputs to a fuzzy inference system. Gaussian membership functions are used to map the edge strength values to linguistic variables of "Low", "Medium", and "High". Fuzzy rules are applied to modify the membership values to classify pixels as edges or non-edges. Experimental results show the fuzzy technique performs better than Sobel and Kirsch operators, producing smoother edges with less noise.
Lec9: Medical Image Segmentation (III) (Fuzzy Connected Image Segmentation)Ulaş Bağcı
Enhancement, Noise Reduction, and Signal Processing • MedicalImageRegistration • MedicalImageSegmentation • MedicalImageVisualization • Machine Learning in Medical Imaging • Shape Modeling/Analysis of Medical Images Deep Learning in Radiology
Fuzzy Connectivity (FC) – Affinity functions
• Absolute FC
• Relative FC (and Iterative Relative FC)
• Successful example applications of FC in medical imaging
• Segmentation of Airway and Airway Walls using RFC based method
Lec11: Active Contour and Level Set for Medical Image SegmentationUlaş Bağcı
ActiveContour(Snake) • LevelSet
• Applications
Enhancement, Noise Reduction, and Signal Processing • MedicalImageRegistration • MedicalImageSegmentation • MedicalImageVisualization • Machine Learning in Medical Imaging • Shape Modeling/Analysis of Medical Images Deep Learning in Radiology Fuzzy Connectivity (FC) – Affinity functions • Absolute FC • Relative FC (and Iterative Relative FC) • Successful example applications of FC in medical imaging • Segmentation of Airway and Airway Walls using RFC based method Energyfunctional – Data and Smoothness terms • GraphCut – Min cut – Max Flow • ApplicationsinRadiologyImages
This paper proposed a facial expression recognition approach based on Gabor wavelet transform. Gabor wavelet filter is first used as pre-processing stage for extraction of the feature vector representation. Dimensionality of the feature vector is reduced using Principal Component Analysis and Local binary pattern (LBP) Algorithms. Experiments were carried out of The Japanese female facial expression (JAFFE) database. In all experiments conducted on JAFFE database, results obtained reveal that GW+LBP has outperformed other approaches in this paper with Average recognition rate of 90% under the same experimental setting.
Adaptive Median Filters
Elements of visual perception
Representing Digital Images
Spatial and Intensity Resolution
cones and rods
Brightness Adaptation
Spatial and Intensity Resolution
Lec10: Medical Image Segmentation as an Energy Minimization ProblemUlaş Bağcı
Enhancement, Noise Reduction, and Signal Processing • MedicalImageRegistration • MedicalImageSegmentation • MedicalImageVisualization • Machine Learning in Medical Imaging • Shape Modeling/Analysis of Medical Images Deep Learning in Radiology Fuzzy Connectivity (FC) – Affinity functions • Absolute FC • Relative FC (and Iterative Relative FC) • Successful example applications of FC in medical imaging • Segmentation of Airway and Airway Walls using RFC based method
Energyfunctional
– Data and Smoothness terms
• GraphCut – Min cut
– Max Flow
• ApplicationsinRadiologyImages
Lec9: Medical Image Segmentation (III) (Fuzzy Connected Image Segmentation)Ulaş Bağcı
Enhancement, Noise Reduction, and Signal Processing • MedicalImageRegistration • MedicalImageSegmentation • MedicalImageVisualization • Machine Learning in Medical Imaging • Shape Modeling/Analysis of Medical Images Deep Learning in Radiology
Fuzzy Connectivity (FC) – Affinity functions
• Absolute FC
• Relative FC (and Iterative Relative FC)
• Successful example applications of FC in medical imaging
• Segmentation of Airway and Airway Walls using RFC based method
Lec11: Active Contour and Level Set for Medical Image SegmentationUlaş Bağcı
ActiveContour(Snake) • LevelSet
• Applications
Enhancement, Noise Reduction, and Signal Processing • MedicalImageRegistration • MedicalImageSegmentation • MedicalImageVisualization • Machine Learning in Medical Imaging • Shape Modeling/Analysis of Medical Images Deep Learning in Radiology Fuzzy Connectivity (FC) – Affinity functions • Absolute FC • Relative FC (and Iterative Relative FC) • Successful example applications of FC in medical imaging • Segmentation of Airway and Airway Walls using RFC based method Energyfunctional – Data and Smoothness terms • GraphCut – Min cut – Max Flow • ApplicationsinRadiologyImages
This paper proposed a facial expression recognition approach based on Gabor wavelet transform. Gabor wavelet filter is first used as pre-processing stage for extraction of the feature vector representation. Dimensionality of the feature vector is reduced using Principal Component Analysis and Local binary pattern (LBP) Algorithms. Experiments were carried out of The Japanese female facial expression (JAFFE) database. In all experiments conducted on JAFFE database, results obtained reveal that GW+LBP has outperformed other approaches in this paper with Average recognition rate of 90% under the same experimental setting.
