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Automatic Brain Tumor Segmentation Using FPGA Platform 1 H.M. William Thomas, 2 S.C. Prasanna Kumar and 3 D. Jayadevappa 1 Department of ECE, BITM, Ballari, India. [email protected] 2 Department of E&IE, RVCE, Bengaluru, India. [email protected] 3 Department of E&IE, JSSATE, Bengaluru, India. [email protected] Abstract This paper is an attempt to develop a brain tumor segmentation using FPGA. The Xilinx platform studio based EDK code is developed on the FPGA Spartan 3E and the edge detection techniques are used to find the brain tumor on the MRI images. Matlab based program is used to convert the image to the bit stream array which would be used as the header file on the Xilinx platform studio. This bit stream is taken and the calculation for the tumour segmentation using the level set technique is developed and the output is sent back to matlab. The experimental results proved that, the time taken by the FPGA to segment the brain tumor is less as compared to MATLAB or C++ environment. Index Terms:Segmentation, MRI, FPGA, fuzzy logic and brain tumor. International Journal of Pure and Applied Mathematics Volume 118 No. 18 2018, 3483-3497 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu 3483

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Page 1: Automatic Brain Tumor Segmentation Using FPGA Platform · transform edge detection algorithm using FPGA approach proposed by Selvathi and Dhara ni [15]. T he above background of current

Automatic Brain Tumor Segmentation Using FPGA

Platform 1H.M. William Thomas, 2S.C. Prasanna Kumar and 3D. Jayadevappa

1Department of ECE, BITM,

Ballari, India. [email protected]

2Department of E&IE, RVCE,

Bengaluru, India. [email protected]

3Department of E&IE, JSSATE,

Bengaluru, India. [email protected]

Abstract

This paper is an attempt to develop a brain tumor segmentation using FPGA. The Xilinx platform studio based EDK code is developed on the FPGA Spartan 3E and the edge detection techniques are used to find the brain tumor on the MRI images. Matlab based program is used to convert the image to the bit stream array which would be used as the header file on the Xilinx platform studio. This bit stream is taken and the calculation for the tumour segmentation using the level set technique is developed and the output is sent back to matlab. The experimental results proved that, the time taken by the FPGA to segment the brain tumor is less as compared to MATLAB or C++ environment. Index Terms:Segmentation, MRI, FPGA, fuzzy logic and brain tumor.

International Journal of Pure and Applied MathematicsVolume 118 No. 18 2018, 3483-3497ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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1. Introduction Medical image segmentation is always the challenging task of any problem in computer guided medical procedures in hospitals. Medical image segmentation is the process of partitioning an object of intersest by labeling each pixel from the medical image database to identify an anatomical structure. The results obtained from this process process leads to a wide range of applications in medical field as well as in visualization of the anatomical structre in 2-D or 3-D forms. Partioining an anatomical structure from medical datasets gives better clarity for the identification of a specific boundary or region in a medical image corresponding to the desired structure. To understand the medical image segmentation process, an enormous amount of information available in the literature concentrating on various issues of medical image segmentation techniques [1], [2], [3] and medical image segmentation has received tremendous amount of response from the hospitals and the research due to its various practical applications of segmentation results.

Algorithms for used for medical image segmentation can applied identify various pathological changes in brain and especially to recognize tumors and lesions in the brain area. This can be performed by first separating the recognizable neuro-anatomical structures. Further, these algorithms can also be used to determine specific disease of human brain. In order to perform this, identifying the genesis of the disease is quite important to decide the cause and to workout the options for treatment depending on the affected anatomical structre of the brain where the pathologis lies. Applications of medical image segmentation depends on the specific disease, imaging techniques and the other factors. As we aware that, there is single technique of medical image segmentation that can cater the medical community who can accept the end results for every medical image. At present scenario, there is a need for the solution where the richer information of anatomical structre can be obtained as compared to the exising systems using medical images automatically with lesser manual intervention. Medical segmentation is also used for constructing an anatomical atlases, determining shapes of various tissues structures and tracking pathological changes in the anatomical structures over the period of time. The main objective of medical image segmentation is to provide the segmented image that allows the doctor or clinician for better visualization qualitatively for shapes and relative positions of complex anatomical structre of the human brain internally and also to measure accurately their volumes quantitatively.

