Search results for: sign coding
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 388

Search results for: sign coding

388 Optimal Image Compression Based on Sign and Magnitude Coding of Wavelet Coefficients

Authors: Mbainaibeye Jérôme, Noureddine Ellouze

Abstract:

Wavelet transforms is a very powerful tools for image compression. One of its advantage is the provision of both spatial and frequency localization of image energy. However, wavelet transform coefficients are defined by both a magnitude and sign. While algorithms exist for efficiently coding the magnitude of the transform coefficients, they are not efficient for the coding of their sign. It is generally assumed that there is no compression gain to be obtained from the coding of the sign. Only recently have some authors begun to investigate the sign of wavelet coefficients in image coding. Some authors have assumed that the sign information bit of wavelet coefficients may be encoded with the estimated probability of 0.5; the same assumption concerns the refinement information bit. In this paper, we propose a new method for Separate Sign Coding (SSC) of wavelet image coefficients. The sign and the magnitude of wavelet image coefficients are examined to obtain their online probabilities. We use the scalar quantization in which the information of the wavelet coefficient to belong to the lower or to the upper sub-interval in the uncertainly interval is also examined. We show that the sign information and the refinement information may be encoded by the probability of approximately 0.5 only after about five bit planes. Two maps are separately entropy encoded: the sign map and the magnitude map. The refinement information of the wavelet coefficient to belong to the lower or to the upper sub-interval in the uncertainly interval is also entropy encoded. An algorithm is developed and simulations are performed on three standard images in grey scale: Lena, Barbara and Cameraman. Five scales are performed using the biorthogonal wavelet transform 9/7 filter bank. The obtained results are compared to JPEG2000 standard in terms of peak signal to noise ration (PSNR) for the three images and in terms of subjective quality (visual quality). It is shown that the proposed method outperforms the JPEG2000. The proposed method is also compared to other codec in the literature. It is shown that the proposed method is very successful and shows its performance in term of PSNR.

Keywords: Image compression, wavelet transform, sign coding, magnitude coding.

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387 Tree Sign Patterns of Small Order that Allow an Eventually Positive Matrix

Authors: Ber-Lin Yu, Jie Cui, Hong Cheng, Zhengfeng Yu

Abstract:

A sign pattern is a matrix whose entries belong to the set {+,−, 0}. An n-by-n sign pattern A is said to allow an eventually positive matrix if there exist some real matrices A with the same sign pattern as A and a positive integer k0 such that Ak > 0 for all k ≥ k0. It is well known that identifying and classifying the n-by-n sign patterns that allow an eventually positive matrix are posed as two open problems. In this article, the tree sign patterns of small order that allow an eventually positive matrix are classified completely.

Keywords: Eventually positive matrix, sign pattern, tree.

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386 A Note on Potentially Power-Positive Sign Patterns

Authors: Ber-Lin Yu, Ting-Zhu Huang

Abstract:

In this note, some properties of potentially powerpositive sign patterns are established, and all the potentially powerpositive sign patterns of order ≤ 3 are classified completely.

Keywords: Sign pattern, potentially eventually positive sign pattern, potentially power-positive sign pattern.

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385 Coding of DWT Coefficients using Run-length Coding and Huffman Coding for the Purpose of Color Image Compression

Authors: Varun Setia, Vinod Kumar

Abstract:

In present paper we proposed a simple and effective method to compress an image. Here we found success in size reduction of an image without much compromising with it-s quality. Here we used Haar Wavelet Transform to transform our original image and after quantization and thresholding of DWT coefficients Run length coding and Huffman coding schemes have been used to encode the image. DWT is base for quite populate JPEG 2000 technique.

Keywords: Lossy compression, DWT, quantization, Run length coding, Huffman coding, JPEG2000.

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384 Near-Lossless Image Coding based on Orthogonal Polynomials

Authors: Krishnamoorthy R, Rajavijayalakshmi K, Punidha R

Abstract:

In this paper, a near lossless image coding scheme based on Orthogonal Polynomials Transform (OPT) has been presented. The polynomial operators and polynomials basis operators are obtained from set of orthogonal polynomials functions for the proposed transform coding. The image is partitioned into a number of distinct square blocks and the proposed transform coding is applied to each of these individually. After applying the proposed transform coding, the transformed coefficients are rearranged into a sub-band structure. The Embedded Zerotree (EZ) coding algorithm is then employed to quantize the coefficients. The proposed transform is implemented for various block sizes and the performance is compared with existing Discrete Cosine Transform (DCT) transform coding scheme.