Adaptive Median Filters
Elements of visual perception
Representing Digital Images
Spatial and Intensity Resolution
cones and rods
Brightness Adaptation
Spatial and Intensity Resolution
Lec10: Medical Image Segmentation as an Energy Minimization ProblemUlaş Bağcı
Enhancement, Noise Reduction, and Signal Processing • MedicalImageRegistration • MedicalImageSegmentation • MedicalImageVisualization • Machine Learning in Medical Imaging • Shape Modeling/Analysis of Medical Images Deep Learning in Radiology Fuzzy Connectivity (FC) – Affinity functions • Absolute FC • Relative FC (and Iterative Relative FC) • Successful example applications of FC in medical imaging • Segmentation of Airway and Airway Walls using RFC based method
Energyfunctional
– Data and Smoothness terms
• GraphCut – Min cut
– Max Flow
• ApplicationsinRadiologyImages
Divide the examined window into cells (e.g. 16x16 pixels for each cell).
2- For each pixel in a cell, compare the pixel to each of its 8 neighbors (on its left-top, leftmiddle,
left-bottom, right-top, etc.). Follow the pixels along a circle, i.e. clockwise or counterclockwise.
3- Where the center pixel's value is greater than the neighbor's value, write "1". Otherwise,
write "0". This gives an 8-digit binary number (which is usually converted to decimal for
convenience).
4- Compute the histogram, over the cell, of the frequency of each "number" occurring (i.e.,
each combination of which pixels are smaller and which are greater than the center).
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
At the end of this lesson, you should be able to;
describe the energy and the EM spectrum.
describe image acquisition methods.
discuss image formation model.
express sampling and quantization.
define dynamic range and image representation.
Divide the examined window into cells (e.g. 16x16 pixels for each cell).
2- For each pixel in a cell, compare the pixel to each of its 8 neighbors (on its left-top, leftmiddle,
left-bottom, right-top, etc.). Follow the pixels along a circle, i.e. clockwise or counterclockwise.
3- Where the center pixel's value is greater than the neighbor's value, write "1". Otherwise,
write "0". This gives an 8-digit binary number (which is usually converted to decimal for
convenience).
4- Compute the histogram, over the cell, of the frequency of each "number" occurring (i.e.,
each combination of which pixels are smaller and which are greater than the center).
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
At the end of this lesson, you should be able to;
describe the energy and the EM spectrum.
describe image acquisition methods.
discuss image formation model.
express sampling and quantization.
define dynamic range and image representation.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
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Performance Evaluation of Image Edge Detection Techniques CSCJournals
The success of an image recognition procedure is related to the quality of the edges marked. The
aim of this research is to investigate and evaluate edge detection techniques when applied to
noisy images at different scales. Sobel, Prewitt, and Canny edge detection algorithms are
evaluated using artificially generated images and comparison criteria: edge quality (EQ) and map
quality (MQ). The results demonstrated that the use of these criteria can be utilized as an aid for
further analysis and arbitration to find the best edge detector for a given image.
Illustration Clamor Echelon Evaluation via Prime Piece PsychotherapyIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
FACE RECOGNITION ALGORITHM BASED ON ORIENTATION HISTOGRAM OF HOUGH PEAKSijaia
In this paper we propose a novel face recognition algorithm based on orientation histogram of Hough Transform Peaks. The novelty of the approach lies in utilizing Hough Transform peaks for determining the orientation angles and computing the histogram from it. For extraction of feature vectors first the images are divided into non overlapping blocks of equal size. Then for each of the blocks the orientation histograms are computed. The obtained histograms are combined to form the final feature vector set. Classification is done using k nearest neighbor classifier. The algorithm has been tested on the ORL
database, Yale B Database & the Essex Grimace Database.97% Recognition rates have been obtained for
ORL database, 100% for Yale B and 100% for Essex Grimace database
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
DESPECKLING OF SAR IMAGES BY OPTIMIZING AVERAGED POWER SPECTRAL VALUE IN CURV...ijistjournal
Synthetic Aperture Radar (SAR) images are inherently affected by multiplicative speckle noise, due to the coherent nature of scattering phenomena. In this paper, a novel algorithm capable of suppressing speckle noise using Particle Swarm Optimization (PSO) technique is presented. The algorithm initially identifies homogenous region from the corrupted image and uses PSO to optimize the Thresholding of curvelet coefficients to recover the original image. Average Power Spectrum Value (APSV) has been used as objective function of PSO. The Proposed algorithm removes Speckle noise effectively and the performance of the algorithm is tested and compared with Mean filter, Median filter, Lee filter, Statistic Lee filter, Kuan filter, frost filter and gamma filter., outperforming conventional filtering methods.
