Search results for: image processing

Authors: Jason Zalev, Reza Sedaghat

Abstract:

This paper describes a complex energy signal model that is isomorphic with digital human fingerprint images. By using signal models, the problem of fingerprint matching is transformed into the signal processing problem of finding a correlation between two complex signals that differ by phase-rotation and time-scaling. A technique for minutiae matching that is independent of image translation, rotation and linear-scaling, and is resistant to missing minutiae is proposed. The method was tested using random data points. The results show that for matching prints the scaling and rotation angles are closely estimated and a stronger match will have a higher correlation.

Keywords: Affine Invariant, Fingerprint Recognition, Matching, Minutiae.

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Authors: B. Bagheri Nakhjavanlo, T. S. Ellis, P.Raoofi, Sh.ziari

Abstract:

This paper presents an application of level sets for the segmentation of abdominal and thoracic aortic aneurysms in CTA datasets. An important challenge in reliably detecting aortic is the need to overcome problems associated with intensity inhomogeneities. Level sets are part of an important class of methods that utilize partial differential equations (PDEs) and have been extensively applied in image segmentation. A kernel function in the level set formulation aids the suppression of noise in the extracted regions of interest and then guides the motion of the evolving contour for the detection of weak boundaries. The speed of curve evolution has been significantly improved with a resulting decrease in segmentation time compared with previous implementations of level sets, and are shown to be more effective than other approaches in coping with intensity inhomogeneities. We have applied the Courant Friedrichs Levy (CFL) condition as stability criterion for our algorithm.

Keywords: Image segmentation, Level-sets, Local fitting binary, Thoracic aorta.

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Authors: Mario Mastriani, Alberto E. Giraldez

Abstract:

In this paper, a new probability density function (pdf) is proposed to model the statistics of wavelet coefficients, and a simple Kalman-s filter is derived from the new pdf using Bayesian estimation theory. Specifically, we decompose the speckled image into wavelet subbands, we apply the Kalman-s filter to the high subbands, and reconstruct a despeckled image from the modified detail coefficients. Experimental results demonstrate that our method compares favorably to several other despeckling methods on test synthetic aperture radar (SAR) images.

Keywords: Kalman's filter, shrinkage, speckle, wavelets.

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Authors: Guo Xiuhua, Sun Tao, Wu Haifeng, He Wen, Liang Zhigang, Zhang Mengxia, Guo Aimin, Wang Wei

Abstract:

Purpose: To explore the use of Curvelet transform to extract texture features of pulmonary nodules in CT image and support vector machine to establish prediction model of small solitary pulmonary nodules in order to promote the ratio of detection and diagnosis of early-stage lung cancer. Methods: 2461 benign or malignant small solitary pulmonary nodules in CT image from 129 patients were collected. Fourteen Curvelet transform textural features were as parameters to establish support vector machine prediction model. Results: Compared with other methods, using 252 texture features as parameters to establish prediction model is more proper. And the classification consistency, sensitivity and specificity for the model are 81.5%, 93.8% and 38.0% respectively. Conclusion: Based on texture features extracted from Curvelet transform, support vector machine prediction model is sensitive to lung cancer, which can promote the rate of diagnosis for early-stage lung cancer to some extent.

Keywords: CT image, Curvelet transform, Small pulmonary nodules, Support vector machines, Texture extraction.

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Authors: Kamran Hameed, Adeel Mumtaz, S.A.M. Gilani

Abstract:

In this paper, we start by first characterizing the most important and distinguishing features of wavelet-based watermarking schemes. We studied the overwhelming amount of algorithms proposed in the literature. Application scenario, copyright protection is considered and building on the experience that was gained, implemented two distinguishing watermarking schemes. Detailed comparison and obtained results are presented and discussed. We concluded that Joo-s [1] technique is more robust for standard noise attacks than Dote-s [2] technique.

Keywords: Digital image, Copyright protection, Watermarking, Wavelet transform.

