Conference Papers

M. Hoviattalab, R. Narimani, A. Yadollahi, and Arash Abadpour, “New Image-based System for Vibration Measurement, Specially Developed for Forced Human Vibration Analysis”, In the ASME International Mechanical Engineering Congress and RD&D Expo, (IMECE2004), Anaheim, California, November 13-19, 2004. (pdf)

The human being in the environments of modern technology has to endure stresses of many and varied kinds of vibrations [1]. Measuring vibration is an important tool in rehabilitation and biomechanical fields of research. We have proposed image processing as a new method to record and determine the frequency response of human body. The subjects were exposed to whole body periodical vibration while standing on a shaking table. Two digital camcorders were used to capture the motion of colored pencil-dot markers on the skin of human body (forehead) and on the edge of the shaking table. After color spotting each frame, the binary image results were processed using new circle factor criteria proposed in this work, for fast finding circles based on second order statistics. The extracted points were calibrated using our own extended version of the direct linear transformation (DLT) method. We subsequently used Borland Delphi 5.0 language to develop useful software for measuring and analyzing human body vibration. As a result, it was clear that the proposed method was lower noise-sensitive in comparison to accelerometer. In order to investigate the validity of the software, the obtained mechanical impedance of the body were compared with other investigations in literature and showed to be compatible. The main advantage of this method is working with a simple user familiar hardware with no external device attached to the subject and also a user-friendly-software.

R. Narimani, M. Hoviattalab, Arash Abadpour, and A. Yadollahi . “Vibration Measurement And Analysis Using Image Processing Method”, In the proceedings of the 7th Biennial Conference on Engineering Systems Design and Analysis, (ESDA), Manchester, UK, July 19-22, 2004. (pdf)

A large number of people are exposed to whole body vibration in their occupational life. Measuring vibration is an important tool in rehabilitation and biomechanical fields of research. We have proposed image processing as a new method to record and determine the frequency response of human body. The arranged set up for forced vibration consisted of an AC motor, a variable speed drive unit and a shaking table for producing one directional sinusoidal vibration. Volunteers were asked to stand on the shaking table at a relaxed posture .Two digital camcorders were used to capture the motion of colored pencil-dot markers on the skin of human body (forehead) and on the edge of the shaking table. After color spotting each frame, the binary image results were processed using new circle factor criteria proposed in this work, for fast finding circles based on second order statistics. The extracted points were calibrated using our own extended version of the direct linear transformation (DLT) method. Subsequently Vibration measuring software has been completely developed in Borland Delphi 5.0. Finally obtained displacement function of the body and the shaking table has been used in conjunction with Matlab 6.5 to prepare a proper algorithm for analyzing human body vibration. We discussed mechanical characteristics of the body by obtaining mechanical impedance and transmissibility from the shaking table to the head as example applications of the conducted software. The important point is the fact that all devices used in our developed measurement system are usually available in a biomechanics laboratory where a Gait system is functioning. This gives the opportunity for such laboratory to add vibration measurement to its capabilities without much excessive costs. The system has the advantage of lower noise sensitivity in comparison to accelerometer. The main advantage of this method is working with a simple user-familiar hardware with no external device attached to the subject and also a user-friendly-software

Arash Abadpour and S. Kasaei, “A New Parametric Linear Adaptive Color Space and its PCA-based Implementation”. In The 9th Annual CSI Computer Conference (CSICC2004), Volume 2, Pages 125-132, Tehran, Iran, February 2004. (pdf) (html)

In many vision applications, color is an important cue that must be applied very fast. In this paper, after giving a brief review on 12 different standard color spaces, the proposed parametric linear adaptive color (PLAC) space is defined. A color-based segmentation process is performed on these color spaces. Experimental results show that the PLAC can be applied at least three times faster than the standard color spaces. In addition, with 10% higher distinguishing power, the PLAC shows the fail rate of half as much of the standard spaces. The best advantage of the PLAC is its ability to remove the entire background in 75% of the objects; compared to the low 1.69% of the standard spaces. As the PLAC needs the semiautomatic tuning stage, the proposed PCA-PLAC method is introduced encapsulating the advantages of the PLAC with less required user supervision even than the standard color spaces. The results show the superiority of the proposed color spaces, while the PCA-PLAC even outperforms

