This document proposes a new method for automatic threshold selection in image segmentation based on discriminant criteria. The method evaluates the "goodness" of thresholds by maximizing between-class variance. It uses only the zeroth- and first-order moments of the grayscale histogram to find the optimal threshold that best separates image classes. The method can be extended to multi-thresholding problems and provides measures of class separability and bimodality. Experimental results demonstrate the validity and simplicity of the proposed automatic threshold selection technique.
Improving Performance of Texture Based Face Recognition Systems by Segmenting...IDES Editor
Textures play an important role in recognition of
images. This paper investigates the efficiency of performance
of three texture based feature extraction methods for face
recognition. The methods for comparative study are Grey Level
Co_occurence Matrix (GLCM), Local Binary Pattern (LBP)
and Elliptical Local Binary Template (ELBT). Experiments
were conducted on a facial expression database, Japanese
Female Facial Expression (JAFFE). With all facial expressions
LBP with 16 vicinity pixels is found to be a better face
recognition method among the tested methods. Experimental
results show that classification based on segmenting face
region improves recognition accuracy.
AUTOMATIC THRESHOLDING TECHNIQUES FOR SAR IMAGEScscpconf
Segmentation of Synthetic Aperture Radar (SAR) images have a great use in observing the global environment, and in analysing the target detection and recognition .But , segmentation of (SAR) images is known as a very complex task, due to the existence of speckle noise. Therefore, in this paper we present a fast SAR images segmentation based on between class variance. Our choice for used (BCV) method, because it is one of the most effective thresholding techniques for most real world images with regard to uniformity and shape measures. Our experiments will be as a test to determine which technique is effective in thresholding (extraction) the oil spill for numerous SAR images, and in the future these thresholding
techniques can be very useful in detection objects in other SAR images
AUTOMATIC THRESHOLDING TECHNIQUES FOR SAR IMAGEScsitconf
Segmentation of Synthetic Aperture Radar (SAR) images have a great use in observing the
global environment, and in analysing the target detection and recognition .But , segmentation
of (SAR) images is known as a very complex task, due to the existence of speckle noise.
Therefore, in this paper we present a fast SAR images segmentation based on between class
variance. Our choice for used (BCV) method, because it is one of the most effective thresholding
techniques for most real world images with regard to uniformity and shape measures. Our
experiments will be as a test to determine which technique is effective in thresholding
(extraction) the oil spill for numerous SAR images, and in the future these thresholding
techniques can be very useful in detection objects in other SAR images
Presented by Adrien Depeursinge, PhD, at MICCAI 2015 Tutorial on Biomedical Texture Analysis (BTA), Munich, Oct 5 2015.
Texture-based imaging biomarkers complement focal, invasive biopsy based biomarkers by providing information on tissue structure over broad regions, non-invasively, and repeatedly across multiple time points. Texture has been used to predict patient survival, tissue function, disease subtypes and genomics (imagenomics and radiogenomics). Nevertheless, several challenges remain, such as: the lack of an appropriate framework for multi-scale, multi-spectral analysis in 2D and 3D; localization uncertainty of texture operators; validation; and, translation to routine clinical applications.
A Secure Color Image Steganography in Transform Domain ijcisjournal
Steganography is the art and science of covert communication. The secret information can be concealed in content such as image, audio, or video. This paper provides a novel image steganography technique to hide both image and key in color cover image using Discrete Wavelet Transform (DWT) and Integer Wavelet Transform (IWT). There is no visual difference between the stego image and the cover image. The extracted image is also similar to the secret image. This is proved by the high PSNR (Peak Signal to Noise Ratio), value for both stego and extracted secret image. The results are compared with the results of similar techniques and it is found that the proposed technique is simple and gives better PSNR values than others.
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.
Improving Performance of Texture Based Face Recognition Systems by Segmenting...IDES Editor
Textures play an important role in recognition of
images. This paper investigates the efficiency of performance
of three texture based feature extraction methods for face
recognition. The methods for comparative study are Grey Level
Co_occurence Matrix (GLCM), Local Binary Pattern (LBP)
and Elliptical Local Binary Template (ELBT). Experiments
were conducted on a facial expression database, Japanese
Female Facial Expression (JAFFE). With all facial expressions
LBP with 16 vicinity pixels is found to be a better face
recognition method among the tested methods. Experimental
results show that classification based on segmenting face
region improves recognition accuracy.
AUTOMATIC THRESHOLDING TECHNIQUES FOR SAR IMAGEScscpconf
Segmentation of Synthetic Aperture Radar (SAR) images have a great use in observing the global environment, and in analysing the target detection and recognition .But , segmentation of (SAR) images is known as a very complex task, due to the existence of speckle noise. Therefore, in this paper we present a fast SAR images segmentation based on between class variance. Our choice for used (BCV) method, because it is one of the most effective thresholding techniques for most real world images with regard to uniformity and shape measures. Our experiments will be as a test to determine which technique is effective in thresholding (extraction) the oil spill for numerous SAR images, and in the future these thresholding
techniques can be very useful in detection objects in other SAR images
AUTOMATIC THRESHOLDING TECHNIQUES FOR SAR IMAGEScsitconf
Segmentation of Synthetic Aperture Radar (SAR) images have a great use in observing the
global environment, and in analysing the target detection and recognition .But , segmentation
of (SAR) images is known as a very complex task, due to the existence of speckle noise.
