Search results for: Iterative Cellular Image Processing Algorithm (ICIPA)

Authors: Javier A. Dominguez Caballero, Graeme A. Manson, Matthew B. Marshall

Abstract:

Cutting tools with ceramic inserts are often used in the process of machining many types of superalloy, mainly due to their high strength and thermal resistance. Nevertheless, during the cutting process, the plastic flow wear generated in these inserts enhances and propagates cracks due to high temperature and high mechanical stress. This leads to a very variable failure of the cutting tool. This article explores the relationship between the continuous wear that ceramic SiAlON (solid solutions based on the Si3N4 structure) inserts experience during a high-speed machining process and the evolution of sparks created during the same process. These sparks were analysed through pictures of the cutting process recorded using an SLR camera. Features relating to the intensity and area of the cutting sparks were extracted from the individual pictures using image processing techniques. These features were then related to the ceramic insert’s crater wear area.

Keywords: Ceramic cutting tools, high speed machining, image processing, tool condition monitoring, tool wear.

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Authors: E. Srinivasan, D. Ebenezer

Abstract:

Median filters with larger windows offer greater smoothing and are more robust than the median filters of smaller windows. However, the larger median smoothers (the median filters with the larger windows) fail to track low order polynomial trends in the signals. Due to this, constant regions are produced at the signal corners, leading to the loss of fine details. In this paper, an algorithm, which combines the ability of the 3-point median smoother in preserving the low order polynomial trends and the superior noise filtering characteristics of the larger median smoother, is introduced. The proposed algorithm (called the combiner algorithm in this paper) is evaluated for its performance on a test image corrupted with different types of noise and the results obtained are included.

Keywords: Image filtering, detail preservation, median filters, nonlinear filters, order statistics filtering, Rank order filtering.

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Authors: N. H. Harun, A. S. Abdul Nasir, M. Y. Mashor, R. Hassan

Abstract:

Leukaemia is a blood cancer disease that contributes to the increment of mortality rate in Malaysia each year. There are two main categories for leukaemia, which are acute and chronic leukaemia. The production and development of acute leukaemia cells occurs rapidly and uncontrollable. Therefore, if the identification of acute leukaemia cells could be done fast and effectively, proper treatment and medicine could be delivered. Due to the requirement of prompt and accurate diagnosis of leukaemia, the current study has proposed unsupervised pixel segmentation based on clustering algorithm in order to obtain a fully segmented abnormal white blood cell (blast) in acute leukaemia image. In order to obtain the segmented blast, the current study proposed three clustering algorithms which are k-means, fuzzy c-means and moving k-means algorithms have been applied on the saturation component image. Then, median filter and seeded region growing area extraction algorithms have been applied, to smooth the region of segmented blast and to remove the large unwanted regions from the image, respectively. Comparisons among the three clustering algorithms are made in order to measure the performance of each clustering algorithm on segmenting the blast area. Based on the good sensitivity value that has been obtained, the results indicate that moving kmeans clustering algorithm has successfully produced the fully segmented blast region in acute leukaemia image. Hence, indicating that the resultant images could be helpful to haematologists for further analysis of acute leukaemia.

Keywords: Acute Leukaemia Images, Clustering Algorithms, Image Segmentation, Moving k-Means.

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Authors: M. Zeghid, M. Machhout, L. Khriji, A. Baganne, R. Tourki

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With the fast evolution of digital data exchange, security information becomes much important in data storage and transmission. Due to the increasing use of images in industrial process, it is essential to protect the confidential image data from unauthorized access. In this paper, we analyze the Advanced Encryption Standard (AES), and we add a key stream generator (A5/1, W7) to AES to ensure improving the encryption performance; mainly for images characterised by reduced entropy. The implementation of both techniques has been realized for experimental purposes. Detailed results in terms of security analysis and implementation are given. Comparative study with traditional encryption algorithms is shown the superiority of the modified algorithm.

Keywords: Cryptography, Encryption, Advanced EncryptionStandard (AES), ECB mode, statistical analysis, key streamgenerator.

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Authors: G. Murugeswari, A. Suruliandi

Abstract:

This paper proposes a rotational invariant texture feature based on the roughness property of the image for psoriasis image analysis. In this work, we have applied this feature for image classification and segmentation. The fuzzy concept is employed to overcome the imprecision of roughness. Since the psoriasis lesion is modeled by a rough surface, the feature is extended for calculating the Psoriasis Area Severity Index value. For classification and segmentation, the Nearest Neighbor algorithm is applied. We have obtained promising results for identifying affected lesions by using the roughness index and severity level estimation.