Arash Abadpour and S. Kasaei, “Performance Analysis of Three Likelihood Measures for Color Image Processing”. In International Workshop on Computer Vision, IPM, Tehran, Iran, April 2004. (pdf) (html)

Image segmentation is a low-level operation, concerned with partitioning an image into homogeneous regions. In a large number of applications, segmentation plays a fundamental role for the subsequent higher-level operations; such as recognition, object-based image/video compression, object tracking, scene analysis, and object-based image editing. Until recently, attention was focused on segmentation of grayscale images, but the advances in computational power and instrumentation has evolved the research on color image segmentation. Although, many researchers have tried to extend the methods of grayscale image segmentation to the color images, working in this multidimensional field, enables the implementation of more efficient methods. At the heart of any color image segmentation method, relies an appropriate likelihood measure or a suitable homogeneity criteria. In this paper, the performance of the three paradigms of Euclidean distance, Mahalonobis distance, and reconstruction error are analyzed in terms of achieving perfect likelihood measures, robustness, and leading to promising homogeneity decisions. While the Euclidean distance is proved to perform poor in all cases, the proposed reconstruction error out-performs the Mahalonobis distance with much lower computation cost.

Arash Abadpour and S. Kasaei, “New PCA-based Compression Method for Natural Color Images”. In International Workshop on Computer Vision, IPM, Tehran, Iran, April 2004. (pdf) (html)

The color information in a natural image can be considered as a highly correlated vector space. This high correlation is the first motivation towards using linear dimensionality reduction methods like principal component analysis for the sake of data compression. In this paper new color image decomposition methods are proposed and compared experimentally. Using a newly proposed gray-scale image colorizing method, a new compression method is proposed for natural color images, that while reducing the spectral redundancy of natural color images, it leaves the spatial redundancy unchanged, to be handled with a specialized spatial-compression method independently, and is proved to be highly efficient.

Arash Abadpour and S. Kasaei, “A New Principle Component Analysis Based Colorizing Method”, In the 12th Iranian Conference on Electrical Engineering (ICEE2004), Mashhad, Iran, May 2004. (pdf) (html)

Although many modern imaging systems are still producing grayscale images, colored-images are more preferred for the larger amount of information they are carrying. Computing the grayscale representation of a color image is a straightforward task, while the inverse problem has no objective solution. The search through out literature has not revealed much history of the past works. In this paper, after a brief review of related research, a new dimension reduction method is proposed for natural color images and approved by both quantitative (PSNR) and subjective tests. Based on it a new class of colorizing methods is proposed and two sample formulations are presented, where the authors are aware of many other formulations available. Subjective test shows dominancy of our proposed method when our method is much faster than others. Our method is leading in face image colorizing where other methods have failed. Such colorization method can be used greatly in medical image processing, surveillance systems, and information visualization.

Arash Abadpour and S. Kasaei, “A New PCA-Based Robust Color Image Watermarking Method”, In the 2nd IEEE Conference on Advancing Technology in the GCC: Challenges, and Solutions (IEEE-GCC 2004), Pages 326-331, Manama, Kingdom of Bahrain, November 2004. (pdf) (html)

Although, the possibility of electronic storage and transmission has been beneficial for extending the intellectual communication, the easiness of copying and transmitting the data in the internet has increased the piracy and illegal use of owned artworks. As a result, digital data watermarking, has been under thorough investigation in recent years. The main aim of data hiding is to add some transparent signature to the data in an attack-resistance fashion, to be used for ownership claims. In this paper a new PCA-based watermarking method is proposed for color images. Rather than the dominant spatial, and the few available semi-spectral approaches, the proposed method uses the true redundancy in the spectral domain. The proposed watermarking method is resistent to available attacks, such as sophisticated geometrical transformations, artistic effects, lossy compression, frequency domain filtering, motion blur, occlusion, and enhancement. Experimental results show the efficiency of the proposed algorithm.

Arash Abadpour and S. Kasaei, “A Fast and Efficient Fuzzy Color Transfer Method”, In the 4th IEEE International Symposium on Signal Processing and Information Technology (ISSPIT 2004), Pages 491-494, Rome, Italy, December 2004. (pdf) (html)

Each image has its own color content that greatly influences the perception of human observer. Being able to transfer the color content of an image into another image, while preserving other features, (like texture), opens a new horizon in human-perception-based image processing. In this paper, after a brief review on the few efficient works performed in the field, a novel fuzzy principle component analysis (PCA) based color transfer method is proposed. The proposed method accomplishes the transformation based on a set of corresponding user-selected regions in images along with a blending ratio parameter set by the user. Results show more robustness and higher speed when comparing our proposed method with other available approaches.