Therefore, in this paper we present a fast SAR images segmentation based on between class
variance. Our choice for used (BCV) method, because it is one of the most effective thresholding
techniques for most real world images with regard to uniformity and shape measures. Our
experiments will be as a test to determine which technique is effective in thresholding
(extraction) the oil spill for numerous SAR images, and in the future these thresholding
techniques can be very useful in detection objects in other SAR images
Presented by Adrien Depeursinge, PhD, at MICCAI 2015 Tutorial on Biomedical Texture Analysis (BTA), Munich, Oct 5 2015.
Texture-based imaging biomarkers complement focal, invasive biopsy based biomarkers by providing information on tissue structure over broad regions, non-invasively, and repeatedly across multiple time points. Texture has been used to predict patient survival, tissue function, disease subtypes and genomics (imagenomics and radiogenomics). Nevertheless, several challenges remain, such as: the lack of an appropriate framework for multi-scale, multi-spectral analysis in 2D and 3D; localization uncertainty of texture operators; validation; and, translation to routine clinical applications.
A Secure Color Image Steganography in Transform Domain ijcisjournal
Steganography is the art and science of covert communication. The secret information can be concealed in content such as image, audio, or video. This paper provides a novel image steganography technique to hide both image and key in color cover image using Discrete Wavelet Transform (DWT) and Integer Wavelet Transform (IWT). There is no visual difference between the stego image and the cover image. The extracted image is also similar to the secret image. This is proved by the high PSNR (Peak Signal to Noise Ratio), value for both stego and extracted secret image. The results are compared with the results of similar techniques and it is found that the proposed technique is simple and gives better PSNR values than others.
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.
Automated Colorization of Grayscale Images Using Texture DescriptorsIDES Editor
A novel example-based process for automated
colorization of grayscale images using texture descriptors
(ACTD) without any human intervention is proposed. By
analyzing a set of sample color images, coherent regions of
homogeneous textures are extracted. A multi-channel filtering
technique is used for texture-based image segmentation. For
each area of interest, state of the art texture descriptors are
then computed and stored, along with corresponding color
information. These texture descriptors and the color
information are used for colorization of a grayscale image with
similar textures. Given a grayscale image to be colorized, the
segmentation and feature extraction processes are repeated.
The texture descriptors are used to perform Content-Based
Image Retrieval (CBIR). The colorization process is performed
by chroma replacement. This research finds numerous
applications, ranging from classic film restoration and
enhancement, to adding valuable information into medical and
satellite imaging, and to enhance the detection of objects from
x-ray images at the airports.
This paper introduces a new concept for the establishment of human-robot symbiotic relationship. The
system is based on the implementation of knowledge-based image processing methodologies for model
based vision and intelligent task scheduling for an autonomous social robot. This paper aims to develop an
automatic translation of static gestures of alphabets and signs in American Sign Language (ASL), using
neural network with backpropagation algorithm. System deals with images of bare hands to achieve the
recognition task. For each individual sign 10 sample images have been considered, which means in
total300 samples have been processed. In order to compare between the training set of signs and the
considered sample images, are converted into feature vectors. Experimental results reveal that this can
recognize selected ASL signs (accuracy of 92.00%). Finally, the system has been implemented issuing hand
gesture commands for ASL to a robot car, named “Moto-robo”.
We propose a novel imaging biomarker of lung cancer relapse from 3-D texture analysis of CT images. Three-dimensional morphological nodular tissue properties are described in terms of 3-D Riesz-wavelets. The responses of the latter are aggregated within nodular regions by means of feature covariances, which leverage rich intra- and inter-variations of the feature space dimensions. The obtained Riesz-covariance descriptors lie on a manifold governed by Riemannian geometry requiring specific geodesic metrics to locally approximate scalar products. The latter are used to construct a kernel for support vector machines (SVM). The effectiveness of the presented models is evaluated on a dataset of 92 patients with non-small cell lung carcinoma (NSCLC) and cancer recurrence information. Disease recurrence within a timeframe of 12 months could be predicted with an accuracy above 80, and highlighted the importance of covariance-based texture aggregation. At the end of the talk, computer tools will be presented to easily extract 3D radiomics quantitative features from PET-CT images.
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.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
We propose an image-based method using Contourlet transform [5] to detect liveness in
fingerprint biometric systems. We observe that real and spoof fingerprint images exhibit
different textural characteristics. Wavelet transform although widely used for liveness detection
is not the ideal one. Wavelets are not very effective in representing images containing lines and
contours [5]. Recent Contourlet transform allows representing contours in a more efficient way
than the wavelets [5]. Fingerprint is made of only contours of ridges; hence Contourlet
transform is more suitable for fingerprint processing than the wavelets. Therefore, we use
Contourlet energy and co-occurrence signatures to capture textural intricacies of images. After
downsizing features with Plus l – take away r method, we test them on various classifiers:
logistic regression, support vector machine and AdTree using our databases consisting of 185
real, 90 Fun-Doh (Play-Doh) and 150 Gummy fingerprint images. We then select the best
classifier and use at as a base classifier to form an ensemble classifier obtained by fusing a
stack of “K” base classifiers using the “Majority Voting Rule” (i.e. bagging). Experimental
results indicate that, the new liveness detection approach is very promising as it needs only one
fingerprint and no extra hardware to detect vitality
ANALYSIS OF INTEREST POINTS OF CURVELET COEFFICIENTS CONTRIBUTIONS OF MICROS...sipij
This paper focuses on improved edge model based on Curvelet coefficients analysis. Curvelet transform is
a powerful tool for multiresolution representation of object with anisotropic edge. Curvelet coefficients
contributions have been analyzed using Scale Invariant Feature Transform (SIFT), commonly used to study
local structure in images. The permutation of Curvelet coefficients from original image and edges image
obtained from gradient operator is used to improve original edges. Experimental results show that this
method brings out details on edges when the decomposition scale increases.