DESPECKLING OF SAR IMAGES BY OPTIMIZING AVERAGED POWER SPECTRAL VALUE IN CURV...ijistjournal
Synthetic Aperture Radar (SAR) images are inherently affected by multiplicative speckle noise, due to the coherent nature of scattering phenomena. In this paper, a novel algorithm capable of suppressing speckle noise using Particle Swarm Optimization (PSO) technique is presented. The algorithm initially identifies homogenous region from the corrupted image and uses PSO to optimize the Thresholding of curvelet coefficients to recover the original image. Average Power Spectrum Value (APSV) has been used as objective function of PSO. The Proposed algorithm removes Speckle noise effectively and the performance of the algorithm is tested and compared with Mean filter, Median filter, Lee filter, Statistic Lee filter, Kuan filter, frost filter and gamma filter., outperforming conventional filtering methods.
Neighbour Local Variability for Multi-Focus Images Fusionsipij
The goal of multi-focus image fusion is to integrate images with different focus objects in order to obtain a
single image with all focus objects. In this paper, we give a new method based on neighbour local
variability (NLV) to fuse multi-focus images. At each pixel, the method uses the local variability calculated
from the quadratic difference between the value of the pixel and the value of all pixels in its
neighbourhood. It expresses the behaviour of the pixel with respect to its neighbours. The variability
preserves the edge function because it detects the sharp intensity of the image. The proposed fusion of each
pixel consists of weighting each pixel by the exponential of its local variability. The quality of this fusion
depends on the size of the neighbourhood region considered. The size depends on the variance and the size
of the blur filter. We start by modelling the value of the neighbourhood region size as a function of the
variance and the size of the blur filter. We compare our method to other methods given in the literature.
We show that our method gives a better result.
NEIGHBOUR LOCAL VARIABILITY FOR MULTIFOCUS IMAGES FUSIONsipij
The goal of multi-focus image fusion is to integrate images with different focus objects in order to obtain a
single image with all focus objects. In this paper, we give a new method based on neighbour local
variability (NLV) to fuse multi-focus images. At each pixel, the method uses the local variability calculated
from the quadratic difference between the value of the pixel and the value of all pixels in its
neighbourhood. It expresses the behaviour of the pixel with respect to its neighbours. The variability
preserves the edge function because it detects the sharp intensity of the image. The proposed fusion of each
pixel consists of weighting each pixel by the exponential of its local variability. The quality of this fusion
depends on the size of the neighbourhood region considered. The size depends on the variance and the size
of the blur filter. We start by modelling the value of the neighbourhood region size as a function of the
variance and the size of the blur filter. We compare our method to other methods given in the literature.
We show that our method gives a better result.
Surveillance refers to the task of observing a scene, often for lengthy periods in search of particular objects or particular behaviour. This task has many applications, foremost among them is security (monitoring for undesirable behaviour such as theft or vandalism), but increasing numbers of others in areas such as agriculture also exist. Historically, closed circuit TV (CCTV) surveillance has been mundane and labour Intensive, involving personnel scanning multiple screens, but the advent of reasonably priced fast hardware means that automatic surveillance is becoming a realistic task to attempt in real time. Several attempts at this are underway.
Denoising and Edge Detection Using SobelmethodIJMER
The main aim of our study is to detect edges in the image without any noise , In many of the images edges carry important information of the image, this paper presents a method which consists of sobel operator and discrete wavelet de-noising to do edge detection on images which include white Gaussian noises. There were so many methods for the edge detection, sobel is the one of the method, by using this sobel operator or median filtering, salt and pepper noise cannot be removed properly, so firstly we use complex wavelet to remove noise and sobel operator is used to do edge detection on the image. Through the pictures obtained by the experiment, we can observe that compared to other methods, the method has more obvious effect on edge detection.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
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During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
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UI automation Sample
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The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
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Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
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Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
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GRUPO 5 : novel fuzzy logic based edge detection technique
1. International Journal of Advanced Science and Technology
Vol. 29, April, 2011
Novel Fuzzy logic Based Edge Detection Technique
Aborisade, D.O
Department of Electronics Engineering,
Ladoke Akintola University of Tech., Ogbomoso. Oyo-state.
doaborisade@yahoo.com
Abstract
This paper is based on the development of a fuzzy logic based edge detection technique in
digital images. The proposed technique used three linear spatial filters to generate three edge
strength values at each pixel of a digital image through spatial convolution process. These
edge strength values are utilized as fuzzy system inputs. Decision on whether pixels in focus
belong to an edge or non-edge is made in the proposed technique based on the Gaussian
membership functions and fuzzy rules. Mamdani defuzzifier method is employed to produce
the final output pixel classification of a given image. Experimental results show the ability
and high performance of proposed algorithm compared with Sobel and Kirsch operators.
