=Paper=
{{Paper
|id=Vol-2267/533-537-paper-102
|storemode=property
|title=An image verification framework development
|pdfUrl=https://ceur-ws.org/Vol-2267/533-537-paper-102.pdf
|volume=Vol-2267
|authors=Andrey Nechaevskiy,Ahmed Elaraby
}}
==An image verification framework development==
https://ceur-ws.org/Vol-2267/533-537-paper-102.pdf
Proceedings of the VIII International Conference "Distributed Computing and Grid-technologies in Science and
Education" (GRID 2018), Dubna, Moscow region, Russia, September 10 - 14, 2018
AN IMAGE VERIFICATION FRAMEWORK DEVELOPMENT
Andrey Nechaevskiy 1, Ahmed Elaraby 2,3,a
1
Joint Institute for Nuclear Research, Dubna, Russia
2
Department of Mathematics &Computer Science, Faculty of Science, South Valley University, Egypt
3
ColourLab, Norwegian University of Science and Technology, Norway
E-mail: a a.elaraby87@gmail.com
An efficient representation and implementation of image are necessary, as a digital image is an
approximation of some real situation, and carries some uncertainty. In order to deal with this
uncertainty we need appropriate image model, which also enable image processing without losing the
information regarding the uncertainty. Interval arithmetic techniques appear as a good option for
handling the uncertainty. In this work we focused the extension of the classical notion of digital image,
in the which each pixel has as degree of intensity an exact value to the interval digital image one,
where each pixel possesses an interval intensity that include lower and upper bound of every pixel of
an image as image verification model. The time consuming process of image data processing can be
address using parallel computing techniques that provide an efficient and convenient way to address
this issue. The paper concludes that considering the interval arithmetic in designing solutions for some
applications may impact the performance of algorithms and the image processing tasks may benefit
from an image verification model.
Keywords: interval arithmetic, image processing, uncertainty, parallel computing.
© 2018 Andrey Nechaevskiy, Ahmed Elaraby
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Proceedings of the VIII International Conference "Distributed Computing and Grid-technologies in Science and
Education" (GRID 2018), Dubna, Moscow region, Russia, September 10 - 14, 2018
1. Introduction
In image processing tasks, there are various sources of ambiguity and uncertainty to be
considered when performing the processing [1]. Images captured situations are not always ideal or
stable; this is one of examples of uncertainty regarding the measured pixel values, Also which in some
cases is related to the spatial position of an image object or technical limitations. So, in practice we
always deal with numerical and spatial approximations of pixel values. To overcome this uncertainty
we need suitable image models, which also enables to image processing without losing the
information regarding the uncertainty. Since information on the level of uncertainty will influence an
expert’s attitude, so the ability to propagate the uncertainty information during image processing tasks
can be very important. In order to deal with the uncertainty – in such a manner that it is incorporated
in an image model and can be processed together with an image – an image verification framework
introduced based on interval arithmetic.
Interval arithmetic is a powerful tool to deal with the uncertain data, the concepts of interval
arithmetic are discussed in [2-3] and some of the related work in interval arithmetic and interval
valued fuzzy set presented in [4-9]. In a grayscale image, the pixel value indicates the amount of white
or black existing at that specific position in an image [10-12]. In image processing, most algorithms
assumes that the pixel values are certain, although in practice the measured values of pixels might be
uncertain and just indicate a likely value of an image at a specific location. The uncertainty of the
pixel value is an immediate fact if considered that any tool will round captured values of pixel down or
up to the finite set of allowed values. The uncertainty of the pixel value is an immediate fact if
considered that any tool will round captured values of pixel down or up to the finite set of allowed
values. This might be the issue under identical registration circumstances, and will grow when these
circumstances change (e.g., weather conditions); Also, the pixels that belong to an edge of an object
might slightly shift position in various takes (e.g., while the camera slightly shifts position), this could
result in large differences in the measured value of a specific pixel, and consequently in a large
uncertainty of the real value of that pixel, i.e., for that specific spatial position in an image; the process
of digitalization, it's naturally a level of uncertainty, as the intensity of gray tones of the pixel in a
digital image will never correspond the existent in the nature, as an image refers to a continuous
function, denoted by I(x, y), where the value of I(x, y) in the coordinates space gives an image
brightness (intensity), the digitalization of value quantification called gray levels and the digitalization
of the space coordinates called sampling of an image. So, for these reasons, it's appropriate to compute
with grayscale intervals, where the interval represents the set to which the actual grayscale values
belongs. Various applications in image processing and bioinformatics may benefit from an image
verification model.
The paper describes the efficiency of applying interval arithmetic in image representation to
get an image verification model. This model allows obtaining better result in image processing tasks,
although it requires a lot of calculations and, as a result, a lot of time to perform the task. To solve this
problem, we suggest the use of parallel computing which is one of the possible solutions of the
problem concerning complex algorithms, as it allows using the available computing resources to the
maximum [13-15]. The use of parallel computing can significantly accelerate the implementation of
program, the degree of parallelism and the acceleration is fixed by the number of independent
computations performed simultaneously and this discuss in section 3.