Keywords: Fuzzy texture feature, psoriasis, roughness feature, skin disease.

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Authors: Rong Zhou, Shun’ich Kaneko, Fumio Tanaka, Miyuki Kayamori, Motoshige Shimizu

Abstract:

In this paper, we propose a robust disease detection method, called adaptive orientation code matching (Adaptive OCM), which is developed from a robust image registration algorithm: orientation code matching (OCM), to achieve continuous and site-specific detection of changes in plant disease. We use two-stage framework for realizing our research purpose; in the first stage, adaptive OCM was employed which could not only realize the continuous and site-specific observation of disease development, but also shows its excellent robustness for non-rigid plant object searching in scene illumination, translation, small rotation and occlusion changes and then in the second stage, a machine learning method of support vector machine (SVM) based on a feature of two dimensional (2D) xy-color histogram is further utilized for pixel-wise disease classification and quantification. The indoor experiment results demonstrate the feasibility and potential of our proposed algorithm, which could be implemented in real field situation for better observation of plant disease development.

Keywords: Cercospora Leaf Spot (CLS), Disease detection, Image processing, Orientation Code Matching (OCM), Support Vector Machine (SVM).

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Authors: V. Masilamani, D.K. Sheena Christy, D.G. Thomas

Abstract:

Image synthesis is an important area in image processing. To synthesize images various systems are proposed in the literature. In this paper, we propose a bio-inspired system to synthesize image and to study the generating power of the system, we define the class of languages generated by our system. We call image as array in this paper. We use a primitive called iso-array to synthesize image/array. The operation is double splicing on iso-arrays. The double splicing operation is used in DNA computing and we use this to synthesize image. A comparison of the family of languages generated by the proposed self restricted double splicing systems on iso-arrays with the existing family of local iso-picture languages is made. Certain closure properties such as union, concatenation and rotation are studied for the family of languages generated by the proposed model.

Keywords: DNA computing, splicing system, iso-picture languages, iso-array double splicing system, iso-array self splicing.

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Authors: Manasi Pathade, Prachi Kadam, Renuka Kulkarni, Tejas Teredesai

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In this paper, we propose a novel concept of relative distance measurement using Stereo Vision Technology and discuss its implementation on a FPGA based real-time image processor. We capture two images using two CCD cameras and compare them. Disparity is calculated for each pixel using a real time dense disparity calculation algorithm. This algorithm is based on the concept of indexed histogram for matching. Disparity being inversely proportional to distance (Proved Later), we can thus get the relative distances of objects in front of the camera. The output is displayed on a TV screen in the form of a depth image (optionally using pseudo colors). This system works in real time on a full PAL frame rate (720 x 576 active pixels @ 25 fps).

Keywords: Stereo Vision, Relative Distance Measurement, Indexed Histogram, Real time FPGA Image Processor

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Authors: Bing-Fei Wu, Yen-Lin Chen, Chung-Cheng Chiu

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In this study, a new criterion for determining the number of classes an image should be segmented is proposed. This criterion is based on discriminant analysis for measuring the separability among the segmented classes of pixels. Based on the new discriminant criterion, two algorithms for recursively segmenting the image into determined number of classes are proposed. The proposed methods can automatically and correctly segment objects with various illuminations into separated images for further processing. Experiments on the extraction of text strings from complex document images demonstrate the effectiveness of the proposed methods.1

Keywords: image segmentation, multilevel thresholding, clustering, discriminant analysis

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Authors: Mahamed G.H. Omran, Andries P Engelbrecht, Ayed Salman

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An end-member selection method for spectral unmixing that is based on Particle Swarm Optimization (PSO) is developed in this paper. The algorithm uses the K-means clustering algorithm and a method of dynamic selection of end-members subsets to find the appropriate set of end-members for a given set of multispectral images. The proposed algorithm has been successfully applied to test image sets from various platforms such as LANDSAT 5 MSS and NOAA's AVHRR. The experimental results of the proposed algorithm are encouraging. The influence of different values of the algorithm control parameters on performance is studied. Furthermore, the performance of different versions of PSO is also investigated.

Keywords: End-members selection, multispectral satellite imagery, particle swarm optimization, spectral unmixing.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually the effects of blurred edges and jagged artifacts in the image to some extent. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to sharpen edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (“jaggies") along the tangent directions. In order to preserve image features such as edges, corners and textures, the nonlinear diffusion coefficients are locally adjusted according to the directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directional derivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different matrix sizes.