Keywords: Fuzzy Logic, Fuzzy inference system, Edge strength, Edge detection.
1. Introduction
An Edge is defined as discontinuities in pixel intensity within an image. The edges of an
image are always the important characteristics that offer an indication for higher frequency.
Detection of edges in an image is used as a preprocessing step to extract some low-level
boundary features, which are then fed into further processing steps, such as object finding and
recognition.
Many edge-detection methods have been suggested in the past years for the purpose of
image analysis and had been attempted by many researchers to support different optimization
goals. Traditional techniques, such as Sobel, Prewitt and Roberts provide false edge detection
and being very sensitive to noise.
Canny [1] proposed a method to counter noise problems and minimize the probability of
false edges. In his work image is convolved with the first order derivatives of Gaussian filter
for smoothing in the local gradient direction followed by edge detection by thresholding [2].
Canny edge detector has major drawbacks of being computational complexity and do not give
a satisfactory results in varying contrast areas. However, improvement in the edge-detection
research area has now resulted in the use of some tools such as neural networks, ant colony
and, fuzzy logic by some presented algorithms [2].
In this paper, fuzzy logic based approach to edge detection in digital images is proposed.
Firstly, for each pixel in the input image „edginess‟ measure is calculated using three 3 3
linear filters after which three fuzzy sets characterized by three (3) Gaussian membership
functions associated to linguistic variable “Low”, “Medium” and “High” were created to
represent each of the edge strengths. The second phase involves application of fuzzy
inference rule to the three fuzzy sets to modify the membership values in such a way that the
fuzzy system output (“edge”) is high only for those pixels belonging to edges in the input
image. Final pixel classification as edge or non-edge using Mamdani defuzzification method
is the last step.
75
2. International Journal of Advanced Science and Technology
Vol. 29, April, 2011
2. Fuzzy Logic Based Application
Fuzzy logic represents a powerful approach to decision making [3], [4], [5]. 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 [6], [7], [8]. In [9], 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 [10], [11]. 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 [12]. In Liang, et al. [13], adjacent points are
assumed as 3 3 sets around the concerned point. By predefining membership function to
detect edges. In these rules discontinuity in the color of different 3 3 sets, edges are
extracted. It uses 5 fuzzy rules and predefined membership function to detect edges. In these
rules discontinuity of adjacent point around the concerned point are investigated. If this
difference is similar to one of predefined sets, the pixel is assumed as edge.
A similar work is proposed by Mansoori, et al. [14], wherein adjacent points of each pixel
are grouped in six different set. Then by using of appropriate bell shape membership function,
the value from zero to one is determined for each group. Based on the membership values,
and fuzzy rules, decision about existing/not existing and direction of edge pixels are obtained.
3. Proposed Algorithm
In this paper, at first an input image is pre-process to accentuate or remove a band of
spatial frequencies and to locate in an image where there is a sudden variation in the grey
level of pixels. For each pixel in the image edge strength value is calculated with three (3)
3 3 linear spatial filters i.e. low-pass, high-pass and edge enhancement filters (Sobel)
through spatial convolution process. In carrying out a 3 3 kernel convolution, nine
convolution coefficients called the convolution mask are defined and labeled as seen below:
a b c
d e f
g h i
Every pixel in the input image is evaluated with its eight neighbors, using each of the
three masks shown in Figure 1 to produce edge strength value. The equation used for the
calculation of edginess values between the center pixel and the neighborhood pixels of the
three (3) masks using spatial convolution process is given by:
76
3. International Journal of Advanced Science and Technology
Vol. 29, April, 2011
O( x, y) aI ( x 1, y 1) bI ( x 1, y) cI ( x 1, y 1)
dI ( x, y 1) eI ( x, y) fI( x, y 1) (1)
gI ( x 1, y 1) hI ( x 1, y) iI ( x 1, y 1)
However, the result of convolution of the two Sobel kernels is combine thus, the approximate
absolute gradient magnitude (edge strength) at each point is computed as:
Og Ox O y (2)
The normalized edge strength is then defined as:
NO( x, y) round (O( x, y) / max( O)) 100 (3)
where x 0,1, . . . , M 1 and y 0,1, . . . , N 1 for an M-by-N image.