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Authors: Nurul-Akidah M. Yusak, Rahmah Mohamed, Noor Zuhaira Abd Aziz

Abstract:

The introduction of degradable plastic materials into agricultural sectors has represented a promising alternative to promote green agriculture and environmental friendly of modern farming practices. Major challenges of developing degradable agricultural films are to identify the most feasible types of degradation mechanisms, composition of degradable polymers and related processing techniques. The incorrect choice of degradable mechanisms to be applied during the degradation process will cause premature losses of mechanical performance and strength. In order to achieve controlled process of agricultural film degradation, the compositions of degradable agricultural film also important in order to stimulate degradation reaction at required interval of time and to achieve sustainability of the modern agricultural practices. A set of photodegradable polyethylene based agricultural film was developed and produced, following the selective optimization of processing parameters of the agricultural film manufacturing system. Example of agricultural films application for oil palm seedlings cultivation is presented.

Keywords: Photodegradable polyethylene, plasticulture, processing schemes.

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Authors: Lai Yi-Hsiu

Abstract:

The present paper aims to examine the language processing of Chinese-speaking seniors with Alzheimer’s disease (AD) from the perspective of temporal cues. Twenty healthy adults, 17 healthy seniors, and 13 seniors with AD in Taiwan participated in this study to tell stories based on two sets of pictures. Nine temporal cues were fetched and analyzed. Oral productions in Mandarin Chinese were compared and discussed to examine to what extent and in what way these three groups of participants performed with significant differences. Results indicated that the age effects were significant in filled pauses. The dementia effects were significant in mean duration of pauses, empty pauses, filled pauses, lexical pauses, normalized mean duration of filled pauses and lexical pauses. The findings reported in the current paper help characterize the nature of language processing in seniors with or without AD, and contribute to the interactions between the AD neural mechanism and their temporal parameters.

Keywords: Language processing, Alzheimer’s disease, Mandarin Chinese, temporal cues.

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Authors: Jia-Hong Lee, Mei-Yi Wu, Hsien-Tsung Kuo

Abstract:

Texture is an important characteristic in real and synthetic scenes. Texture analysis plays a critical role in inspecting surfaces and provides important techniques in a variety of applications. Although several descriptors have been presented to extract texture features, the development of object recognition is still a difficult task due to the complex aspects of texture. Recently, many robust and scaling-invariant image features such as SIFT, SURF and ORB have been successfully used in image retrieval and object recognition. In this paper, we have tried to compare the performance for texture classification using these feature descriptors with k-means clustering. Different classifiers including K-NN, Naive Bayes, Back Propagation Neural Network , Decision Tree and Kstar were applied in three texture image sets － UIUCTex, KTH-TIPS and Brodatz, respectively. Experimental results reveal SIFTS as the best average accuracy rate holder in UIUCTex, KTH-TIPS and SURF is advantaged in Brodatz texture set. BP neuro network works best in the test set classification among all used classifiers.

Keywords: Texture classification, texture descriptor, SIFT, SURF, ORB.

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Authors: Sanghoon Kim, Sun-Tae Chung, Souhwan Jung, Dusik Oh, Jaemin Kim, Seongwon Cho

Abstract:

Eye localization is necessary for face recognition and related application areas. Most of eye localization algorithms reported so far still need to be improved about precision and computational time for successful applications. In this paper, we propose an eye location method based on multi-scale Gabor feature vectors, which is more robust with respect to initial points. The eye localization based on Gabor feature vectors first needs to constructs an Eye Model Bunch for each eye (left or right eye) which consists of n Gabor jets and average eye coordinates of each eyes obtained from n model face images, and then tries to localize eyes in an incoming face image by utilizing the fact that the true eye coordinates is most likely to be very close to the position where the Gabor jet will have the best Gabor jet similarity matching with a Gabor jet in the Eye Model Bunch. Similar ideas have been already proposed in such as EBGM (Elastic Bunch Graph Matching). However, the method used in EBGM is known to be not robust with respect to initial values and may need extensive search range for achieving the required performance, but extensive search ranges will cause much more computational burden. In this paper, we propose a multi-scale approach with a little increased computational burden where one first tries to localize eyes based on Gabor feature vectors in a coarse face image obtained from down sampling of the original face image, and then localize eyes based on Gabor feature vectors in the original resolution face image by using the eye coordinates localized in the coarse scaled image as initial points. Several experiments and comparisons with other eye localization methods reported in the other papers show the efficiency of our proposed method.

Keywords: Eye Localization, Gabor features, Multi-scale, Gabor wavelets.