Arash Abadpour and S. Kasaei, “A New FPCA-Based Fast Segmentation Method for Color Images”, In the 4th IEEE International Symposium on Signal Processing and Information Technology (ISSPIT 2004), Pages 72-75, Rome, Italy, December 2004. (pdf)

Fuzzy objective function-based clustering methods are proved to be fast tools for classification and segmentation purposes. Unfortunately, most of the available fuzzy clustering methods are using the spherical or ellipsoidal distances, which are proved to result in spurious clusters, when working on color data. In this paper, a general case of clustering is discussed and a general method is proposed and its convergence is proved. Also, it is proved that the FCM and the FCV methods are special cases of the proposed method. Based on the general method, a special case for color image processing is proposed. The clustering method is based on a likelihood measure, and is proved to outperform the Euclidean and the Mahalanobis distances, in color fields. Based on the proposed color clustering method, a new fast fuzzy segmentation method is proposed and is proved to be highly efficient. Comparison of the results with the FCM, proves the superiority of the proposed segmentation method.

Arash Abadpour, S. Bagheri S, and S. Kasaei, “A New Method for Agent-based Color Clustering”, In the World Congress on Fuzzy Logic, Soft Computing and Computational Intelligence Theories and Applications (IFSA2005), Beijing, China, July 2005. (pdf)

Fuzzy objective function-based clustering methods are proved to be fast tools for classification and segmentation purposes. Unfortunately, most of the available fuzzy clustering methods are using the spherical or ellipsoidal measures, which have been proved to result in spurious clusters, when working with color data. Also, the local minima is an unsolved problem in this field. In this paper, a cylindrical fuzzy clustering agent for color fields is proposed. Embedding a few such agents in a cooperating set, it is shown that the set converges very quickly. To avoid the probable trapping in local minima and non-perceptual results, a new cluster validity measure is proposed. The proposed clustering method for color images uses the results of the competition between different cooperative sets. Using various experimental results, the repeatability of the proposed method and the quality of its results are shown. Keyword: Fuzzy Clustering, Color Image Processing, Agent-Based Processing.

Arash Abadpour and S. Kasaei, “Novel Method for Unsupervised Fuzzy Change Detection in Multispectral Remotely Sensed Images”, In the third Conference on Machine Vision, Image Processing & Applications, (MVIP2005), Volume 1, Pages 270-277, Tehran, Iran, February 2005. (pdf)

Analysis of the multi-spectral remotely sensed images of the areas destructed by an earthquake is proved to be a helpful tool for construction assessments. In this paper, we propose a new fast and reliable fuzzy change detection method for multi-spectral images. The proposed fuzzy change detection method is mathematically and experimentally investigated and shown to be efficient and effective.

Arash Abadpour and S. Kasaei, “Novel Color Image Compression Method using Eigenimages”, In the third Conference on Machine Vision, Image Processing & Applications, (MVIP2005), volume 1, Pages 340-346, Tehran, Iran, Februrary 2005. (pdf)

From the birth of multi-spectral imaging techniques, there has been a tendency to consider and process this new type of data as a set of parallel gray-scale images, (instead of an ensemble of an n-D realization). Although, even now, some researchers make the same assumption, it is proved that using vector geometries leads to more realistic results. In this paper, based on the proposed method for extracting the eigenimages of a color image, a new color image compression method is proposed and analyzed which performs in the vectorial domain. Experimental results show that the proposed compression method is highly efficient.

Arash Abadpour and S. Kasaei, “A New Fast Fuzzy Method for Query Region Extraction from Color Images”. In the 10th Annual CSI Computer Conference (CSICC2005), Pages 53-59, Tehran, Iran, February 2005. (pdf)

Finding the region similar to a given query region has many applications in computer vision and computer graphics. The first step towards an efficient query region extraction is to have a proper likelihood measure. This issue has been neglected in the computer vision community and the researchers commonly use the Euclidean distance for query region extraction in some standard color spaces. In this paper, we analyze the performance of the Euclidean distance in 12 standard color spaces, each one examined in 7 distinct possible representations. Also, we investigate the Mahalanobis distance and the linear partial reconstruction error (LPRE). Here, a new query region extraction method is proposed and its repeatability, robustness, and time efficiency are investigated. Also, the effects of the used parameters are comprehensively analyzed.