Novel DCT based watermarking scheme for digital imagesIDES Editor
There is an ever growing interest in copyright
protection of multimedia content, thus digital
watermarking techniques are widely practiced. Due to
the internet connectivity and digital libraries the
research interest of protecting digital content
watermarking is extensively researched. In this paper
we present a novel watermark generation scheme
based on the histogram of the image and apply it to the
original image in the transform(DCT) domain. Further
we study the performance of the watermark against
some common attacks that can take place with images.
Experimental results show that the embedded
watermark is imperceptible and image quality is not
degraded.
IOSR Journal of Computer Engineering (IOSR-JCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of computer engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in computer technology. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
REMOVING OCCLUSION IN IMAGES USING SPARSE PROCESSING AND TEXTURE SYNTHESISIJCSEA Journal
We provide a solution to problem of occlusion in images by removing the occluding region and filling in the gap left behind. Inpainting algorithms fail in filling occlusions when the occluding region is large since there is loss of both structure and texture. We decompose the image into structure and texture images using a decomposition method based on sparseness of the image. The sparse reconstruction of the decomposed images result in an inpainted image with all the structures made intact. A texture synthesis is performed on the texture only image. Finally the structure and texture images are combined to get an image where the occlusion is filled. The performance of our algorithm in terms of visual effectiveness is compared with other algorithms used for inpainting.
Automated Colorization of Grayscale Images Using Texture DescriptorsIDES Editor
A novel example-based process for automated
colorization of grayscale images using texture descriptors
(ACTD) without any human intervention is proposed. By
analyzing a set of sample color images, coherent regions of
homogeneous textures are extracted. A multi-channel filtering
technique is used for texture-based image segmentation. For
each area of interest, state of the art texture descriptors are
then computed and stored, along with corresponding color
information. These texture descriptors and the color
information are used for colorization of a grayscale image with
similar textures. Given a grayscale image to be colorized, the
segmentation and feature extraction processes are repeated.
The texture descriptors are used to perform Content-Based
Image Retrieval (CBIR). The colorization process is performed
by chroma replacement. This research finds numerous
applications, ranging from classic film restoration and
enhancement, to adding valuable information into medical and
satellite imaging, and to enhance the detection of objects from
x-ray images at the airports.
This paper introduces a new concept for the establishment of human-robot symbiotic relationship. The
system is based on the implementation of knowledge-based image processing methodologies for model
based vision and intelligent task scheduling for an autonomous social robot. This paper aims to develop an
automatic translation of static gestures of alphabets and signs in American Sign Language (ASL), using
neural network with backpropagation algorithm. System deals with images of bare hands to achieve the
recognition task. For each individual sign 10 sample images have been considered, which means in
total300 samples have been processed. In order to compare between the training set of signs and the
considered sample images, are converted into feature vectors. Experimental results reveal that this can
recognize selected ASL signs (accuracy of 92.00%). Finally, the system has been implemented issuing hand
gesture commands for ASL to a robot car, named “Moto-robo”.
We propose a novel imaging biomarker of lung cancer relapse from 3-D texture analysis of CT images. Three-dimensional morphological nodular tissue properties are described in terms of 3-D Riesz-wavelets. The responses of the latter are aggregated within nodular regions by means of feature covariances, which leverage rich intra- and inter-variations of the feature space dimensions. The obtained Riesz-covariance descriptors lie on a manifold governed by Riemannian geometry requiring specific geodesic metrics to locally approximate scalar products. The latter are used to construct a kernel for support vector machines (SVM). The effectiveness of the presented models is evaluated on a dataset of 92 patients with non-small cell lung carcinoma (NSCLC) and cancer recurrence information. Disease recurrence within a timeframe of 12 months could be predicted with an accuracy above 80, and highlighted the importance of covariance-based texture aggregation. At the end of the talk, computer tools will be presented to easily extract 3D radiomics quantitative features from PET-CT images.
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.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
We propose an image-based method using Contourlet transform [5] to detect liveness in
fingerprint biometric systems. We observe that real and spoof fingerprint images exhibit
different textural characteristics. Wavelet transform although widely used for liveness detection
is not the ideal one. Wavelets are not very effective in representing images containing lines and
contours [5]. Recent Contourlet transform allows representing contours in a more efficient way
than the wavelets [5]. Fingerprint is made of only contours of ridges; hence Contourlet
transform is more suitable for fingerprint processing than the wavelets. Therefore, we use
Contourlet energy and co-occurrence signatures to capture textural intricacies of images. After
downsizing features with Plus l – take away r method, we test them on various classifiers:
logistic regression, support vector machine and AdTree using our databases consisting of 185
real, 90 Fun-Doh (Play-Doh) and 150 Gummy fingerprint images. We then select the best
classifier and use at as a base classifier to form an ensemble classifier obtained by fusing a
stack of “K” base classifiers using the “Majority Voting Rule” (i.e. bagging). Experimental
results indicate that, the new liveness detection approach is very promising as it needs only one
fingerprint and no extra hardware to detect vitality
ANALYSIS OF INTEREST POINTS OF CURVELET COEFFICIENTS CONTRIBUTIONS OF MICROS...sipij
This paper focuses on improved edge model based on Curvelet coefficients analysis. Curvelet transform is
a powerful tool for multiresolution representation of object with anisotropic edge. Curvelet coefficients
contributions have been analyzed using Scale Invariant Feature Transform (SIFT), commonly used to study
local structure in images. The permutation of Curvelet coefficients from original image and edges image
obtained from gradient operator is used to improve original edges. Experimental results show that this
method brings out details on edges when the decomposition scale increases.