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Authors: H. Sagha, S. Kasaei, E. Enayati, M. Dehghani

Abstract:

Although Face detection is not a recent activity in the field of image processing, it is still an open area for research. The greatest step in this field is the work reported by Viola and its recent analogous is Huang et al. Both of them use similar features and also similar training process. The former is just for detecting upright faces, but the latter can detect multi-view faces in still grayscale images using new features called 'sparse feature'. Finding these features is very time consuming and inefficient by proposed methods. Here, we propose a new approach for finding sparse features using a genetic algorithm system. This method requires less computational cost and gets more effective features in learning process for face detection that causes more accuracy.

Keywords: Face Detection, Genetic Algorithms, Sparse Feature.

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Authors: Mingxin Zhang, Zhaogan Lu, Junyi Shen

Abstract:

In current common research reports, salient regions are usually defined as those regions that could present the main meaningful or semantic contents. However, there are no uniform saliency metrics that could describe the saliency of implicit image regions. Most common metrics take those regions as salient regions, which have many abrupt changes or some unpredictable characteristics. But, this metric will fail to detect those salient useful regions with flat textures. In fact, according to human semantic perceptions, color and texture distinctions are the main characteristics that could distinct different regions. Thus, we present a novel saliency metric coupled with color and texture features, and its corresponding salient region extraction methods. In order to evaluate the corresponding saliency values of implicit regions in one image, three main colors and multi-resolution Gabor features are respectively used for color and texture features. For each region, its saliency value is actually to evaluate the total sum of its Euclidean distances for other regions in the color and texture spaces. A special synthesized image and several practical images with main salient regions are used to evaluate the performance of the proposed saliency metric and other several common metrics, i.e., scale saliency, wavelet transform modulus maxima point density, and important index based metrics. Experiment results verified that the proposed saliency metric could achieve more robust performance than those common saliency metrics.

Keywords: salient regions, color and texture features, image segmentation, saliency metric

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Authors: A. Elmarhomy, S. Karungaru, K. Terada

Abstract:

Understanding the number of people and the flow of the persons is useful for efficient promotion of the institution managements and company-s sales improvements. This paper introduces an automated method for counting passerby using virtualvertical measurement lines. The process of recognizing a passerby is carried out using an image sequence obtained from the USB camera. Space-time image is representing the human regions which are treated using the segmentation process. To handle the problem of mismatching, different color space are used to perform the template matching which chose automatically the best matching to determine passerby direction and speed. A relation between passerby speed and the human-pixel area is used to distinguish one or two passersby. In the experiment, the camera is fixed at the entrance door of the hall in a side viewing position. Finally, experimental results verify the effectiveness of the presented method by correctly detecting and successfully counting them in order to direction with accuracy of 97%.

Keywords: counting passersby, virtual-vertical measurement line, passerby speed, space-time image

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Authors: Hatem. Elmeddeb, Noureddine, Hamdi, Ammar. Bouallègue

Abstract:

In this paper, a joint source-channel coding (JSCC) scheme for time-varying channels is presented. The proposed scheme uses hierarchical framework for both source encoder and transmission via QAM modulation. Hierarchical joint source channel codes with hierarchical QAM constellations are designed to track the channel variations which yields to a higher throughput by adapting certain parameters of the receiver to the channel variation. We consider the problem of still image transmission over time-varying channels with channel state information (CSI) available at 1) receiver only and 2) both transmitter and receiver being informed about the state of the channel. We describe an algorithm that optimizes hierarchical source codebooks by minimizing the distortion due to source quantizer and channel impairments. Simulation results, based on image representation, show that, the proposed hierarchical system outperforms the conventional schemes based on a single-modulator and channel optimized source coding.

Keywords: Channel-optimized VQ (COVQ), joint optimization, QAM, hierarchical systems.

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Authors: Shivali D. Kulkarni, Ameya K. Naik, Nitin S. Nagori

Abstract:

In this paper we present simulation results for the application of a bandwidth efficient algorithm (mapping algorithm) to an image transmission system. This system considers three different real valued transforms to generate energy compact coefficients. First results are presented for gray scale and color image transmission in the absence of noise. It is seen that the system performs its best when discrete cosine transform is used. Also the performance of the system is dominated more by the size of the transform block rather than the number of coefficients transmitted or the number of bits used to represent each coefficient. Similar results are obtained in the presence of additive white Gaussian noise. The varying values of the bit error rate have very little or no impact on the performance of the algorithm. Optimum results are obtained for the system considering 8x8 transform block and by transmitting 15 coefficients from each block using 8 bits.