1 1 1
9 9 9
- 1 -1 -1
hHP - 1 - 1
1 1 1
hLP , 9
9 9 9
- 1
-1 -1
1 1 1
9
9 9
-1 0 1 1 2 1
hx - 2
0 2 ,
hy 0
0 0
-1
0 1
-1
-2 -1
Figure 1. 3 3 Kernels Used for Edge Detection
The edge strength values derived from the three (3) masks served as the inputs used in the
construction of the fuzzy inference system based on which decision on pixel as belonging to
an edge or not are made. Membership functions are defined for fuzzy system inputs. Many
membership functions have been introduced in the literature. In the proposed edge detection
Gaussian membership functions are used. To apply these functions, each of the edge strength
values of O g , O Hp , and O Lp are mapped into fuzzy domain between 0 and 1 , relative to the
normalized gray levels between 0 and 100, using Gaussian membership functions given as
/ 2 2 ]
mn G( xmn ) e[( xmax xmn )
2
(4)
where G ( x mn ) is a Gaussian function, x m ax , x mn are the maximum and (m, n)th gray values
respectively and is the standard deviation associated with the input variable. Each of the
mapped values are partition into three fuzzy regions “Low”, “Medium”, and “High”. The
defined regions and membership functions are shown in Fig. 2.
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Po
Figure 2. Gaussian Membership Functions
Fuzzy inference rules are applied to assign the three fuzzy sets characterized by
membership functions Low , Medium , and High to the output set. The rules, tabulated in
Table 1 are defined in such a way that in the fuzzy inference system, output set
E L , E M , and E H correspond to pixels with low, medium and high probability value
respectively. The output of the system PFinal representing the probability used for final pixel
classification as edge or non-edge was computed using a singleton fuzzifier, Mamdani
defuzzifier method given by;
y ( ( ))
M n
1 i 1 ki i
p Final (5)
( ( ))
M n
1 i 1 ki i
where i are the fuzzy sets associated with the antecedent part of the fuzzy rule base, y is
the output class center and M is the number of fuzzy rules being considered.
4. 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(c). 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).
5. Conclusion
Effective fuzzy logic based edge detection has been presented in this paper. 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-
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based techniques. The three edge strength values used as fuzzy system inputs were fuzzified
using Gaussian membership functions. Fuzzy if-then 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 technique is far less
computationally expensive; its application on digital image improves 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.
Acknowledgement
The author is grateful to Engineer I. A Isaiah at Ladoke Akintola University of
Technology, Ogbomoso, Nigeria for his helpful advice.
Table 1. Fuzzy Inference Rules
If edginess Lp is LO and edginessSo is LO and edginessHp is LO then p edge is E L
If edginess Lp is LO and edginessSo is LO and edginessHp is MD then p edge is E L
If edginess Lp is LO and edginessSo is LO and edginessHp is HI then p edge is E L
If edginess Lp is LO and edginessSo is MD and edginessHp is LO then p edge is E L
If edginess Lp is LO and edginessSo is MD and edginessHp is MD then p edge is E L
If edginess Lp is LO and edginessSo is MD and edginessHp is HI then p edge is E M
If edginess Lp is LO and edginessSo is HI and edginessHp is LO then p edge is E L
If edginess Lp is LO and edginessSo is HI and edginessHp is MD then p edge is E H
If edginess Lp is LO and edginessSo is HI and edginessHp is HI then p edge is E H
If edginess Lp is MD and edginessSo is LO and edginessHp is LO then p edge is E L
If edginess Lp is MD and edginessSo is MD and edginessHp is LO then p edge is E L
.
.
.
If edginess Lp is HI and edginessSo is LO and edginessHp is HI then p edge is E H
If edginess Lp is HI and edginessSo is MD and edginessHp is HI then p edge is E H
If edginess Lp is HI and edginessSo is HI and edginessHp is HI then p edge is E H
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(a) (b) (c) (d)
Figure 3. (a) Original Images, (b) Sobel Operator Results, (c) Kirsch Operator
Results, (d) Proposed Fuzzy Edge Detection Algorithm Results
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Authors
Aborisade, David O. received the B. Eng. degree in Electronic and
Electrical Engineering Technology from Federal University of
Technology, Owerri, in 1989. He received M.Eng. and Ph.D. degrees
in Electrical Engineering from University of Ilorin, in 1995 and
2006, respectively. He is currently a Senior Lecturer with the
Department Electronic and Electrical Engineering, Ladoke Akintola
University of Technology, Ogbomoso. His research interests include
computer vision, pattern recognition, image and signal processing,
neural networks, and fuzzy logic.
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