Novel DCT based watermarking scheme for digital imagesIDES Editor
There is an ever growing interest in copyright
protection of multimedia content, thus digital
watermarking techniques are widely practiced. Due to
the internet connectivity and digital libraries the
research interest of protecting digital content
watermarking is extensively researched. In this paper
we present a novel watermark generation scheme
based on the histogram of the image and apply it to the
original image in the transform(DCT) domain. Further
we study the performance of the watermark against
some common attacks that can take place with images.
Experimental results show that the embedded
watermark is imperceptible and image quality is not
degraded.
IOSR Journal of Computer Engineering (IOSR-JCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of computer engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in computer technology. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
REMOVING OCCLUSION IN IMAGES USING SPARSE PROCESSING AND TEXTURE SYNTHESISIJCSEA Journal
We provide a solution to problem of occlusion in images by removing the occluding region and filling in the gap left behind. Inpainting algorithms fail in filling occlusions when the occluding region is large since there is loss of both structure and texture. We decompose the image into structure and texture images using a decomposition method based on sparseness of the image. The sparse reconstruction of the decomposed images result in an inpainted image with all the structures made intact. A texture synthesis is performed on the texture only image. Finally the structure and texture images are combined to get an image where the occlusion is filled. The performance of our algorithm in terms of visual effectiveness is compared with other algorithms used for inpainting.
Face recognition using gaussian mixture model & artificial neural networkeSAT Journals
Abstract
Face recognition is a non-contact and friendly biometric identification technology. It has broad application prospects in the
military, public security and economic security. In this work, we also consider illumination variable database. The images have
taken from far distance and do not consider the close view face of the individual as in most of the face databases, clear face view
has been considered. In this first we located face as region of interest and then LBP and LPQ descriptors are used which is
illuminance invariant in nature. After this GMM has been used to reduce feature set by taking negative log-likelihood from each
LBP and LPQ descripted image histograms. After this ANN consumes stayed used for organization purposes. The investigational
consequencesshow excellent correctness rates in overall testing of input data.
Keywords: Illumination invariant, face recognition, LBP, LPQs,GMM,ANN
Neural Network based Supervised Self Organizing Maps for Face Recognition ijsc
The word biometrics refers to the use of physiological or biological characteristics of human to recognize and verify the identity of an individual. Face is one of the human biometrics for passive identification with uniqueness and stability. In this manuscript we present a new face based biometric system based on neural networks supervised self organizing maps (SOM). We name our method named SOM-F. We show that the proposed SOM-F method improves the performance and robustness of recognition. We apply the proposed method to a variety of datasets and show the results.
NEURAL NETWORK BASED SUPERVISED SELF ORGANIZING MAPS FOR FACE RECOGNITIONijsc
The word biometrics refers to the use of physiological or biological characteristics of human to recognize
and verify the identity of an individual. Face is one of the human biometrics for passive identification with
uniqueness and stability. In this manuscript we present a new face based biometric system based on neural
networks supervised self organizing maps (SOM). We name our method named SOM-F. We show that the
proposed SOM-F method improves the performance and robustness of recognition. We apply the proposed
method to a variety of datasets and show the results.
Satellite image classification and content base image retrieval using type-2 ...Shirish Agale
The detection of oceanic structures, such as upwelling’s or eddies, from satellite images has significance for marine environmental studies, coastal resource management, and ocean dynamics studies. There is a lack of tools that allow us to retrieve automatically relevant structures from large satellite image databases. This presentation focuses on the development and validation of a Content-Based Image Retrieval (CBIR) system to classify and retrieve oceanic structures from satellite images.
Robust Adaptive Threshold Algorithm based on Kernel Fuzzy Clustering on Image...cscpconf
Using thresholding method to segment an image, a fixed threshold is not suitable if the
background is rough here, we propose a new adaptive thresholding method using KFCM. The
method requires only one parameter to be selected and the adaptive threshold surface can be
found automatically from the original image. An adaptive thresholding scheme using adaptive
tracking and morphological filtering. KFCM algorithm computes the fuzzy membership values
for each pixel. Our method is good for detecting large and small images concurrently. It is also
efficient to denoise and enhance the responses of images with low local contrast can be detected. The efficiency and accuracy of the algorithm is demonstrated by the experiments on the MR brain images.
Review paper on segmentation methods for multiobject feature extractioneSAT Journals
Abstract Feature extraction and representation plays a vital role in multimedia processing. It is still a challenge in computer vision system to extract ideal features that represents intrinsic characteristics of an image. Multiobject feature extraction system means a system that can extract features and locations of multiple objects in an image. In this paper we have discuss various methods to extract location and features of multiple objects and describe a system that can extract locations and features of multiple objects in an image by implementing an algorithm as hardware logic on a field-programmable gate array-based platform. There are many multiobject extraction methods which can be use for image segmentation based on motion, color intensity and texture. By calculating zeroth and first order moments of objects it is possible to obtain locations and sizes of multiple objects in an image. Keywords: multiobject extraction, image segmentation
Activity Recognition From IR Images Using Fuzzy Clustering TechniquesIJTET Journal
Infrared sensors ensures that activity recognition is possible in the day and night times. It is used especially for activity monitoring of older adults as falls are more prevalent at night than the day. This paper focus on an application of fuzzy set techniques and it is capable of accurately detecting several different activity states related to fall detection and fall risk assessment and it also includes sitting, standing and being on the floor to ensure that elderly residents gets the help they need quickly in case of emergencies. Fall detection and fall risk assessment is used for an aging in place facility for the elderly people. It describes the silhouette extraction process, the image features , and the fuzzy clustering technique.