Keywords: Additive white Gaussian noise channel, mapping algorithm, peak signal to noise ratio, transform encoding.

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Authors: Samiah Alammari, Nassim Ammour

Abstract:

When providing a massive number of tasks successively to a deep learning process, a good performance of the model requires preserving the previous tasks data to retrain the model for each upcoming classification. Otherwise, the model performs poorly due to the catastrophic forgetting phenomenon. To overcome this shortcoming, we developed a successful continual learning deep model for remote sensing hyperspectral image regions classification. The proposed neural network architecture encapsulates two trainable subnetworks. The first module adapts its weights by minimizing the discrimination error between the land-cover classes during the new task learning, and the second module tries to learn how to replicate the data of the previous tasks by discovering the latent data structure of the new task dataset. We conduct experiments on hyperspectral image (HSI) dataset on Indian Pines. The results confirm the capability of the proposed method.

Keywords: Continual learning, data reconstruction, remote sensing, hyperspectral image segmentation.

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Authors: Nang Thwe Thwe Oo

Abstract:

Traditional object segmentation methods are time consuming and computationally difficult. In this paper, onedimensional object detection along the secant lines is applied. Statistical features of texture images are computed for the recognition process. Example matrices of these features and formulae for calculation of similarities between two feature patterns are expressed. And experiments are also carried out using these features.

Keywords: 1-D object segmentation, secant lines, objectoccurrence(frequency) matrix, contiguity matrix, statistical features.

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Authors: Shiraz Ahmad, Zhe-Ming Lu

Abstract:

An effective visual error concealment method has been presented by employing a robust rotation, scale, and translation (RST) invariant partial patch matching model (RSTI-PPMM) and exemplar-based inpainting. While the proposed robust and inherently feature-enhanced texture synthesis approach ensures the generation of excellent and perceptually plausible visual error concealment results, the outlier pruning property guarantees the significant quality improvements, both quantitatively and qualitatively. No intermediate user-interaction is required for the pre-segmented media and the presented method follows a bootstrapping approach for an automatic visual loss recovery and the image and video error concealment.

Keywords: Exemplar-based image and video inpainting, outlierpruning, RST-invariant partial patch matching model (RSTI-PPMM), visual error concealment.

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Authors: B. Bagheri Nakhjavanlo, T. J. Ellis, P. Raoofi, J. Dehmeshki

Abstract:

This paper presents a customized deformable model for the segmentation of abdominal and thoracic aortic aneurysms in CTA datasets. An important challenge in reliably detecting aortic aneurysm is the need to overcome problems associated with intensity inhomogeneities and image noise. Level sets are part of an important class of methods that utilize partial differential equations (PDEs) and have been extensively applied in image segmentation. A Gaussian kernel function in the level set formulation, which extracts the local intensity information, aids the suppression of noise in the extracted regions of interest and then guides the motion of the evolving contour for the detection of weak boundaries. The speed of curve evolution has been significantly improved with a resulting decrease in segmentation time compared with previous implementations of level sets. The results indicate the method is more effective than other approaches in coping with intensity inhomogeneities.

Keywords: Abdominal and thoracic aortic aneurysms, intensityinhomogeneity, level sets, local fitting binary.

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Authors: Sun Lim, Sewoong Jun, Il-Kyun Jung

Abstract:

This paper presents a wrap-around view system with 4 smart cameras module and remote motion mobile robot control equipped with smart camera module system. The two-level scheme for remote motion control with smart-pad(IPAD) is introduced on this paper. In the low-level, the wrap-around view system is controlled or operated to keep the reference points lying around top view image plane. On the higher level, a robot image based motion controller is utilized to drive the mobile platform to reach the desired position or track the desired motion planning through image feature feedback. The design wrap-around view system equipped on presents such advantages as follows: 1) a satisfactory solution for the FOV and affine problem; 2) free of any complex and constraint with robot pose. The performance of the wrap-around view equipped on mobile robot remote control is proven by experimental results.

Keywords: four smart camera, wrap-around view, remote mobile robot control

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Authors: S. Hu, J. Mortensen, Bernard F. Buxton

Abstract:

A real-time tracking system was built to track performers on an interactive stage. Using an ordinary, up to date, desktop workstation, the performers- silhouette was segmented from the background and parameterized by calculating the normalized central image moments. In the stage system, the silhouette moments were then sent to a parallel workstation, which used them to generate corresponding 3D virtual geometry and projected the generated graphic back onto the stage.