Keywords: Near-lossless Coding, Orthogonal Polynomials Transform, Embedded Zerotree Coding

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383 A Preliminary Study on the Eventual Positivity of Irreducible Tridiagonal Sign Patterns

Authors: Berlin Yu

Abstract:

Motivated by Berman et al. [Sign patterns that allow eventual positivity, ELA, 19(2010): 108-120], we concentrate on the potential eventual positivity of irreducible tridiagonal sign patterns. The minimal potential eventual positivity of irreducible tridiagonal sign patterns of order less than six is established, and all the minimal potentially eventually positive tridiagonal sign patterns of order · 5 are identified. Our results indicate that if an irreducible tridiagonal sign pattern of order less than six A is minimal potentially eventually positive, then A requires the eventual positivity.

Keywords: Eventual positivity, potentially positive sign pattern, tridiagnoal sign pattern, minimal potentially positive sign pattern.

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382 Some Results of Sign patterns Allowing Simultaneous Unitary Diagonalizability

Authors: Xin-Lei Feng, Ting-Zhu Huang

Abstract:

Allowing diagonalizability of sign pattern is still an open problem. In this paper, we make a carefully discussion about allowing unitary diagonalizability of two sign pattern. Some sufficient and necessary conditions of allowing unitary diagonalizability are also obtained.

Keywords: Sign pattern, unitary diagonalizability, eigenvalue, allowing diagonalizability.

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381 Construction Methods for Sign Patterns Allowing Nilpotence of Index k

Authors: Jun Luo

Abstract:

In this paper, the smallest such integer k is called by the index (of nilpotence) of B such that Bk = 0. In this paper, we study sign patterns allowing nilpotence of index k and obtain four methods to construct sign patterns allowing nilpotence of index at most k, which generalizes some recent results.

Keywords: Sign pattern, Nilpotence, Jordan block.

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380 Peak-to-Average Power Ratio Reduction in OFDM Systems using Huffman Coding

Authors: Ashraf A. Eltholth, Adel R. Mikhail, A. Elshirbini, Moawad I. Moawad, A. I. Abdelfattah

Abstract:

In this paper we proposed the use of Huffman coding to reduce the PAR of an OFDM system as a distortionless scrambling technique, and we utilize the amount saved in the total bit rate by the Huffman coding to send the encoding table for accurate decoding at the receiver without reducing the effective throughput. We found that the use of Huffman coding reduces the PAR by about 6 dB. Also we have investigated the effect of PAR reduction due to Huffman coding through testing the spectral spreading and the inband distortion due to HPA with different IBO values. We found a complete match of our expectation from the proposed solution with the obtained simulation results.

Keywords: HPA, Huffman coding, OFDM, PAR

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379 Eukaryotic Gene Prediction by an Investigation of Nonlinear Dynamical Modeling Techniques on EIIP Coded Sequences

Authors: Mai S. Mabrouk, Nahed H. Solouma, Abou-Bakr M. Youssef, Yasser M. Kadah

Abstract:

Many digital signal processing, techniques have been used to automatically distinguish protein coding regions (exons) from non-coding regions (introns) in DNA sequences. In this work, we have characterized these sequences according to their nonlinear dynamical features such as moment invariants, correlation dimension, and largest Lyapunov exponent estimates. We have applied our model to a number of real sequences encoded into a time series using EIIP sequence indicators. In order to discriminate between coding and non coding DNA regions, the phase space trajectory was first reconstructed for coding and non-coding regions. Nonlinear dynamical features are extracted from those regions and used to investigate a difference between them. Our results indicate that the nonlinear dynamical characteristics have yielded significant differences between coding (CR) and non-coding regions (NCR) in DNA sequences. Finally, the classifier is tested on real genes where coding and non-coding regions are well known.

Keywords: Gene prediction, nonlinear dynamics, correlation dimension, Lyapunov exponent.