A PSO-Based Subtractive Data Clustering AlgorithmIJORCS
There is a tremendous proliferation in the amount of information available on the largest shared information source, the World Wide Web. Fast and high-quality clustering algorithms play an important role in helping users to effectively navigate, summarize, and organize the information. Recent studies have shown that partitional clustering algorithms such as the k-means algorithm are the most popular algorithms for clustering large datasets. The major problem with partitional clustering algorithms is that they are sensitive to the selection of the initial partitions and are prone to premature converge to local optima. Subtractive clustering is a fast, one-pass algorithm for estimating the number of clusters and cluster centers for any given set of data. The cluster estimates can be used to initialize iterative optimization-based clustering methods and model identification methods. In this paper, we present a hybrid Particle Swarm Optimization, Subtractive + (PSO) clustering algorithm that performs fast clustering. For comparison purpose, we applied the Subtractive + (PSO) clustering algorithm, PSO, and the Subtractive clustering algorithms on three different datasets. The results illustrate that the Subtractive + (PSO) clustering algorithm can generate the most compact clustering results as compared to other algorithms.
Video surveillance systems are very important in our everyday life. Video surveillance applications are
used in airports, banks, offices and even our homes to remain us secure. Night vision is the ability to see in
low light conditions. Surveillance video may not be seen clearly. Especially under the weak illumination
conditions. The details of the image are very poor at night. Most of the previous work has focused on
daytime Surveillance. This paper proposes a method of Human detection in hours of darkness (night time)
using Gaussian Mixture Model (GMM) in real night environment employing an infrared radiation camera.
Infrared video is taken as Input to perform Human detection at night. Then the video was processed using
Gaussian mixture model algorithm, it was confirmed that by using this method accurate detection of human
at night is possible.
Optimized Neural Network for Classification of Multispectral ImagesIDES Editor
The proposed work involves the multiobjective PSO
based optimization of artificial neural network structure for
the classification of multispectral satellite images. The neural
network is used to classify each image pixel in various land
cove types like vegetations, waterways, man-made structures
and road network. It is per pixel supervised classification using
spectral bands (original feature space). Use of neural network
for classification requires selection of most discriminative
spectral bands and determination of optimal number of nodes
in hidden layer. We propose new methodology based on
multiobjective particle swarm optimization (MOPSO) to
determine discriminative spectral bands and the number of
hidden layer node simultaneously. The result obtained using
such optimized neural network is compared with that of
traditional classifiers like MLC and Euclidean classifier. The
performance of all classifiers is evaluated quantitatively using
Xie-Beni and â indexes. The result shows the superiority of
the proposed method.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
1. 62 2EEE TRANSACTIONS ON SYSTREMS, MAN, AND CYBERNETICS, VOL. SMC-9, NO. 1, JANUARY 1979
ments," Proc. ofthe 3rd Sym. on Nonlinear Estimation Theory and its Applications,
San Diego, CA, Sept. 1972.
[4] P. Smith and G. Buechler, "A branching algorithm for discrimination and track-
ing multiple objects," IEEE Trans. Automat. Contr., vol. AC-20, pp. 101-104,
1975.
[5] D. L. Alspach, 'A Gaussian sum approach to the multitarget-tracking problem,"
Automatica, vol. 11, pp. 285-296,1975.
[6] C. L. Morefield, Application of 0-1 Integer Programming to a Track Assembly
Problem, TR-0075(5085-10II, Aerospace Corp. El Segundo, CA, Apr. 1975.
7*
[7] D. B. Reid, A Multiple Hypothesis Filter for Tracking Multiple Targets in a
Cluttered Environment, LMSC-D560254, Lockheed Palo Alto Research Labora-
tories, Palo Alto, CA, Sept. 1977.
[8] P. L. Smith, "Reduction of sea surveillance data using binary matrices," IEEE
Trans. Syst., Man, Cybern., vol. SMC-6 (8), pp. 531-538, Aug. 1976.
LONGITUDE
Fig. 6. ID plot of ship 10001 after the second round of operator-imposed assign- A Tlreshold Selection Method
ment constraints. from Gray-Level Histograms
NOBUYUKI OTSU
Abstract-A nonparametric and unsupervised method of automa-
tic threshold selection for picture segmentation is presented. An
optimal threshold is selected by the discriminant criterion, namely,
so as to maximize the separability of the resultant classes in gray
levels. The procedure is very simple, utilizing only the zeroth- and the
first-order cumulative moments of the gray-level histogram. It is
t straightforward to extend the method to multithreshold problems.
Several experimental results are also presented to support the
validity of the method.
I. INTRODUCTION
It is important in picture processing to select an adequate thre-
shold of gray level for extracting objects from their background. A
variety of techniques have been proposed in this regard. In an
ideal case, the histogram has a deep and sharp valley between two
LONGITUDE peaks representing objects and background, respectively, so that
Fig. 7. Actual ship movements. the threshold can be chosen at the bottom of this valley [1].
However, for most real pictures, it is often difficult to detect the
of the two last sighted locations. The true trajectories are shown in valley bottom precisely, especially in such cases as when the valley
Fig. 7 where it can be seen that ship 10001 did, in fact, turn toward is flat and broad, imbued with noise, or when the two peaks are
the coast. extremely unequal in height, often producing no traceable valley.