FPGAs are capably used as a touch of cutting Edge imaging applications picture sifting pleasing imaging picture weight remote correspondence downside the vast majority of frameworks is that they utilize a bizarre state for coding.Target incite to the utilization of Xilinx System Generator (XSG), contraption with a sporadic state graphical interface under the Matlab. Simulink based squares which makes it simple to manage concerning other programming for rigging depiction The unmistakable applications where picture sifting operations related

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are unsettling influence launch, upgrading edges and structures, blurring etc.This paper presents framework of sifting pictures for edge territory utilizing System Generator, which is an improvement of Simulink and includes models called "XILINX BLOCKS" which are mapped into structures, parts, signs and ports.

2. Background Most of the image processing applications such as medical image segmentation algorithms [4], [5] uses FPGAs to segment the desired object with a faster rate. These systems are are typically programmed with Hardware Description Languages (HDL) and microprocessor-based DSP design methodologies [6]. The hardware configuaration is designed in such a way that, all the required functions of image processing applications can be transferred to FPGA that allows faster processing of the task. It is not necessary to split the individual instructions for fetching, decoding which is generally used in typical processing unit of a computer system [7]. However, in most of the low level image processing applications, the parallelism inherent was exploited to its full extent for partitioning into subsystems and all of which can run concurrently with each other. Hence, the objective of this paper will be to propose the medical image segmentation algorithm and implementing it for segmenting the brain tumor accurately. Then, for faster segmentation, the program is transferred to hardware so that the processing speed of the components of the system is bounded within a specified timing constraint considered typical of such systems. The outcome of this proposed work is that, implementing image segmentation algorithms on FPGA hardware reduces the segmkentation time drastically and complex algorithms can be implemented without debugging and much varification. Hence, FPGAs based medical image segmentation techniques are the preferred choice for the implementation of such algorithms [8].

The technique of edge based segmentation by applying wavelet transform in Synthetic Aperture Radar (SAR) images was introduced by Marivi Tello Alonso et al. [9]. This technique adapts a novel technique for the detection of edges automatically. Mohammad Saleh Miri et al. [10] and S.Allin Christe et al. [11] were proposed the techniques based on curvelet transform and then transformed the algorithm for the efficient FPGA implementation of segmentation algorithms for brain MR images for tumour characterization using Xilinx System Generator. This technique will be able to reduce the amount of time required for the segmentation process considerable. Alba M. Sanchez et al. [12] came out with an architecture for segmenting filtered images using Xilinx system generator to improve the segmentation accuracy as compared to the Aba m et al.. Another technique based on reconfigurable architecture using C-based hardware descriptive languages was proposed by Daggu Venkateshwar Rao et al.[13] which was applied for implementation and evaluation of image segmentation aigorithms. The improved version of the FPGA used for the MRI brain segmentation was designed and devleped by Mohd Fauzi Bin Othman et al.[14] which proved the better specificity as compared to the Daggu Venkateshvar Rao

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method. Similarly, the FPGA implementation of image realization of beamlet transform edge detection algorithm using FPGA approach proposed by Selvathi and Dharani [15].

The above background of current methods, a new automatic brain tumor segmentation based on FPGA flatform is proposed. The proposed method uses medical image processing technique to segment the tumor from MR images to recalculate pixel values.

3. Generic Structre of FPGA FPGA is an electronic technology implemented with VLSI digital circuits by means of the software based reconfiguration of a large integrated array, consisting of similar configurable digital blocks may have variety of elementary logic gates, look-up tables and flip-flops. The routing system of FPGA [16] states each application using wide network of horizontal and vertical channels that may be interconnected in any possible way by transistorized interconnecting matrices. FPGA is a field reprogrammable leading hardware and software technologies. The generalized structre of FPGA is shown in figure 1. The whole execution of corner identification design utilizing Simulink and Xilinx squares experiences 3 stages, image pre-processing blocks, XSG used for edge detection, image post-processing blocks. Image pre-processing block sets and the circuit based layout used for picture pre-get ready squares utilized here are looked into underneath. Input pictures which could shade or grayscale are given as obligation to the archive piece. A shading space change square changes over RGB to grayscalepicture and this data in 2-D changed over to 1-D to get ready of the required part.