Arash Abadpour and S. Kasaei, “New Tree Decomposition Method for Color Images”. In the 10th Annual CSI Computer Conference (CSICC2005), Pages 48-52, Tehran, Iran, February 2005. (pdf)

Two decades ago, quad-tree decomposition was proposed as a fast tool for decomposing an image into a set of homogenous rectangular regions. Since then, many researchers have tried to generalize the method to enhance the results. In this paper, a new tree decomposition method is proposed which uses the rectangular regions in a more adaptive way. This paper gives a comprehensive performance comparison between the quad-tree and the new proposed bi-tree decomposition methods.

Arash Abadpour and S. Kasaei, “Fast Registration of Remotely Sensed Images”, In the 10th Annual CSI Computer Conference (CSICC2005), Pages 61-67, Tehran, Iran, February 2005. (pdf)

The developments in remote-sensing technologies has offered new opportunities and applications in environmental monitoring. In recent years, researchers have focused on using this information to assess earthquake damages and afterwards reconstructions. A crucial step in change detection processes is to register the multi-spectral temporal images. In this paper, we propose a new, fast, and efficient PCA-based method for remote-sensing image registration. The proposed method works in realtime.

Arash Abadpour and S. Kasaei, “A New Fast Robust Color Image Watermarking Method using FPCA Clustering”, In the 10th Annual CSI Computer Conference (CSICC2005), Pages 246-251, Tehran, Iran, February 2005. (pdf)

There is a generally-accepted tendency to consider and process color images as a set of parallel gray-scale planes (instead of an ensemble of a 3-D realization). Although, even now, many researchers make the same assumption, but it is proved that using vector geometries leads to more promising results. In this paper, by processing the color images as vector geometries, a novel method is proposed to decompose a natural image into three eigenimages. Based on the proposed eigenimage extraction method, a new color image watermarking method is proposed. Experimental results show that the proposed watermarking method is highly resistant to the subsequent probable attacks while it is also very fast.

Arash Abadpour and S. Kasaei, “An Unsupervised Fast Color Transfer Method”, In the 13th Iranian Conference on Electrical Engineering (ICEE2005), Zanjan, Iran, 2005. (pdf)

Each image has its own color that greatly influences the perception of human observer. In this paper, after a very brief review of the available literature on color transfer among color images, a novel fuzzy principle component analysis (FPCA) based color transfer method is proposed that uses an efficient fuzzy clustering method. Results show more robustness and higher speed when comparing the performance of the proposed method with other available approaches.

Arash Abadpour and S. Kasaei, “Wavelet-PCA-Based Compression Method for Color Images (Invited Paper)”, In the First Symposium on Wavelet and its Applications, Tehran, Iran, February 2005. (pdf)

From the birth of multi-spectral imaging techniques, there has been a tendency to consider and process this new type of data as a set of parallel gray-scale images, (instead of an ensemble of an n-D realization). Although, even now, some researchers make the same assumption, it is proved that using vector geometries leads to more realistic results. In this paper, using a proposed PCA-based eigenimage extraction method, incorporated with a wavelet-based grayscale image compression algorithm, a new compression method is proposed. The paper includes comprehensive performance analysis of the proposed eigenimage extraction and compression methods.

Arash Abadpour and S. Kasaei, “Comprehensive Evaluation of the Pixel-Based Skin Detection Approach for Pornography Filtering in the Internet Resources”, In the International Symposium on Telecommunications, (IST 2005), Pages 829-834, Shiraz, Iran, September 2005. (pdf)

A robust skin detector is the primary need of many fields of computer vision, including face detection, gesture recognition, and pornography filtering. Less than 10 years ago, the first paper on automatic pornography filtering was published. Since then, different researchers claim different color spaces to be the best choice for skin detection in pornography filtering. Unfortunately, no comprehensive work is performed on evaluating different color spaces and their performance for detecting naked people. In this way, researchers refer to the results ion skin detection for face detection, which underlies different imaging conditions. In this paper, we examine 21 color spaces in all their possible representations for pixel.based skin detection in pornographic images. In this way, this paper holds the largest investigation in the field of skin detection, and only one run on the pornographic images.