There have been some techniques proposed in order to overcome
IV. CONCLUDING REMARKS these difficulties. They are, for example, the valley sharpening
The procedure of ship identification from DF sightings has technique [2], which restricts the histogram to the pixels with
been oversimplified in this discussion. Often DF sightings are not large absolute values of derivative (Laplacian or gradient), and
completely identified but, instead, contain only ship class informa- the difference histogram method [3], which selects the threshold at
tion. The interactive technique still applies, but additional the gray level with the maximal amount of difference. These utilize
identification and display flexibility must be provided. information concerning neighboring pixels (or edges) in the ori-
Any additional information contained in the sightings can be ginal picture to modify the histogram so as to make it useful for
used to discriminate among radar and DF sightings. Factors such thresholding. Another class of methods deals directly with the
as measured heading and visual ID will permit further automatic gray-level histogram by parametric techniques. For example, the
reduction of the P and Q matrices. histogram is approximated in the least square sense by a sum of
It is also possible to automate some of the more routine manual Gaussian distributions, and statistical decision procedures are
functions. However, experience has shown that better results are applied [4]. However, such a method requires considerably ted-
obtained by having a human operator resolve ambiguous situa- ious and sometimes unstable calculations. Moreover, in many
tions arising from sparse data. cases, the Gaussian distributions turn out to be a meager approxi-
mation of the real modes.
REFERENCES In any event, no "goodness" of threshold has been evaluated in
[I] R. W. Sittler, "An optimal data association problem in surveillance theory,"
IEEE Trans. Mil. Elect., vol. MIL-8, pp. 125-139, 1964.
[2] M. S. White, "Finding events in a sea of bubbles," IEEE Trans. Comput., voL Manuscript received October 13, 1977;revised April 17,1978 and August 31, 1978.
C-20 (9) pp. 988-1006, 1971. The author is with the Mathematical Engineering Section, Information Science
[3} A. G. Jaffer and Y. Bar-Shalom. "On optimal tracking in multiple-target environ- Division, Electrotechnical Laboratory, Chiyoda-ku, Tokyo 100, Japan.
0018-9472/79/0100-0062$00.75 (D 1979 IEEE
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2. CORRESPONDENCE 63
most of the methods so far proposed. This would imply that it These require second-order cumulative moments (statistics).
could be the right way of deriving an optimal thresholding method In order to evaluate the "goodness" of the threshold (at level k),
to establish an appropriate criterion for evaluating the "goodness" we shall introduce the following discriminant criterion measures
of threshold from a more general standpoint. (or measures of class separability) used in the discriminant
In this correspondence, our discussion will be confined to the analysis [5]:
elementary case of threshold selection where only the gray-level
histogram suffices without other a priori knowledge. It is not only A = a22 K = (T2/a2WK =/2/a2
= (12)
important as a standard technique in picture processing, but also where
essential for unsupervised decision problems in pattern recogni- 2 2 2
tion. A new method is proposed from the viewpoint of discrimin- UW = 6oJoU + 0J1ff1 (13)
ant analysis; it directly approaches the feasibility of evaluating the 2 = o(po PT) + 1G(i1 PT)
"goodness" of threshold and automatically selecting an optimal
threshold. = iOO(Y1 -PTo)T (14)
II. FORMULATION (due to (9)) and
Let the pixels of a given picture be represented in L gray levels L
[1, 2, ,L]. The number of pixels at level i is denoted by ni and JT = E (i - p2p
2 )p (15)
i=1
the total number of pixels by N = n1 + n2 + + nL* In order to
simplify the discussion, the gray-level histogram is normalized are the within-class variance, the between-class variance, and the
and regarded as a probability distribution: total variance of levels, respectively. Then our problem is reduced
L
to an optimization problem to search for a threshold k that maxi-
pi = nilN, pi >0, Z Pi-1 (1) mizes one of the object functions (the criterion measures) in (12).
This standpoint is motivated by a conjecture that well-
Now suppose that we dichotomize the pixels into two classes thresholded classes would be separated in gray levels, and con-
CO and C 1 (background and objects, or vice versa) by a threshold versely, a threshold giving the best separation of classes in gray
at level k; CO denotes pixels with levels [1, , k], and C1 denotes levels would be the best threshold.
pixels with levels [k + 1, , L]. Then the probabilities of class The discriminant criteria maximizing A, K, and q, respectively,
occurrence and the class mean levels, respectively, are given by for k are, however, equivalent to one another; e.g., K = i + 1 and
= )/(2 + 1) in terms of 2, because the following basic relation
k
wo = Pr (Co)= E Pi= (k) (2) always holds:
i=1
a2 + a2 = 52
1w + TB (16)
L
i-,
w01 = Pr (Ci)= E pi = 1-@(k) t9" It is noticed that U2 and U2 are functions of threshold level k, but
i =k+ I
and CT is independent of k. It is also noted that cr2 is based on the
k k second-order statistics (class variances), while (T2 is based on the
Po = i Pr (i Co)- E ipi Io = p(k)/w(k) (4) first-order statistics (class means). Therefore, q is the simplest
measure with respect to k. Thus we adopt q as the criterion meas-
L L ItT P(k) ure to evaluate the "goodness" (or separability) of the threshold at
k=k+
i=k+lI co(k)
(5) level k.
The optimal threshold k* that maximizes t, or equivalently
where maximizes a2 is selected in the following sequential search by
k
6 using the simple cumulative quantities (6) and (7), or explicitly
o(k) = pi (6) using (2)-(5):
and l(k) = us(k)l/T (17)
I
p(k)= i=1 ipi (7) a2k =[p7(k) --(k)]2
cB(k = (k)[1 w)(k)]- (18)
are the zeroth- and the first-order cumulative moments of the
histogram up to the kth level, respectively, and and the optimal threshold k* is
L
(8)
2
(k* ) = max o2(k). (19)
PT P- (L) = Z ipi 1 <k<L
i =1
is the total mean level of the original picture. We can easily verify From the problem, the range of k over which the maximum is
the following relation for any choice of k: sought can be restricted to
OP00 + O+IU1=P T, (Oo+ Ui=
I (9) SF = {k; (loow = w(k)[I- ((k)] > 0, or 0 < o(k) < 1}.