2. Image Verification Framework
2.1 Interval Arithmetic Fundamentals
The concept of interval analysis is to compute with intervals of real numbers instead of real
numbers and it considers a powerful tool to determine the effects of uncertain data. The closed interval
denoted by [a , b] is the set of real numbers given by
[a , b] = {x ∈ R ∶ a ≤ x ≤ b} (1)
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Proceedings of the VIII International Conference "Distributed Computing and Grid-technologies in Science and
Education" (GRID 2018), Dubna, Moscow region, Russia, September 10 - 14, 2018
The left and right endpoints of an interval [x] will be denoted by x and x, respectively. Thus,
two intervals [x] = [x , x] and [y] = [y , y] are said to be equal if they are the same sets. Operationally,
this happens if their corresponding endpoints are equal:
[x] = [y] 𝑖𝑓𝑓 x = y and x = y (2)
The midpoint of [x] is given by
𝑚𝑖𝑑([x] ) = (x + x ) / 2 (3)
We are about to define the basic arithmetic operations between intervals. The key point in
these definitions is that computing with intervals is computing with sets. For example, when we add
two intervals, the resulting interval is a set containing the sums of all pairs of numbers, one from each
of the two initial sets. By definition then, the sum of two intervals [x] and [y] is the set
[x] + [y] = [x + y, x + y ] (4)
We will return to an operational description of addition momentarily (that is, to the task of
obtaining a formula by which addition can be easily carried out). But let us define the remaining three
arithmetic operations. The difference of two intervals [x] and [y] is the set
[x] - [y] = [x − y , x − y] (5)
The product of [x] and [y] is given by
[x] ∗ [y] ≔ {x ∗ y|x ∈ [x] ∈ y ∈ [y]} (6)
The division of [x] and [y] is given by
[x]/[y] ≔ {x/y|x ∈ [x] ∈ y ∈ [y]} (7)
Note that the result of an interval operation is also an interval (except for the special case of
division by an interval containing zero). Specific equations for interval operations are
[x] ∙ [y] = [𝑚𝑖𝑛 (xy, xy, xy, xy ) , 𝑚𝑎𝑥 (xy, xy, xy, xy )] (8)
2.2 Verification Image Model
To overcome the various types of uncertainty and vagueness when doing image processing
tasks, as most of those types are contextual, in the sense that they could be present (or not) in an
image, based on the situation of an image was captured at. We use a verification interval-valued
representation of an image. From an image I, we generate the verification interval-valued images IV(L),
IV(U) and IV(M) as following:
IV(L) = [𝑚𝑎𝑥(0, I(x,y) −1)] (9)
IV(U) = [𝑚𝑖𝑛(255, I(x,y) + 1)] (10)
IV(L) +IV(U)
IV(M) = [ ] (11)
2
That is, we assign to each image position an interval as IV(L) and IV(U) images encompassing
all of the brightness values modified by ± 1 tone and IV(M) is the midpoint image of an interval
images IV(L) and IV(U) . So, once we have interval representation images, then we can apply different
strategies of computing as; we can apply the computing strategies individually for IV(L), IV(U) and
IV(M) images or together. Figure 1, includes an example of the “Blood Cell” image, together with the
verification interval-valued representation.
535
Proceedings of the VIII International Conference "Distributed Computing and Grid-technologies in Science and
Education" (GRID 2018), Dubna, Moscow region, Russia, September 10 - 14, 2018
Figure 1. Schematic overview of an interval valued model of “Blood Cell” image where different steps can be
observed, Original image (a) is divided into two parts (Upper bound IV(U) image (b) and lower bound IV(L)
image (c)) following the midpoint IV(M) image (d)
3. JINR Parallel Computing Infrastructure
JINR actively participates in different international projects which are relied on advanced
computing technologies. A unique computer infrastructure has been created at LIT JINR [14], which
makes it possible to use a supercomputer, a hybrid cluster, and cloud computing for research.
The cloud computing successfully develops in the field of computer technologies. This
direction is the development of such technologies as the use of remote computer resources by Internet.
The reason for the development of cloud computing platforms is the increased need for supercomputer
resources available to end users for parallel computing.
“HybriLIT” heterogeneous cluster is a computation component of a multifunctional centre for
data storage, processing and analysis of the LIT JINR [15]. It is intended for performing computations
with the use of parallel programming technologies. Heterogeneous structure of computational nodes
allows developing parallel applications for the solution of a wide range of mathematical resource-
intensive tasks using the whole capacity of Multicore component and computation accelerators. The
main goal of the project is the development and implementation of a software package for analysis of
the large set of images with the ability to perform computations on high-performance computing
systems. Following the trends of the last decade, as the high-performance system selected the most
promising for today - heterogeneous computing systems that include in their structure not only multi-
core processors, but also NVIDIA graphics accelerators and processors Intel Xeon Phi. To use all the
capabilities of such systems, it is necessary to develop parallel algorithms for already existing single-
threaded versions of algorithms implementations.