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378 MIM: A Species Independent Approach for Classifying Coding and Non-Coding DNA Sequences in Bacterial and Archaeal Genomes

Authors: Achraf El Allali, John R. Rose

Abstract:

A number of competing methodologies have been developed to identify genes and classify DNA sequences into coding and non-coding sequences. This classification process is fundamental in gene finding and gene annotation tools and is one of the most challenging tasks in bioinformatics and computational biology. An information theory measure based on mutual information has shown good accuracy in classifying DNA sequences into coding and noncoding. In this paper we describe a species independent iterative approach that distinguishes coding from non-coding sequences using the mutual information measure (MIM). A set of sixty prokaryotes is used to extract universal training data. To facilitate comparisons with the published results of other researchers, a test set of 51 bacterial and archaeal genomes was used to evaluate MIM. These results demonstrate that MIM produces superior results while remaining species independent.

Keywords: Coding Non-coding Classification, Entropy, GeneRecognition, Mutual Information.

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377 A Fast Sign Localization System Using Discriminative Color Invariant Segmentation

Authors: G.P. Nguyen, H.J. Andersen

Abstract:

Building intelligent traffic guide systems has been an interesting subject recently. A good system should be able to observe all important visual information to be able to analyze the context of the scene. To do so, signs in general, and traffic signs in particular, are usually taken into account as they contain rich information to these systems. Therefore, many researchers have put an effort on sign recognition field. Sign localization or sign detection is the most important step in the sign recognition process. This step filters out non informative area in the scene, and locates candidates in later steps. In this paper, we apply a new approach in detecting sign locations using a new color invariant model. Experiments are carried out with different datasets introduced in other works where authors claimed the difficulty in detecting signs under unfavorable imaging conditions. Our method is simple, fast and most importantly it gives a high detection rate in locating signs.

Keywords: Sign localization, color-based segmentation.

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376 Parallel Joint Channel Coding and Cryptography

Authors: Nataša Živić, Christoph Ruland

Abstract:

Method of Parallel Joint Channel Coding and Cryptography has been analyzed and simulated in this paper. The method is an extension of Soft Input Decryption with feedback, which is used for improvement of channel decoding of secured messages. Parallel Joint Channel Coding and Cryptography results in improved coding gain of channel decoding, which achieves more than 2 dB. Such results are an implication of a combination of receiver components and their interoperability.

Keywords: Block length, Coding gain, Feedback, L-values, Parallel Joint Channel Coding and Cryptography, Soft Input Decryption.

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375 A Motion Dictionary to Real-Time Recognition of Sign Language Alphabet Using Dynamic Time Warping and Artificial Neural Network

Authors: Marcio Leal, Marta Villamil

Abstract:

Computacional recognition of sign languages aims to allow a greater social and digital inclusion of deaf people through interpretation of their language by computer. This article presents a model of recognition of two of global parameters from sign languages; hand configurations and hand movements. Hand motion is captured through an infrared technology and its joints are built into a virtual three-dimensional space. A Multilayer Perceptron Neural Network (MLP) was used to classify hand configurations and Dynamic Time Warping (DWT) recognizes hand motion. Beyond of the method of sign recognition, we provide a dataset of hand configurations and motion capture built with help of fluent professionals in sign languages. Despite this technology can be used to translate any sign from any signs dictionary, Brazilian Sign Language (Libras) was used as case study. Finally, the model presented in this paper achieved a recognition rate of 80.4%.

Keywords: Sign language recognition, computer vision, infrared, artificial neural network, dynamic time warping.

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374 Using Different Aspects of the Signings for Appearance-based Sign Language Recognition

Authors: Morteza Zahedi, Philippe Dreuw, Thomas Deselaers, Hermann Ney

Abstract:

Sign language is used by the deaf and hard of hearing people for communication. Automatic sign language recognition is a challenging research area since sign language often is the only way of communication for the deaf people. Sign language includes different components of visual actions made by the signer using the hands, the face, and the torso, to convey his/her meaning. To use different aspects of signs, we combine the different groups of features which have been extracted from the image frames recorded directly by a stationary camera. We combine the features in two levels by employing three techniques. At the feature level, an early feature combination can be performed by concatenating and weighting different feature groups, or by concatenating feature groups over time and using LDA to choose the most discriminant elements. At the model level, a late fusion of differently trained models can be carried out by a log-linear model combination. In this paper, we investigate these three combination techniques in an automatic sign language recognition system and show that the recognition rate can be significantly improved.