The class variances are given by
We shall call it the effective range of the gray-level histogram.
k k
From the definition in (14), the criterion measure i' (or q) takes a
2 E (i - P0)2 Pr (i C0)= Z (i - po)2pi/o (10)
minimum value of zero for such k as k e S - S* = {k; (o(k) = 0 or
ii= =i
L L
1} (i.e., making all pixels either Cl or CO, which is, of course, not
I2 = E (i _ pl)2 Pr (i IC,) = (i - p)2p Wi, (11) our concern) and takes a positive and bounded value for k e S*. It
i=k+ I i k+ I is, therefore, obvious that the maximum always exists.
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3. 64 IEEE TRANSACnONS ON SYSTEMS, MAN, AND CYBERNEnCS, VOL SMC-9, NO. 1, JANUARY 1979
Ill. DISCUSSiON AND REMARKS
A. Analysis offurther important aspects
The method proposed in the foregoing affords further means to
analyze important aspects other than selecting optimal
thresholds.
For the selected threshold k*, the class probabilities (2) and (3),
respectively, indicate the portions of the areas occupied by the
classes in the picture so thresholded. The class means (4) and (5)
serve as estimates of the mean levels of the classes in the original
gray-level picture.
The maximum value ti(k*), denoted simply by 1*, can be used as
a measure to evaluate the separability of classes (or ease of thre-
sholding) for the original picture or the bimodality of the histo-
gram. This is a significant measure, for it is invariant under affine
transformations of the gray-level scale (i.e., for any shift and dila-
tation, g' = agj + b) It is uniquely determined within the range (a) (b)
0 < q < 1.
The lower bound (zero) is attainable by, and only by, pictures PT, 4.2 al=8.831
having a single constant gray level, and the upper bound (unity) is
attainable by, and only by, two-valued pictures.
K=6 7 =0.894
B. Extension to Multithresholding
The extension of the method to multihresholding problems is W" = 0.818 pO= 2.8
straightforward by virtue of the discriminant criterion. For exam- 0.182 p,l= 10.1
w, =
ple, in the case of three-thresholding, we assume two thresholds:
1 < k1 < k2 < for separating three classes, CO for [1, * * *, kl], C, (d)
for [k1 + 1, , k2], and C2 for [k2 + 1, --, L]. The criterion 5 1 (
measure or (also q) is then a function of two variables k, and k2, (c)
and an optimal set of thresholds kt and kt is selected by maximiz-
ing r7:
a2(ki,, kt) = max o2(kI, k2)-
1!kl<k2<L
It should be noticed that the selected thresholds generally
become less credible as the number of classes to be separated
increases. This is because the criterion measure (e2), defined in
one-dimensional (gray-level) scale, may gradually lose its meaning
as the number of classes increases. The expression of U2 and the
maximization procedure also become more and more com-
plicated. However, they are very simple for M = 2 and 3, which
cover almost all practical applications, so that a special method to
reduce the search processes is hardly needed. It should be
remarked that the parameters required in the present method for (e) (f
M-thresholding are M - 1 discrete thresholds themselves, while
the parametric method, where the gray-level histogram is approx-
imated by the sum of Gaussian distributions, requires 3M - 1 PT 4.3 CUT 5.052
continuous parameters.
C. Experimental Results K=6 n'= 0.853
Several examples of experimental results are shown in Figs. 1-3. t ('
Throughout these figures, (a) (as also (e)) is an original gray-level w =0.858 PO= 3.4
picture; (b) (and (f)) is the result of thresholding; (c) (and (g)) is a w,=0. 142 p1= 9.4
set of the gray-level histogram (marked at the selected threshold)
and the criterion measure q1(k) related thereto; and (d) (and (h)) is (h)
the result obtained by the analysis. The original gray-level pic-
tures are all 64 x 64 in size, and the numbers of gray levels are 16
in Fig. 1, 64 in Fig. 2, 32 in Fig. 3(a), and 256 in Fig. 3(e). (They all (g)
Fig. 1. Application to characters.
had equal outputs in 16 gray levels by superposition of symbols by
reason of representation, so that they may be slightly lacking in
precise detail in the gray levels.)
Fig. 1 shows the results of the application to an identical char-
acter "A" typewritten in different ways, one with a new ribbon (a)
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4. CORRESPONDENCE 65
..::
.........
.... ...... i,t,,~~~~~~~~~~. ............
(a) () . . ...:..
(a) (b) (a) (b)
2
=T 34.4 l=418 033 pT 7.3 Cr2= 23.347
K;= 7 K2=15 '= 0.873
K = 33 7 = 0.887
EL| w, = 0.633 hP= 4.3
..11 w,= 0.478 P&= 14.2 W, = 0.296 05
10.5=
w2 = 0.071 z2=20.2
w, = 0.522 JJ1= 52.8 111111111,-......
I
II (d) (c) (d)
(c)
'' iliE, , , , i~...........
,,l
I
*1'. -. .t
(f)--
(e) (f) (e)
T 38.3 a2= 143982 PT 80.7 CT 3043.561
K:=61 K2=136 7=0.893
I_. . . IIIIIIIIIIIII KI = 32 7 = 0.767
w0=0.395 PJO=.24.1
wo= 0.266 0e 20.8 w, 0.456
z Pi= 99.2
7
I =0. 734 P,=44.6
W2=0.1t49
w
(h)
PZ=174.0
(g) (h)
(g) Fig. 3. Application to cells. Critenon measures f(kt, k2) are omitted in (c) and (g)
Fig. 2. Application to textures. by reason of illustration.