Keywords: Cholesky Decomposition, Fixed-point, Matrixinversion, Reconfigurable processing.

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Authors: N. N. Mosola, S. J. Molete, L. S. Masoebe, M. Letsae

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Hand gesture recognition is a technique used to locate, detect, and recognize a hand gesture. Detection and recognition are concepts of Artificial Intelligence (AI). AI concepts are applicable in Human Computer Interaction (HCI), Expert systems (ES), etc. Hand gesture recognition can be used in sign language interpretation. Sign language is a visual communication tool. This tool is used mostly by deaf societies and those with speech disorder. Communication barriers exist when societies with speech disorder interact with others. This research aims to build a hand recognition system for Lesotho’s Sesotho and English language interpretation. The system will help to bridge the communication problems encountered by the mentioned societies. The system has various processing modules. The modules consist of a hand detection engine, image processing engine, feature extraction, and sign recognition. Detection is a process of identifying an object. The proposed system uses Canny pruning Haar and Haarcascade detection algorithms. Canny pruning implements the Canny edge detection. This is an optimal image processing algorithm. It is used to detect edges of an object. The system employs a skin detection algorithm. The skin detection performs background subtraction, computes the convex hull, and the centroid to assist in the detection process. Recognition is a process of gesture classification. Template matching classifies each hand gesture in real-time. The system was tested using various experiments. The results obtained show that time, distance, and light are factors that affect the rate of detection and ultimately recognition. Detection rate is directly proportional to the distance of the hand from the camera. Different lighting conditions were considered. The more the light intensity, the faster the detection rate. Based on the results obtained from this research, the applied methodologies are efficient and provide a plausible solution towards a light-weight, inexpensive system which can be used for sign language interpretation.

Keywords: Canny pruning, hand recognition, machine learning, skin tracking.

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Authors: Rajiv Kumar, Arthanariee A. M.

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Image segmentation is the process to segment a given image into several parts so that each of these parts present in the image can be further analyzed. There are numerous techniques of image segmentation available in literature. In this paper, authors have been analyzed the edge-based approach for image segmentation. They have been implemented the different edge operators like Prewitt, Sobel, LoG, and Canny on the basis of their threshold parameter. The results of these operators have been shown for various images.

Keywords: Edge Operator, Edge-based Segmentation, Image Segmentation, Matlab 10.4.

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Authors: M. S. Muhammad, S. M. W. Masra, K. Kipli, N. Zamhari

Abstract:

The capturing of gel electrophoresis image represents the output of a DNA computing algorithm. Before this image is being captured, DNA computing involves parallel overlap assembly (POA) and polymerase chain reaction (PCR) that is the main of this computing algorithm. However, the design of the DNA oligonucleotides to represent a problem is quite complicated and is prone to errors. In order to reduce these errors during the design stage before the actual in-vitro experiment is carried out; a simulation software capable of simulating the POA and PCR processes is developed. This simulation software capability is unlimited where problem of any size and complexity can be simulated, thus saving cost due to possible errors during the design process. Information regarding the DNA sequence during the computing process as well as the computing output can be extracted at the same time using the simulation software.

Keywords: DNA computing, PCR, POA, simulation software

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Authors: S.Baskar, P.S.Ramkumar, R.Kesavan

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This paper presents a new heuristic algorithm useful for long-term planning of survivable WDM networks. A multi-period model is formulated that combines network topology design and capacity expansion. The ability to determine network expansion schedules of this type becomes increasingly important to the telecommunications industry and to its customers. The solution technique consists of a Genetic Algorithm that allows generating several network alternatives for each time period simultaneously and shortest-path techniques to deduce from these alternatives a least-cost network expansion plan over all time periods. The multi-period planning approach is illustrated on a realistic network example. Extensive simulations on a wide range of problem instances are carried out to assess the cost savings that can be expected by choosing a multi-period planning approach instead of an iterative network expansion design method.