Arash Abadpour and S. Kasaei, “Deliberate distortion of color image and video resources for copyright protection”, In the 5th IEEE International Symposium on Signal Processing and Information Technology (ISSPIT 2005), Athens, Greece, 2005. (pdf)

The easiness of data-flow in digital media, seriously claims the ownership of intellectual material. To solve this problem, researchers have worked on different watermarking methods to embed ownership data into original signals. Unfortunately, none of the available techniques have been able to assure an acceptable level of security. Though, recently some senior members of the image processing community are expressing essential doubt about the appropriateness of watermarking for data protection and declare it more as a nonsecure tool for data embedding. In this paper, we propose a fast method for copy protection of color visual objects. The proposed method, deliberately embeds fake edges and color alterations into a given a color image in the way that it carries the content of the original image. Using this damaged image prevents the unauthorized users to pirate the demo version of images and video placed at homepages to help consumers select the images they wish to purchase. The main contribution of the proposed method is that there is a small key for the distorted image that reverts all degradations in a lossless manner. To the knowledge of the authors, this is the first time this kind of copy protection is addressed. While there are literally infinite ways to encrypt a given image, it is proved both experimentally and mathematically that there is no practical chance to crack the code.

Arash Abadpour and S. Kasaei, “Multi-Layer Representation of Grayscale Images and Its Generalization”, In the 14th Iranian Conference on Electrical Engineering (ICEE2006), Iran. (pdf)

Thresholding is one of the earliest concepts developed in the image processing community. Many researchers have worked on the generalization of the thresholding problem as multithresholding. However, multithresholding only increases the number of threshold values used in the process. Here, we define multithresholding as computing layers which add up together to give better approximations of the given image. The paper contains comprehensive mathematical formulation of the problem and a proper solution to it. Simulation results show the efficiency of the proposed algorithm.

Arash Abadpour, Attahiru Sule Alfa, and Anthony C.K. Soong, “Closed Form Solution for QoS-Constrained Information-Theoretic Sum Capacity of Reverse Link CDMA Systems”, In the 2nd ACM Q2SWinet 2006, Torremolinos, Malaga, Spain. (pdf) (html)

The information-theoretic maximum system capacity in a CDMA network, which guarantees fairness to mobile stations, can be achieved by optimally allocating transmit powers to the mobile stations while imposing individual QoS constraints. Even though this optimization is carried out in a multi-dimensional space we show that the optimal solution can be reduced to a search in a one-dimensional space. In this paper we first show that the previous results can be obtained by a simpler and more intuitive approach. Also, we show that the optimal solution is actually bang{bang. In addition, we show that the candidate solutions can be determined in a closed form. This considerably reduces the computational e ort. Because rather than carrying out numerical search on a set of intervals, only a few explicitly determined points should now be examined.

Arash Abadpour, Attahiru Sule Alfa, and Anthony C.K. Soong, “Information-Theoretic Sum Capacity of Reverse Link CDMA Systems in A Single Cell, An Optimization Perspective., In the 8th Annual Conference for Canadian Queueing Theorists and Practitioners, CanQueue 2006, Banff, Calgary, Canada (abstract) (poster).

The information-theoretic approach to maximizing the aggregate capacity of the reverse link in a CDMA system looks for the best pattern of transmission power of the stations. In this framework, where the transmission from each station is noise to all others, extra constraints should be considered to lead to a practically applicable solution. The previous research has suggested a minimum guaranteed quality of service plus bounds on individual transmissions and the aggregate one as constraints. However, extensive analysis has revealed that these two constraints are not enough to produce a solution which can be realized in an actual system. Basically, lack of any constraint including the maximum capacity of each station or dealing with the unfairness of the whole system has been found to be responsible for the partial solution in which all stations except for one are left to transmit at the lowest possible bandwidth, while the selected station is served with a non-realistic bandwidth of couple of hundreds more. In this paper we devise a maximum capacity constraint and give an algorithm for solving the problem. Then, empirical evidence are analyzed to show that the system actually becomes more balanced and practical when the new constraint is added.