The transition to advanced digital technology, such as high-performance hybrid computing
technologies (parallel computing technologies on a cluster, on a graphic cards, etc.), for solution of a
similar class of problems, allows in a short time to obtain physically significant world-class results.
Thus, the research tasks consist in the parallelization of the computational algorithms,
choosing of hardware platform and optimization of the programs taking into account its features. The
realization of these works suggests the development of the Verification Framework for Image
Analysis based on Interval Arithmetic using resources of the Multifunctional Information and
Computing Complex LIT JINR.
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Proceedings of the VIII International Conference "Distributed Computing and Grid-technologies in Science and
Education" (GRID 2018), Dubna, Moscow region, Russia, September 10 - 14, 2018
4. Conclusion
In this paper we introduced and justify an interval-based representation of images, proposed
for better managing their inherent ambiguity. An image verification framework presented based on
concepts of interval arithmetic, to overcome the uncertainty and enables to propagate this uncertainty
through image processing tasks. In image processing applications, experts will be able to judge the
uncertainty of the results, and can modify their attitude towards the information accordingly. Also, we
discussed the use of parallel computing techniques to overcome the time consuming of image
processing using image verification framework model.
References
[1] M. Nachtegael, P. Sussner, T. Melange, E.E. Kerre. Foundations of the Interval-Valued Image
Model to Model and Process Uncertainty in Image Capture. IWSSIP 2010 - 17th International
Conference on Systems, Signals and Image Processing., Rio de Janeiro, Brazil, June 17-19, 2010.
[2] Moore, R.E. Methods and Applications of Interval Analysis.SIAM Studies in Applied
Mathematics, Philadelphia. 1979.
[3] G. Alefeld and J. Herzberger."Introduction to Interval Computations". Computer Science and
Applied Mathematics, Academic Press, New York, NY, USA, 1983.
[4] Aarão Lyra, Roberto CallejasBedregal, Adrião Duarte DóriaNeto, Benjamín René
CallejasBedregal. The Interval Digital Images Processing, WSEAS International Conferences of
Mathematical Methods And Computational Techniques In Electrical Engineering, Vouliagmeni,
Athens, Greece, December 29-31, 2003.
[5]Younis Hijazi, Hans Hagen, Charles Hansen, Kenneth I. Joy. Why interval arithmetic is so useful.
Conference: Visualization of Large and Unstructured Data Sets, Kaiserslautern, Germany, September
9-11, 2007.
[6] L. Jaulin and S. Bazeille.Image shape extraction using interval methods.In Proc. of the 15th IFAC
Symposium on System Identification, 2009.
[7]Takimoto, R.Y.; Chalella das Neves, A.; Mafalda, R. ; Sato, A.K. ; Tavares, R.S. ; Stevo, N.A.; et
al. Detecting Function Patterns with Interval Hough Transform. IEEE International Conference on
Industry Applications (INDUSCON), 1 – 5, Sao Paulo, 8-10 Nov. 2010.
[8]Teruya Minamoto and Kentaro Aoki, A blind digital image watermarking method using interval
wavelet decomposition.International Journal of Signal Processing, Image Processing and Pattern
Recognition, Vol. 3, No. 2, June, 2010.
[9] M. Galar, E. Barrenechea, J. Fernandez, H. Bustince, G. Beliakov,Representing Images By Means
Of Interval-Valued Fuzzy Sets: Application To Stereo Matching. In Ssci 2011 - T2fuzz 2011, 134-
141, Paris, Francia, 2011.
[10] S. E. Umbaugh. Computer Imaging: Digital Image Analysis and Processing. CRC Press; 2005.
[11] R. C. Gonzalez and R. E. Woods.Digital Image Processing. Prentice Hall,New Jersey; 2008.
[12] Scott E Umbaugh. Digital Image Processing and Analysis: Human and Computer Vision
Applications with CVIP tools, Second Edition, CRC Press; 2010.
[13] Hui Liang Khor ,Siau-ChuinLiew and JasniMohd. Zain, A Review on Parallel Medical Image
Processing on GPU, 4th International Conference on Software Engineering and Computer Systems
(ICSECS), Kuantan, Pahang, Malaysia. August 19-21, 2015.
[14] Multifunctional Information and Computing Complex [Electronic resource]:
https://miccom.jinr.ru/(accessed 23.10.2018).
[15]Heterogeneous platform “HybriLIT”[Electronic resource]: http://hlit.jinr.ru/en/(accessed
25.10.2018).
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