Keywords: Wavelength Division Multiplexing, Genetic Algorithm, Network topology, Multi-period reliable network planning

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Authors: Abobaker Mohammed Qasem Farhan, Shangming Yang, Mohammed Al-Nehari

Abstract:

Pneumonia is a kind of lung disease that creates congestion in the chest. Such pneumonic conditions lead to loss of life due to the severity of high congestion. Pneumonic lung disease is caused by viral pneumonia, bacterial pneumonia, or COVID-19 induced pneumonia. The early prediction and classification of such lung diseases help reduce the mortality rate. We propose the automatic Computer-Aided Diagnosis (CAD) system in this paper using the deep learning approach. The proposed CAD system takes input from raw computerized tomography (CT) scans of the patient's chest and automatically predicts disease classification. We designed the Hybrid Deep Learning Algorithm (HDLA) to improve accuracy and reduce processing requirements. The raw CT scans are pre-processed first to enhance their quality for further analysis. We then applied a hybrid model that consists of automatic feature extraction and classification. We propose the robust 2D Convolutional Neural Network (CNN) model to extract the automatic features from the pre-processed CT image. This CNN model assures feature learning with extremely effective 1D feature extraction for each input CT image. The outcome of the 2D CNN model is then normalized using the Min-Max technique. The second step of the proposed hybrid model is related to training and classification using different classifiers. The simulation outcomes using the publicly available dataset prove the robustness and efficiency of the proposed model compared to state-of-art algorithms.

Keywords: CT scans, COVID-19, deep learning, image processing, pneumonia, lung disease.

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Authors: Axel Panning, Robert Niese, Ayoub Al-Hamadi, Bernd Michaelis

Abstract:

The segmentation of mouth and lips is a fundamental problem in facial image analyisis. In this paper we propose a method for lip segmentation based on rg-color histogram. Statistical analysis shows, using the rg-color-space is optimal for this purpose of a pure color based segmentation. Initially a rough adaptive threshold selects a histogram region, that assures that all pixels in that region are skin pixels. Based on that pixels we build a gaussian model which represents the skin pixels distribution and is utilized to obtain a refined, optimal threshold. We are not incorporating shape or edge information. In experiments we show the performance of our lip pixel segmentation method compared to the ground truth of our dataset and a conventional watershed algorithm.

Keywords: Feature extraction, Segmentation, Image processing, Application

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Authors: Xingsheng Yuan, Zhengzhi Wang

Abstract:

Color constancy algorithms are generally based on the simplified assumption about the spectral distribution or the reflection attributes of the scene surface. However, in reality, these assumptions are too restrictive. The methodology is proposed to extend existing algorithm to applying color constancy locally to image patches rather than globally to the entire images. In this paper, a method based on low-level image features using superpixels is proposed. Superpixel segmentation partition an image into regions that are approximately uniform in size and shape. Instead of using entire pixel set for estimating the illuminant, only superpixels with the most valuable information are used. Based on large scale experiments on real-world scenes, it can be derived that the estimation is more accurate using superpixels than when using the entire image.

Keywords: color constancy, illuminant estimation, superpixel

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (''jaggies'') along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first and second order directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directionalderivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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Authors: Liping Zhang, Kelin Li

Abstract:

In this paper, a class of impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms is formulated and investigated. By establishing a delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.

Keywords: Global exponential stability, bidirectional associative memory, fuzzy cellular neural networks, leakage delays, impulses.

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Authors: Yuji Kageyama, Shin Nagata, Tatsuya Takino, Izuru Nomura, Hiroyuki Kamata

Abstract:

In previous study, technique to estimate a self-location by using a lunar image is proposed.We consider the improvement of the conventional method in consideration of FPGA implementationin this paper. Specifically, we introduce Artificial Bee Colony algorithm for reduction of search time.In addition, we use fixed point arithmetic to enable high-speed operation on FPGA.

Keywords: SLIM, Artificial Bee Colony Algorithm, Location Estimate.

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Authors: Say Wei Foo, Qi Dong

Abstract:

In this paper, a novel feature-based image watermarking scheme is proposed. Zernike moments which have invariance properties are adopted in the scheme. In the proposed scheme, feature points are first extracted from host image and several circular patches centered on these points are generated. The patches are used as carriers of watermark information because they can be regenerated to locate watermark embedding positions even when watermarked images are severely distorted. Zernike transform is then applied to the patches to calculate local Zernike moments. Dither modulation is adopted to quantize the magnitudes of the Zernike moments followed by false alarm analysis. Experimental results show that quality degradation of watermarked image is visually transparent. The proposed scheme is very robust against image processing operations and geometric attacks.

Keywords: Image watermarking, Zernike moments, Featurepoint, Invariance, Robustness.

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Authors: A.Tajaddini

Abstract:

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

Keywords: Bisymmetric matrices, Paige’s algorithms, Least square.

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Authors: N. Parandin, M. A. Fariborzi Araghi

Abstract:

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.

Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.

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Authors: Sang-Hun Lee, Bum-Soo Kim, Yang-Sae Moon, Jinho Kim

Abstract:

In this paper we present a photo mosaic smartphone application in client-server based large-scale image databases. Photo mosaic is not a new concept, but there are very few smartphone applications especially for a huge number of images in the client-server environment. To support large-scale image databases, we first propose an overall framework working as a client-server model. We then present a concept of image-PAA features to efficiently handle a huge number of images and discuss its lower bounding property. We also present a best-match algorithm that exploits the lower bounding property of image-PAA. We finally implement an efficient Android-based application and demonstrate its feasibility.

Keywords: smartphone applications; photo mosaic; similarity search; data mining; large-scale image databases.

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Authors: Dipti Patra, Mridula J

Abstract:

In this paper, we propose a new image segmentation approach for colour textured images. The proposed method for image segmentation consists of two stages. In the first stage, textural features using gray level co-occurrence matrix(GLCM) are computed for regions of interest (ROI) considered for each class. ROI acts as ground truth for the classes. Ohta model (I1, I2, I3) is the colour model used for segmentation. Statistical mean feature at certain inter pixel distance (IPD) of I2 component was considered to be the optimized textural feature for further segmentation. In the second stage, the feature matrix obtained is assumed to be the degraded version of the image labels and modeled as Markov Random Field (MRF) model to model the unknown image labels. The labels are estimated through maximum a posteriori (MAP) estimation criterion using ICM algorithm. The performance of the proposed approach is compared with that of the existing schemes, JSEG and another scheme which uses GLCM and MRF in RGB colour space. The proposed method is found to be outperforming the existing ones in terms of segmentation accuracy with acceptable rate of convergence. The results are validated with synthetic and real textured images.

Keywords: Texture Image Segmentation, Gray Level Cooccurrence Matrix, Markov Random Field Model, Ohta colour space, ICM algorithm.

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Authors: M. F. Haroun, T. A. Gulliver

Abstract:

In this paper, an encryption algorithm is proposed for real-time image encryption. The scheme employs a dual chaotic generator based on a three dimensional (3D) discrete Lorenz attractor. Encryption is achieved using non-autonomous modulation where the data is injected into the dynamics of the master chaotic generator. The second generator is used to permute the dynamics of the master generator using the same approach. Since the data stream can be regarded as a random source, the resulting permutations of the generator dynamics greatly increase the security of the transmitted signal. In addition, a technique is proposed to mitigate the error propagation due to the finite precision arithmetic of digital hardware. In particular, truncation and rounding errors are eliminated by employing an integer representation of the data which can easily be implemented. The simple hardware architecture of the algorithm makes it suitable for secure real-time applications.

Keywords: Chaotic systems, image encryption, 3D Lorenz attractor, non-autonomous modulation, FPGA.

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Authors: Yasunori Sugita, Toshinori Yoshikawa, Naoyuki Aikawa

Abstract:

Variable digital filters are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied. In this paper, we propose a design method of variable FIR digital filters with an approximate linear phase characteristic in the passband. The proposed variable FIR filters have some large attenuation in stopband and their large attenuation can be varied by spectrum parameters. In the proposed design method, a quasi-equiripple characteristic can be obtained by using an iterative weighted least square method. The usefulness of the proposed design method is verified through some examples.

Keywords: Weighted Least Squares Approximation, Variable FIR Filters, Low-Delay, Quasi-Equiripple

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Authors: Michael Zimba, Darlison Nyirenda

Abstract:

A novel copy-move image forgery, CMIF, detection method is proposed. The proposed method presents a new approach which relies on electrostatic field theory, EFT. Solely for the purpose of reducing the dimension of a suspicious image, the proposed algorithm firstly performs discrete wavelet transform, DWT, of the suspicious image and extracts only the approximation subband. The extracted subband is then bijectively mapped onto a virtual electrostatic field where concepts of EFT are utilized to extract robust features. The extracted features are invariant to additive noise, JPEG compression, and affine transformation. Finally, same affine transformation selection, SATS, a duplication verification method, is applied to detect duplicated regions. SATS is a better option than the common shift vector method because SATS is insensitive to affine transformation. Consequently, the proposed CMIF algorithm is not only fast but also more robust to attacks compared to the existing related CMIF algorithms. The experimental results show high detection rates, as high as 100% in some cases.

Keywords: Affine transformation, Radix sort, SATS, Virtual electrostatic field.

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