Arash Abadpour, Attahiru Sule Alfa, and Anthony C.K. Soong, “A More Realistic Approach to Information-Theoretic Sum Capacity of Reverse Link CDMA Systems in a Single Cell”, Submitted to the IEEE International Conference on Communications (ICC 2007), Glasgow, Scotland. (pdf) (html)

.The information-theoretic approach to maximizing the aggregate capacity of the reverse link in a CDMA system looks for the best pattern of transmission power of the stations. In this framework, where the transmission from each station is noise to all others, extra constraints should be considered to lead to a practically applicable solution. The previous research has suggested a minimum guaranteed quality of service plus bounds on individual transmissions and the aggregate one as constraints. However, extensive analysis has revealed that these two constraints are not enough to produce a solution which can be realized in an actual system. Basically, lack of any constraint including the maximum capacity of each station or dealing with the unfairness of the whole system has been found to be responsible for the partial solution in which all stations except for one are left to transmit at the lowest possible bandwidth, while the selected station is served with a non-realistic bandwidth of couple of hundreds more. In this paper we devise a maximum capacity constraint and give an algorithm for solving the problem. Then, empirical evidence are analyzed to show that the system actually becomes more balanced and practical when the new constraint is added.

Arash Abadpour, Attahiru Sule Alfa, and Anthony C.K. Soong, “Capacity-Share Controlled Information-Theoretic Sum Capacity of Reverse Link Single-Cell CDMA Systems”, Submitted to the 2007 IEEE 65th Vehicular Technology Conference, (VTC2007 Spring), Dublin, Ireland.

By controlling the pattern of transmission powers of the stations in a CDMA system the aggregate capacity of the reverse link can be optimized. To make this problem practically applicable appropriate constraints should be added to it. In previous research bounds on transmission power, signal to noise ratio, and maximum capacity of single stations plus a maximum bound for the aggregate transmission power of the system were analyzed. However, none of these constraints controls the capacity share of single stations. Hence, we may reach to a transmission power pattern in which one third of the whole capacity is given to a single station. This increases the probability of the base station depending massively on one station, resulting in a major loss when that station stops transmission. In this paper we introduce another constraint into the available set. We reformulate the available problem by adding a maximum capacity share constraint and propose an algorithm for solving it. The paper includes mathematical analysis of the problem and experimental results.

Arash Abadpour, Attahiru Sule Alfa, and Jeff Diamond, “Fuzzy Design of A Video-on-Demand Network”, Accepted in 7th IEEE International Symposium on Signal Processing and Information Technology (ISSPIT 2007). (pdf) (html) (slides)

Designing a Video-on-Demand (VoD) system is in essence an optimization task aimed at minimizing the cost of communication and storage in the corresponding network. The decision variables of this problem are the locations of the nodes plus the content which should be cached in each node. Furthermore, an assignment strategy is needed to determine, for each customer, which node should be contacted for each video file. While this problem is categorized in the general group of network optimization problems, its specific characteristics demand a new solution to be sought for it. In this paper, inspired by the success of fuzzy optimization for similar problems in coding, a fuzzy objective function is derived which is heuristically shown to minimize the communication cost in a VoD network, while controlling the storage cost as well. Then, an iterative algorithm is proposed to find an optimum solution to the proposed problem. After addressing the mathematical details of the proposed method, a sample problem is presented followed by the solution produced for it by the proposed method. This solution is then extensively analyzed.

Arash Abadpour and Attahiru Sule Alfa, “Approximate Algorithms for Maximizing the Capacity of the Reverse Link in Multiple-Class CDMA System”, Accepted for publication in the proceedings of the 11th INFORMS Computing Society Conference, Charleston 2009 (ICS’09). (pdf) (html) (slides)

Code Division Multiple Access (CDMA) has proved to be an efficient and stable means of communication between a group of users which share the same physical medium. Therefore, with the rising demands for high-bandwidth multimedia services on mobile stations, it has become necessary to devise methods for more rigorous management of capacity in these systems. While a major method for regulating capacity in CDMA systems is through power control, the mathematical complexity of the regarding model inhibits useful generalizations. In this paper, a linear and a quadratic approximation for the aggregate capacity of the reverse link in a CDMA system are proposed. It is shown that the error induced by the approximations is reasonably low and that rewriting the optimization problem based on these approximations makes the implementation of the system in a multiple-class scenario feasible. This issue has been outside the scope of the available methods which work on producing an exact solution to a single-class problem.

Last Update: November 2014