Keywords: Image moment, interactive stage, real-time, silhouette.

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Authors: J. I. Asnor, S. Rosnah, Z. W. H. Wan, H. A. B. Badrul

Abstract:

Pineapples can be classified using an index with seven levels of maturity based on the green and yellow color of the skin. As the pineapple ripens, the skin will change from pale green to a golden or yellowish color. The issues that occur in agriculture nowadays are to do with farmers being unable to distinguish between the indexes of pineapple maturity correctly and effectively. There are several reasons for why farmers cannot properly follow the guideline provide by Federal Agriculture Marketing Authority (FAMA) and one of reason is that due to manual inspection done by experts, there are no specific and universal guidelines to be adopted by farmers due to the different points of view of the experts when sorting the pineapples based on their knowledge and experience. Therefore, an automatic system will help farmers to identify pineapple maturity effectively and will become a universal indicator to farmers.

Keywords: Artificial Neural Network, Image Processing, Index of Maturity, Pineapple

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Authors: Yen-Yu Chen, Pao-Ching Chu, Ya-Ling Tsai

Abstract:

The algorithm represents the DCT coefficients to concentrate signal energy and proposes combination and dictator to eliminate the correlation in the same level subband for encoding the DCT-based images. This work adopts DCT and modifies the SPIHT algorithm to encode DCT coefficients. The proposed algorithm also provides the enhancement function in low bit rate in order to improve the perceptual quality. Experimental results indicate that the proposed technique improves the quality of the reconstructed image in terms of both PSNR and the perceptual results close to JPEG2000 at the same bit rate.

Keywords: JPEG 2000, enhancement filter

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Authors: Seyyed Yasser Hashemi, Khalil Monfaredi

Abstract:

Automatic transformation of paper documents into electronic documents requires document segmentation at the first stage. However, some parameters restrictions such as variations in character font sizes, different text line spacing, and also not uniform document layout structures altogether have made it difficult to design a general-purpose document layout analysis algorithm for many years. Thus in most previously reported methods it is inevitable to include these parameters. This problem becomes excessively acute and severe, especially in Persian/Arabic documents. Since the Persian/Arabic scripts differ considerably from the English scripts, most of the proposed methods for the English scripts do not render good results for the Persian scripts. In this paper, we present a novel parameter-free method for segmenting the Persian/Arabic document images which also works well for English scripts. This method segments the document image into maximal homogeneous regions and identifies them as texts and non-texts based on a pyramidal image structure. In other words the proposed method is capable of document segmentation without considering the character font sizes, text line spacing, and document layout structures. This algorithm is examined for 150 Arabic/Persian and English documents and document segmentation process are done successfully for 96 percent of documents.

Keywords: Persian/Arabic document, document segmentation, Pyramidal Image Structure, skew detection and correction.

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Authors: Rajlaxmi Chouhan, Pritee Khanna

Abstract:

In this manuscript, a wavelet-based blind watermarking scheme has been proposed as a means to provide security to authenticity of a fingerprint. The information used for identification or verification of a fingerprint mainly lies in its minutiae. By robust watermarking of the minutiae in the fingerprint image itself, the useful information can be extracted accurately even if the fingerprint is severely degraded. The minutiae are converted in a binary watermark and embedding these watermarks in the detail regions increases the robustness of watermarking, at little to no additional impact on image quality. It has been experimentally shown that when the minutiae is embedded into wavelet detail coefficients of a fingerprint image in spread spectrum fashion using a pseudorandom sequence, the robustness is observed to have a proportional response while perceptual invisibility has an inversely proportional response to amplification factor “K". The DWT-based technique has been found to be very robust against noises, geometrical distortions filtering and JPEG compression attacks and is also found to give remarkably better performance than DCT-based technique in terms of correlation coefficient and number of erroneous minutiae.