Keywords: American sign language, appearance-based features, Feature combination, Sign language recognition

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373 Enhanced Frame-based Video Coding to Support Content-based Functionalities

Authors: Prabhudev Hosur, Rolando Carrasco

Abstract:

This paper presents the enhanced frame-based video coding scheme. The input source video to the enhanced frame-based video encoder consists of a rectangular-size video and shapes of arbitrarily-shaped objects on video frames. The rectangular frame texture is encoded by the conventional frame-based coding technique and the video object-s shape is encoded using the contour-based vertex coding. It is possible to achieve several useful content-based functionalities by utilizing the shape information in the bitstream at the cost of a very small overhead to the bitrate.

Keywords: Video coding, content-based, hyper video, interactivity, shape coding, polygon.

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372 Extracting Road Signs using the Color Information

Authors: Wen-Yen Wu, Tsung-Cheng Hsieh, Ching-Sung Lai

Abstract:

In this paper, we propose a method to extract the road signs. Firstly, the grabbed image is converted into the HSV color space to detect the road signs. Secondly, the morphological operations are used to reduce noise. Finally, extract the road sign using the geometric property. The feature extraction of road sign is done by using the color information. The proposed method has been tested for the real situations. From the experimental results, it is seen that the proposed method can extract the road sign features effectively.

Keywords: Color information, image processing, road sign.

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371 Sign Pattern Matrices that Admit P0 Matrices

Authors: Ling Zhang, Ting-Zhu Huang

Abstract:

A P0-matrix is a real square matrix all of whose principle minors are nonnegative. In this paper, we consider the class of P0-matrix. Our main aim is to determine which sign pattern matrices are admissible for this class of real matrices.

Keywords: Sign pattern matrices, P0 matrices, graph, digraph.

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370 Hand Gesture Recognition: Sign to Voice System (S2V)

Authors: Oi Mean Foong, Tan Jung Low, Satrio Wibowo

Abstract:

Hand gesture is one of the typical methods used in sign language for non-verbal communication. It is most commonly used by people who have hearing or speech problems to communicate among themselves or with normal people. Various sign language systems have been developed by manufacturers around the globe but they are neither flexible nor cost-effective for the end users. This paper presents a system prototype that is able to automatically recognize sign language to help normal people to communicate more effectively with the hearing or speech impaired people. The Sign to Voice system prototype, S2V, was developed using Feed Forward Neural Network for two-sequence signs detection. Different sets of universal hand gestures were captured from video camera and utilized to train the neural network for classification purpose. The experimental results have shown that neural network has achieved satisfactory result for sign-to-voice translation.

Keywords: Hand gesture detection, neural network, signlanguage, sequence detection.

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369 Pakistan Sign Language Recognition Using Statistical Template Matching

Authors: Aleem Khalid Alvi, M. Yousuf Bin Azhar, Mehmood Usman, Suleman Mumtaz, Sameer Rafiq, RaziUr Rehman, Israr Ahmed

Abstract:

Sign language recognition has been a topic of research since the first data glove was developed. Many researchers have attempted to recognize sign language through various techniques. However none of them have ventured into the area of Pakistan Sign Language (PSL). The Boltay Haath project aims at recognizing PSL gestures using Statistical Template Matching. The primary input device is the DataGlove5 developed by 5DT. Alternative approaches use camera-based recognition which, being sensitive to environmental changes are not always a good choice.This paper explains the use of Statistical Template Matching for gesture recognition in Boltay Haath. The system recognizes one handed alphabet signs from PSL.

Keywords: Gesture Recognition, Pakistan Sign Language, DataGlove, Human Computer Interaction, Template Matching, BoltayHaath

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368 A Multi-Signature Scheme based on Coding Theory

Authors: Mohammed Meziani, Pierre-Louis Cayrel

Abstract:

In this paper we propose two first non-generic constructions of multisignature scheme based on coding theory. The first system make use of the CFS signature scheme and is secure in random oracle while the second scheme is based on the KKS construction and is a few times. The security of our construction relies on a difficult problems in coding theory: The Syndrome Decoding problem which has been proved NP-complete [4].

Keywords: Post-quantum cryptography, Coding-based cryptography, Digital signature, Multisignature scheme.