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5. 66 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. SMC-9, No. 1, JANI'ARY 1979
and another with an old one (e), respectively. In Fig. 2, the results is feasible by virtue of the criterion on which the method is based.
are shown for textures, where the histograms typically show the 3) An optimal threshold (or set of thresholds) is selected auto-
difficult cases of a broad and flat valley (c) and a unimodal peak matically and stably, not based on the differentiation (i.e.. a local
(g). In order to appropriately illustrate the case of three- property such as valley), but on the integration (i.e., a global
thresholding, the method has also been applied to cell images with property) of the histogram.
successful results, shown in Fig. 3, where CO stands for the back- 4) Further important aspects can also be analyzed (e.g., estima-
ground, C1 for the cytoplasm, and C2 for the nucleus. They are tion of class mean levels, evaluation of class separability, etc.).
indicated in (b) and (f) by ( ), (=), and (*), respectively. 5) The method is quite general: it covers a wide scope of un-
A number of experimental results so far obtained for various supervised decision procedure.
examples indicate that the present method derived theoretically is The range of its applications is not restricted only to the thre-
of satisfactory practical use. sholding of the gray-level picture, such as specifically described in
the foregoing, but it may also cover other cases of unsupervised
D. Unimodality of the object function classification in which a histogram of some characteristic (or feat-
The object function 52(k), or equivalently, the criterion measure ure) discriminative for classifying the objects is available.
1(k), is always smooth and unimodal, as can be seen in the exper- Taking into account these points, the method suggested in this
imental results in Figs. 1-2. It may attest to an advantage of the correspondence may be recommended as the most simple anid
suggested criterion and may also imply the stability of the standard one for automatic threshold selection that can be
method. The rigorous proof of the unimodality has not yet been applied to various practical problenms,
obtained. However, it can be dispensed with from our standpoint
concerning only the maximum. AcK NOWLEDGMENT
The author wishes to thank Dr. H. Nishino, Head of the Infor-
mation Science Division, for his hospitality and encouragement.
IV. CONCLUSION Thanks are also due to Dr. S. Mori, Chief of the Picture Proces-
A method to select a threshold automatically from a gray level sing Section, for the data of characters and textures and valuable
histogram has been derived from the viewpoint of discriminant discussions, and to Dr. Y. Nogucli for cell data. The author is also
analysis. This directly deals with the problem of evaluating the very grateful to Professor S. Amari of the University of Tokyo for
goodness of thresholds. An optimal threshold (or set of thre- his cordial and helpful suggestions for revising the presentation of
sholds) is selected by the discriminant criterion; namely, by maxi- the manuscript.
mizing the discriminant measure q (or the measure of separability REFERENCIES
of the resultant classes in gray levels). [1] J. M. S. Prewitt and M. L. Mendelsolhn, "The analysis of cell images," nn.
The proposed method is characterized by its nonparametric Acad. Sci., vol. 128, pp. 1035-1053, 1966
and unsupervised nature of threshold selection and has the follow- [2] J. S. Weszka, R. N. Nagel, and A. Rosenfeld, "A threshold selection technique."
IEEE Trans. Comput., vol. C-23, pp. 1322 -1326, 1974
ing desirable advantages. [3] S. Watanabe and CYBEST Group. "An automated apparatus for cancer
1) The procedure is very simple; only the zeroth and the first prescreening: CYBEST," Comp. Graph. Imiage Process. vol. 3. pp. 350--358, 1974.
order cumulative moments of the gray-level histogram are [4] C. K. Chow and T. Kaneko, "Automatic boundary detection of the left ventricle
from cineangiograms," Comput. Biomed. Res., vol. 5, pp. 388- 410, 1972.
utilized. [5] K, Fukunage, Introduction to Statisticul Pattern Recogniition. New York:
2) A straightforward extension to multithresholding problems Academic, 1972, pp. 260-267.
Book Reviews
Orthogonal Transforms for Digital Signal Processing---N. Ahmed and K. tation using orthogonal functions. Fourier methods of representating sig-
R. Rao (New York: Springer-Verlag, 1975, 263 pp.). Reviewed by Lokenatlh nals. relation between the Fourier series and the Fourier transform, and
Debnath, Departments of Mathematics and Physics, East Carolina Unit er- some aspects of cross correlation. autocorrelation. and consolution. Thlese
sity, Greenville, NC 27834. chapters provide a systematic transition from the Fourier represenitation
of analog signals to that of digital sigials.
With the advent of high-speed digital computers and the rapid advances The third chapter is concerned with the F'ourier representation of
in digital technology, orthogonal transforms have received considerable discrete and digital signals througlh the discrete Fourier tranisfornm (D)[ I).
attention in recent years, especially in the area of digital signal processing. Some important properties of the DFT including thc conv olution anld
This book presents the theory and applications of discrete orthogonal correlation theorems are discussed in some detail, The concept of ampli-
transforms. With some elementary knowledge of Fourier series trans- tude, power. and phase spectra is introduced. It is shown that the 1)1F is
forms, differential equations, and matrix algebra as prerequisites, this directly related to the Fourier transform series representation ol data sc-
book is written as a graduate level text for electrical and computer engi- quences tX(rn)). The two-dimensional DlFT anid its possible extensioni to
neering students. higher dimensions are insestigated. and the chapter closes "it}h ;omc
The first two chapters are essentially tutorial and cover signal represen- discussion on time-varying power andt phase spectra.
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