Design change piece sets yield flag to chart based information and accommodated un bolster square which change over this bundling to scalar illustrations yield at a higher testing rate [17]. The Xilinx structure generator instrument is another application in picture planning, and offers a model based arrangement for taking care of.

Pieces orchestrate the channels and commonly sponsorships with Matlab codes through client adaptable squares. It also offers straight forwardness of masterminding with GUI condition.

This instrument bolster programming increase, however particularly it makes enter documents for use in all Xilinx FPGAs, with the parallelism, vivacious, fast and modified area diminishing. These parts are stray pieces constantly picture dealing with.The structure building utilized as a bit of this venture can be utilized for all Xilinx FPGA pack with legitimate client layout in system generator square and could be reached out to tireless picture arranging. In addition to driving any type of high resolution display devices, FPGAs are capable for image enhancement, segmentation, pattern recognition and image compression etc.

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Figure 1: Generalized Structure of FPGA

4. Enhancement and Tumor Boundary Detection

MR images of human brain contains noise which is very common during the scanning and trnasmiision of image data through various communication channels. Generally, preprocessing techniques are used for the removal of such image noises effectively. For instant, in wavelet transform, wavelet coefficients are altered or varied in order to remove the noisy points and then an inverse wavelet transform is applied to reconstruct the image. The smooth and linear variations Daubechies-4 can be applied for as preprocessing which can give better resolution for slow changing properties of images [18]. This type of wavelet are belongs to the orthogonal family wavelets resulting to discrete wavelet transform domain. These are characterized by a maximal number of vanishing moments for some given support. The practical applications of wavelets can be used in fast wavelet ransform domain, therefore the compational complexity can be reduced.

Figure 2: Two Level Decomposition of the MR Image using Wavelet

Transform

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In this paper, the preprocessing is performed using DAUB-4 wavelet approximation coefficients for better resolution of the MR brain images. These coefficients were used as feature vector for classification. The reason behind using wavelet transform for image preprocessing is that, MR images of barin are variable in nature and the tissue structure of the brain is overlap in nature. Such images required efficient transformation technique.

Figure 3: Result of 2-Level Daubechies 4 on Brain MR Image

The demonatration DAUB-4 wavelet transform which was implemented using the wavelet toolbox for barin MR image shown in figure 3. The MR decomposition is illustrated by considering an input MR T1-weighted image. This image is decomposed into four levels by the DAUB4 wavelet approximation. Top most band shown in figure 3 is a low pass image. For LP directions, n is used. At each successive level the number of directional sub-bands is 4, 8 and 16 respectively. This figure also illustred the process of an image being decomposed into detailed components having different decomposition of wavelet transform.

An efficient segmentation of brain tumor boundary is one of the most challenging task in medical image analysis and to achive this, many algorithms have been developed and implemented which is established in the available literature. A boundary is the connected points of sharp change in a region of an image where pixel locations have abrupt intensity variations i.e. a discontinuity in gray level values. In other words, the boundary consists of connected edges between an object and the background.

The proposed work brain tumor segmentation method uses level set [19] for the detection of the tumor boundary from MR image. The level set technique is based on the active contour models which offers energy minimization of the contour. This is a long-range attraction generated by the object boundary and acting on the evolving contour for solving the segmentation problem for MR images. This method is very common technique which can be used the image

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which is blur and has weak edges with intensity in-homogeneity. As we know that, the Level set is an important group of deformable models.