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367 Usage of Channel Coding Techniques for Peak-to-Average Power Ratio Reduction in Visible Light Communications Systems

Authors: P.L.D.N.M. de Silva, S.G. Edirisinghe, R. Weerasuriya

Abstract:

High Peak-to-Average Power Ratio (PAPR) is a concern of Orthogonal Frequency Division Multiplexing (OFDM) based Visible Light Communication (VLC) systems. Discrete Fourier Transform spread (DFT-s) OFDM is an alternative single carrier modulation scheme which would address this concern. Employing channel coding techniques is another mechanism to reduce the PAPR. In this study, the improvement which can be harnessed by hybridizing these two techniques for VLC system is being studied. Within the study, efficient techniques such as Hamming coding and Convolutional coding have been studied. Thus, we present the impact of the hybrid of DFT-s OFDM and Channel coding (Hamming coding and Convolutional coding) on PAPR in VLC systems, using MATLAB simulations.

Keywords: Convolutional Coding, Discrete Fourier Transform spread Orthogonal Frequency Division Multiplexing (DFT-s OFDM), Hamming Coding, Peak-to-Average Power Ratio (PAPR), Visible Light Communications (VLC).

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366 Segmentation of Korean Words on Korean Road Signs

Authors: Lae-Jeong Park, Kyusoo Chung, Jungho Moon

Abstract:

This paper introduces an effective method of segmenting Korean text (place names in Korean) from a Korean road sign image. A Korean advanced directional road sign is composed of several types of visual information such as arrows, place names in Korean and English, and route numbers. Automatic classification of the visual information and extraction of Korean place names from the road sign images make it possible to avoid a lot of manual inputs to a database system for management of road signs nationwide. We propose a series of problem-specific heuristics that correctly segments Korean place names, which is the most crucial information, from the other information by leaving out non-text information effectively. The experimental results with a dataset of 368 road sign images show 96% of the detection rate per Korean place name and 84% per road sign image.

Keywords: Segmentation, road signs, characters, classification.

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365 High Quality Speech Coding using Combined Parametric and Perceptual Modules

Authors: M. Kulesza, G. Szwoch, A. Czyżewski

Abstract:

A novel approach to speech coding using the hybrid architecture is presented. Advantages of parametric and perceptual coding methods are utilized together in order to create a speech coding algorithm assuring better signal quality than in traditional CELP parametric codec. Two approaches are discussed. One is based on selection of voiced signal components that are encoded using parametric algorithm, unvoiced components that are encoded perceptually and transients that remain unencoded. The second approach uses perceptual encoding of the residual signal in CELP codec. The algorithm applied for precise transient selection is described. Signal quality achieved using the proposed hybrid codec is compared to quality of some standard speech codecs.

Keywords: CELP residual coding, hybrid codec architecture, perceptual speech coding, speech codecs comparison.

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364 Optimal and Generalized Multiple Descriptions Image Coding Transform in the Wavelet Domain

Authors: Bahi brahim, El hassane Ibn Elhaj, Driss Aboutajdine

Abstract:

In this paper we propose a Multiple Description Image Coding(MDIC) scheme to generate two compressed and balanced rates descriptions in the wavelet domain (Daubechies biorthogonal (9, 7) wavelet) using pairwise correlating transform optimal and application method for Generalized Multiple Description Coding (GMDC) to image coding in the wavelet domain. The GMDC produces statistically correlated streams such that lost streams can be estimated from the received data. Our performance test shown that the proposed method gives more improvement and good quality of the reconstructed image when the wavelet coefficients are normalized by Gaussian Scale Mixture (GSM) model then the Gaussian one ,.

Keywords: Multiple description coding (MDC), gaussian scale mixture (GSM) model, joint source-channel coding, pairwise correlating transform, GMDCT.

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363 Scintigraphic Image Coding of Region of Interest Based On SPIHT Algorithm Using Global Thresholding and Huffman Coding

Authors: A. Seddiki, M. Djebbouri, D. Guerchi

Abstract:

Medical imaging produces human body pictures in digital form. Since these imaging techniques produce prohibitive amounts of data, compression is necessary for storage and communication purposes. Many current compression schemes provide a very high compression rate but with considerable loss of quality. On the other hand, in some areas in medicine, it may be sufficient to maintain high image quality only in region of interest (ROI). This paper discusses a contribution to the lossless compression in the region of interest of Scintigraphic images based on SPIHT algorithm and global transform thresholding using Huffman coding.