Keywords: Fingerprint watermarking, minutiae, discrete wavelet transform, PN sequence

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Authors: Jimeng Shi, Mahek Jain, Giri Narasimhan

Abstract:

Time Series Forecasting (TSF) is used to predict the target variables at a future time point based on the learning from previous time points. To keep the problem tractable, learning methods use data from a fixed length window in the past as an explicit input. In this paper, we study how the performance of predictive models change as a function of different look-back window sizes and different amounts of time to predict into the future. We also consider the performance of the recent attention-based transformer models, which had good success in the image processing and natural language processing domains. In all, we compare four different deep learning methods (Recurrent Neural Network (RNN), Long Short-term Memory (LSTM), Gated Recurrent Units (GRU), and Transformer) along with a baseline method. The dataset (hourly) we used is the Beijing Air Quality Dataset from the website of University of California, Irvine (UCI), which includes a multivariate time series of many factors measured on an hourly basis for a period of 5 years (2010-14). For each model, we also report on the relationship between the performance and the look-back window sizes and the number of predicted time points into the future. Our experiments suggest that Transformer models have the best performance with the lowest Mean   Absolute Errors (MAE = 14.599, 23.273) and Root Mean Square Errors (RSME = 23.573, 38.131) for most of our single-step and multi-steps predictions. The best size for the look-back window to predict 1 hour into the future appears to be one day, while 2 or 4 days perform the best to predict 3 hours into the future.

Keywords: Air quality prediction, deep learning algorithms, time series forecasting, look-back window.

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Authors: Tlotlollo Sidwell Hlalele, Shengzhi Du

Abstract:

High-voltage power transmission lines are the back bone of electrical power utilities. The stability and continuous monitoring of this critical infrastructure is pivotal. Nine-Sigma representing Eskom Holding SOC limited, South Africa has a major problem on proactive detection of fallen power lines and real time sagging measurement together with slipping of such conductors. The main objective of this research is to innovate RFID technology to solve this challenge. Various options and technologies such as GPS, PLC, image processing, MR sensors and etc., have been reviewed and draw backs were made. The potential of RFID to give precision measurement will be observed and presented. The future research will look at magnetic and electrical interference as well as corona effect on the technology.

Keywords: Precision Measurement, RFID and Sag.

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Authors: Rodrigo Montufar-Chaveznava

Abstract:

The colors of the human skin represent a special category of colors, because they are distinctive from the colors of other natural objects. This category is found as a cluster in color spaces, and the skin color variations between people are mostly due to differences in the intensity. Besides, the face detection based on skin color detection is a faster method as compared to other techniques. In this work, we present a system to track faces by carrying out skin color detection in four different color spaces: HSI, YCbCr, YES and RGB. Once some skin color regions have been detected for each color space, we label each and get some characteristics such as size and position. We are supposing that a face is located in one the detected regions. Next, we compare and employ a polling strategy between labeled regions to determine the final region where the face effectively has been detected and located.

Keywords: Tracking, face detection, image processing, colorspaces.

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Authors: D. Karthikeyan, G. Balakrishnan

Abstract:

Human faces, as important visual signals, express a significant amount of nonverbal info for usage in human-to-human communication. Age, specifically, is more significant among these properties. Human age estimation using facial image analysis as an automated method which has numerous potential real‐world applications. In this paper, an automated age estimation framework is presented. Support Vector Regression (SVR) strategy is utilized to investigate age prediction. This paper depicts a feature extraction taking into account Gray Level Co-occurrence Matrix (GLCM), which can be utilized for robust face recognition framework. It applies GLCM operation to remove the face's features images and Active Appearance Models (AAMs) to assess the human age based on image. A fused feature technique and SVR with GA optimization are proposed to lessen the error in age estimation.

Keywords: Support vector regression, feature extraction, gray level co-occurrence matrix, active appearance models.

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Authors: Hassan El Maia, Ahmed Hammouch, Driss Aboutajdine

Abstract:

This work presents an approach for the construction of a hybrid color-texture space by using mutual information. Feature extraction is done by the Laws filter with SVM (Support Vectors Machine) as a classifier. The classification is applied on the VisTex database and a SPOT HRV (XS) image representing two forest areas in the region of Rabat in Morocco. The result of classification obtained in the hybrid space is compared with the one obtained in the RGB color space.

Keywords: Color, texture, laws filter, mutual information, SVM, hybrid space.

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Authors: Serkan Narlı, Ahmet Z. Ozcelik

Abstract:

The theory of rough sets is generalized by using a filter. The filter is induced by binary relations and it is used to generalize the basic rough set concepts. The knowledge representations and processing of binary relations in the style of rough set theory are investigated.

Keywords: Rough set, fuzzy set, membership function, knowledge representation and processing, information theory

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