Level set which is used to segment the brain tumor from MR image is formulated using active contours was first introduced by Osher and Sethian [20]. The segmentation process using level set uses energy minimization of active contour [21], [22] surfaces in one higher dimension. In level set, the evolving a surface is φ instead of contour or curve .C In level set method the contour ( )C s is represented by ( ), ,φ x y t as an an implicit function and the front is then defined implicitly as the zero level set 0.φ =

Given an initial φ at 0,=t it would be possible to know φ at any time t with the

motion equation φ∂∂t

.

Figure 4: Representation of Level Set [17]

From the chain rule, ( )( ),

0φ∂

=∂

x t tt

(1)

( )( )

0φ φ∂∂ ∂+ =

∂ ∂

x t tx t t t t

(2)

( )0φ φ∂

+ =∂ t txx t

(3)

Here, φ φ∂= ∇

∂x also, the speed tx is given by a force F normal to the surface, then

( )( )=tx F x t n , where ,φφ

∇=∇

n now equation (3) can be rewritten as,

0φ φ+∇ =t tx (4) 0φ φ+∇ =t Fn (5)

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0φφ φφ

∇+ ∇ =

∇t F (6)

0φ φ+ ∇ =t F (7)

Equation (7) is used for the contour evolution of the level set function φ which is known as level set equation. The parameter F is called the speed function, the function F depends on the image data and the level set function φ for effective segmentation.

5. Implementation for the Proposed Methodology

Multiresolution image analysis has attracted a considerable amount of attention in medical image processing. Due to the efficiency of multiresolution data representation, wavelets are considered for medical image segmentation in conjunction with the level sets. In this method a novel frame work of level set technique is applied to detect the tumour boundary accurately. In wavelet transform, the directional information is preserved in each sub-band and is captured by computing its energy. This energy is capable of enhancing weak and complex boundaries in details. Further, due its directional image expansion property, smoothness along the contours can be easily achieved. Therefore, wavelet transforms are well suited for the further enhancement of the object boundary.

In the proposed algorithm level set is used in conjunction with the wavelet transform for the segmentation of tumor boundary. The reason using level set in this method is that, Snake models cannot handle topological changes and it has a tendency to produce degenerate contours or self-intersections [24], [25]. The treatment of the proposed algorithm is divided into two stages. The first stage is used to compute the energy of the wavelet transform decomposed MR image.

Figure 5: Implementaion of the Propoed Methodology with FPGA

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The second stage corresponds to integration of this energy using level sets [23].

FPGA execution incorporates building an inserted structure required for the particular applications here we build up an implanted framework on little scale affect processor. In this paper an Altera Cyclone chip is incorporated as the FPGA accelerator and is implemented as a System On a Programmable Chip (SOPC). However, some of the hardware components are difficult to be re-designed and transferred on a FPGA board from scratch, when they are already a functional part of a computer-based system. The following block diagram shown in figure 5 illustrates the proposed methodology.

The FPGA with Virtex series is desirable one for the proposed methodto implement the medical image segmentation algorithm. The advantage of incorporating hardware implementation is that, The segmentation process time can be saved because of the high parallelism in the algorithm. This transfer will enable to use the medical image segmentation algorithms for the real time applications. The following table shows the specifications of the VERTEX 5 FPGA kit used to implement the proposed methodology. A bit stream is loaded into the device through special configuration pins.

Table I: Vertex 5 FPGA Specifications Descriptions

Device used XC4VSX25-10FF668 Logic cells 23,040 No of slices 10,240 Extreme DSP slices 128 Speed of RAM 3.9 GHZ Block RAM 0.99GB Dedicated multiplier 104 DCMs 4 Max select I/O 320

To implement the proposed segmentation algorithm on FPGA, Xilinx blockset architecture is derived and subsequently implemented on it. This architecture can be applied with the suitable image size and for different image sizes, the parameters has to be modified in the architecture for the desired results. In figure 6, The design of the component’s architecture is illustrated. In the Xilinx M-Code, logic for the component is encoded, which act as a container that can be used for Simulink blockset supplied with Mat Lab functions with Simulink [26]. Therefore, this block excutes the MAT Lab functions for the calculations of the output during the simulation process.