Keywords: Global Thresholding Transform, Huffman Coding, Region of Interest, SPIHT Coding, Scintigraphic images.

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362 Network Coding-based ARQ scheme with Overlapping Selection for Resource Limited Multicast/Broadcast Services

Authors: Jung-Hyun Kim, Jihyung Kim, Kwangjae Lim, Dong Seung Kwon

Abstract:

Network coding has recently attracted attention as an efficient technique in multicast/broadcast services. The problem of finding the optimal network coding mechanism maximizing the bandwidth efficiency is hard to solve and hard to approximate. Lots of network coding-based schemes have been suggested in the literature to improve the bandwidth efficiency, especially network coding-based automatic repeat request (NCARQ) schemes. However, existing schemes have several limitations which cause the performance degradation in resource limited systems. To improve the performance in resource limited systems, we propose NCARQ with overlapping selection (OS-NCARQ) scheme. The advantages of OS-NCARQ scheme over the traditional ARQ scheme and existing NCARQ schemes are shown through the analysis and simulations.

Keywords: ARQ, Network coding, Multicast/Broadcast services, Packet-based systems.

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361 Facial Expression Phoenix (FePh): An Annotated Sequenced Dataset for Facial and Emotion-Specified Expressions in Sign Language

Authors: Marie Alaghband, Niloofar Yousefi, Ivan Garibay

Abstract:

Facial expressions are important parts of both gesture and sign language recognition systems. Despite the recent advances in both fields, annotated facial expression datasets in the context of sign language are still scarce resources. In this manuscript, we introduce an annotated sequenced facial expression dataset in the context of sign language, comprising over 3000 facial images extracted from the daily news and weather forecast of the public tv-station PHOENIX. Unlike the majority of currently existing facial expression datasets, FePh provides sequenced semi-blurry facial images with different head poses, orientations, and movements. In addition, in the majority of images, identities are mouthing the words, which makes the data more challenging. To annotate this dataset we consider primary, secondary, and tertiary dyads of seven basic emotions of "sad", "surprise", "fear", "angry", "neutral", "disgust", and "happy". We also considered the "None" class if the image’s facial expression could not be described by any of the aforementioned emotions. Although we provide FePh as a facial expression dataset of signers in sign language, it has a wider application in gesture recognition and Human Computer Interaction (HCI) systems.

Keywords: Annotated Facial Expression Dataset, Sign Language Recognition, Gesture Recognition, Sequenced Facial Expression Dataset.

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360 Low Computational Image Compression Scheme based on Absolute Moment Block Truncation Coding

Authors: K.Somasundaram, I.Kaspar Raj

Abstract:

In this paper we have proposed three and two stage still gray scale image compressor based on BTC. In our schemes, we have employed a combination of four techniques to reduce the bit rate. They are quad tree segmentation, bit plane omission, bit plane coding using 32 visual patterns and interpolative bit plane coding. The experimental results show that the proposed schemes achieve an average bit rate of 0.46 bits per pixel (bpp) for standard gray scale images with an average PSNR value of 30.25, which is better than the results from the exiting similar methods based on BTC.

Keywords: Bit plane, Block Truncation Coding, Image compression, lossy compression, quad tree segmentation

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359 Network Coding with Buffer Scheme in Multicast for Broadband Wireless Network

Authors: Gunasekaran Raja, Ramkumar Jayaraman, Rajakumar Arul, Kottilingam Kottursamy

Abstract:

Broadband Wireless Network (BWN) is the promising technology nowadays due to the increased number of smartphones. Buffering scheme using network coding considers the reliability and proper degree distribution in Worldwide interoperability for Microwave Access (WiMAX) multi-hop network. Using network coding, a secure way of transmission is performed which helps in improving throughput and reduces the packet loss in the multicast network. At the outset, improved network coding is proposed in multicast wireless mesh network. Considering the problem of performance overhead, degree distribution makes a decision while performing buffer in the encoding / decoding process. Consequently, BuS (Buffer Scheme) based on network coding is proposed in the multi-hop network. Here the encoding process introduces buffer for temporary storage to transmit packets with proper degree distribution. The simulation results depend on the number of packets received in the encoding/decoding with proper degree distribution using buffering scheme.

Keywords: Encoding and decoding, buffer, network coding, degree distribution, broadband wireless networks, multicast.

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