In this paper, the hardware used for embedding the components belongs to the Xilinx Virtex-5 family with a PCI connector for reliable interface to a PC. This board is an ideal one for implementing the medical image segmentation algorithms because of its support in high-speed I/O and also designed for filtering and other image processing applications.

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Figure 6: Design of the Component’s Architecture

6. Resuts and Disussion The proposed methodology was implemented using FGGA platform. In the first stage, the given input is preproceed by applying wavelet transform. In the second step, tumor segmentation is carriedout using level sets. Then the segmented tumor boundary is converted into samples using MAT lab codes and implemented using FPGA kit. The proposed methodology uses two brain MR images for testing and evaluation process. System model of the component has been compiled successfully in the Simulink environment. The hardware co-simulation block was generated without any errors and the processing speed was obtained using the synthesis and ISE implementation tool. To fulfill the objective of our research, the processing speed of the component on the FPGA is compared with its corresp onding speed in MATLAB and C++. This will enable us to ensure that the timing constraint imposed on segmentation for the proposed system is met.

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(a) (b) (c)

Figure 7: Segmentation Results for the MR Image 1. (a) Original Image (b) Enhanced by Wavelet Transform (C) Extracted

Boundaries of the Enhanced Image

(a) (b) (c)

Figure 8: Segmentation Results for the MR Image 2. (a) Original Image (b) Enhanced by Wavelet Transform (C) Extracted Boundaries of the Enhanced

Image

Two images of different sizes (large, medium and small) were selected and run using the same component on three different platforms namely MATLAB, C++ and FPGA kit.

7. Conclusion The Xilinx platform studio based EDK code is developed on the FPGA Vertex 5 series and the tumor boundary detection techniques were used to find the brain tumor on the MRI images. Matlab based program is used to convert the image to the bit stream array which would be used as the header file on the Xilinx platform studio. This bit stream is taken and the calculation for the tumour detection using the level set based technique is developed and the output is sent back to matlab. The tumour detected image is given to the matlab for displaying the final results. The results of the proposed technique proves that, there is a signican improvements in the segmentation accuracy and reduction of computational time as compared the existing medical image segmentation algorithms.

References [1] Clarke L., Velthuizen R., Camacho M., Heine J., Vaydianathan

M., Hall L., Thatcher R., Silbiger M., MRI Segmentation: Methods

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and Applications, Magnetic Resonance Imaging 13(3) (1995), 343–368.

[2] Pham D.L., Xu C., Prince J.L., Current methods in Medical Image Segmentation, Annual Review of Biomedical Engineering 2 (2000), 315–337.

[3] Daniel J., Withey Z.J.K., A Review of Medical Image Segmentation: Methods and Available Software, International Journal of Bioelectromagnetism 10(3) (2008), 125-148.

[4] Leeser M., Coric S., Miller E., Yu H., Trepanier M., Parallel-Beam backprojection: An FPGA implementation optimized for medical imaging, Journal of VLSI Signal Process. Syst. Signal, Image, Video Technol (2005), 295-311.

[5] Maslennikow O., Sergiyenko A., Mapping DSP Algorithms into FPGA, Proceedings of the International Symposium on Parallel Computing in Electrical Engineering, IEEE Xplore Press, Bialystok (2006), 208-213.

[6] Chang C., Design and Applications of a Reconfigurable Computing System for High Performance Digital Signal Processing, Ph.D. Thesis, University of California, Berkeley, (2005).

[7] Rao D.V., Patil S., Babu N.A., Muthukumar V., Implementation and Evaluation of Image Processing Algorithms on Reconfigurable Architecture using C-based Hardware Description Languages, International Journal of Theoretical and Applied Computer Sciences 1(1) (2006), 9-34.

[8] Yahia Said, Taoufik Saidani, Fethi Smach, Mohamed Atri and Hichem Snoussi, Embedded Real-Time Video Processing System on FPGA, ICISP LNCS, Springer-Verlag Berlin Heidelberg (2012), 85–92.

[9] Marivi Tello Alonso, Carlos L6pez-Martinez, Jordi Mallorqui, Philippe Salembier, Edge Enhancement Aigorithm Based on the Wavelet Transform for Automatie Edge Deteetion in SAR Images, IEEE Transactions on Geoseienee and Remote Sensing 49 (I) (2011).

[10] Mohammad Saleh Miri, Ali Mahloojifar, Retinal Image Analysis Using Curvelet Transform and Multistrueture Elements Morphology by Reeonstruetion, IEEE Transactions on Biomedieal Engineering 58 (5) (2011).

[11] Allin Christe S., Vignesh M., Kandaswamy A., AnEffieient FPGA Implementation of MRI Image Filtering and Tumour

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Charaeterization using Xilinx System Generator, International Journal of VLSI design & Communieation Systems 2(4) (2011).

[12] Alba M., Sanehez G., Rieardo Alvarez G., Sully Sanehez G, Arehiteeture for filtering Ximages using Xilinx System Generator, International Journal of Mathematieal Models and Methods in Applied Sciences 1(5) (2007).

[13] Daggu Venkateshwar Rao, Shruti Patil, Naveen Anne Babu, V Muthukumar, Implementation and Evaluation of Image Processing Aigorithms on Reeonfigurable Arehiteeture using C-based Hardware Deseriptive Languages, International Journal of Theoretieal and Applied Computer Seiences 1(1) (2006), 9-34.

[14] Mohd Fauzi Bin Othman, Norarmalina Abdullah, Nur Aizudin Bin Ahmad Rusli, An Overview of MRI Brain Classification using FPGA Implementation, IEEE Symposium on Industrial Eleetronies & Applications (2010).

[15] Selvathi D., Dharani, Realization of Beamlet Transform Edge Detection Algorithm using FPGA, International Conference on Signal Processing, Image Processing and Pattern Recognition (2013).

[16] Sami Hasan, Said Boussakta, Alex Yakovlev, FPGA-Based Architecture for a Generalized Parallel 2-D MRI Filtering Algorithm, American J. of Engineering and Applied Sciences 4 (4) (2011), 566-575.

[17] Hemalatha, Santhiyakumari, Suresh S., Implementation of Medical Image Segmentation using Virtex FPGA kit, SPACES (2015), 358-362.

[18] Shan Z., Aviyente S., Image denoising based on the wavelet co-occurrence matrix, Proc. IEEE ICASSP, Philadelphia, USA (2005), 645–648.

[19] Jayadevappa D., Srinivas Kumar S., Murty D.S., Medical Image Segmentation Algorithms using Deformable Models: a Review, IETE Technical Review 28(3) (2011).

[20] Osher S., Sethian J.A., Fronts Propagating with Curvature Dependent Speed:Algorithms based on Hamiton–Jacobi Formulations, Journal of Computer Physics 79(1) (1988) 12- 49.

[21] Sethian J.A., Level Set Methods and Fast Marching Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Second edition, Monograph on Applied and computationa Mathematics, Cambridge University Press (1999).

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[22] Jayadevappa D., Srinivas Kumar S., Murthy D.S., A New Deformable model based on Level sets for medical Image segmentation, International Journal of Computer Science 36(3) (2009), 199-207.

[23] Hai Min, Xiao-Feng Wang, De-Shuang Huang, Wei Jia, A novel dual minimization based level set method for image segmentation, Neurocomputing 214 (2016), 910-926.

[24] Sanping Zhou, Jinjun Wang, Mengmng Zhang, Quing, Cue, Yihong Gong, Correntropy-based level set method for medical image segmentation and bias correction, Neuro computing 234 (2017), 216-229.

[25] Sijie Niu, Qiang Chen, Luis De Sisternes, Zexuan Ji, Zeming Zhou, Daniel L.R., Robust noise region-based active contour model via local similarity factor for image segmentation, Neurocomputing, Pattern Recognition 61 (2017), 104-119.

[26] Xilinx Inc., www.xilinx.com

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