CC BY
13Journal of Siberian Federal University. Engineering & Technologies 6 (2014 7) 636-640
УДК 004.9
Carrying Out of Effective Recovery Algorithms of Distorted Images
Vasily A. Maistrenko and Vladimir V. Maistrenko*
Omsk State Technical University 11 Prospect Mira, Omsk, 644050, Russia
Received 21.07.2014, received in revised form 08.08.2014, accepted 04.09.2014
Methods of distorted images reconstructing are considered and there are developed algorithms to recover images distorted by noise arising in the environment and movement of objects relative to each other. Distortion of the «blurring» type is considered to be the most difficult to restore, so the purpose of this work is to develop algorithms to recover images after this type of interference exposure.
Keywords: optoelectronic vision, image processing.
Выполнение алгоритмов эффективного восстановления искаженных изображений
В.А. Майстренко, В.В. Майстренко
Омский государственный технический университет Россия, 644050, Омск, пр. Мира, 11
Рассмотрены методы реконструкции искаженных изображений, присутствуют разработанные алгоритмы для восстановления изображений, искаженных помехами, возникающими в окружающей среде, и движением объектов относительно друг друга. Искажение типа «размытие» считается самым трудным для восстановления, поэтому цель исследования заключается в разработке алгоритмов для восстановления изображения после этого типа воздействия помех.
Ключевые слова: оптоэлектронное зрение, обработка изображений.
Currently, there is a wide use of optoelectronic spatial positioning of objects. In paper [1] the hardware and software implementation of optoelectronic system ranging shows the main approaches to solving problems related to accuracy in determining the distance to the object by using stereoscopic rangefinder created with two cameras running synchronously at different angles. Important part in
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* Corresponding author E-mail address: [email protected]
developing such aystems conststs of weir-chosen image reconstrucaion algorithms, as the system accuracy depends on these algorithms. Optoelectoonic system wonking in real should accurately track the object and its borders, as the environment interferes with nhe following: fog, smoke, dust, linear movement of objects relative to each other at sufficiently high speed, which leads to blurring of the image. Taking into account the above factors there is a serious peobrem of distoated image recovery, and the sntution is possible onlywite tine use; of modorn algoeithms for digi-al imnge peocessing. In the simple case when the objects are ctationaey and there is only interference auch as «salt and pepper» effect or additive Geussian noise, oee can use the algo rithms implemented with a median filter. Detailed informotion abnut the ways of the rr covsaing is presented in paper [2].
The task of image secovery ir to impsove thee; image quality on perception criterion obtained during image processing. Improving imoee quality is a subjeciive process, while the image recovery procrdures are quiee objective. The sotetion of reeovery tank is to reconstouct the image that has been distorted as a resutt o- external influences, with sufficient a priori determined information. Therefore, the metho die of image recovesy are based an modeling interfere nce o ccuering in the environment, and on using of appropriate algorithms for reconetruction of the original image. With this approach, it is neesssaey to fermulate properly the qualipy criteria that will evaluete tme oecult oa recovery.
When solving the problem oa image improving another approach is useq based on the heuristic peoceduits, their eesults depend on ehe human vision. For example, contrast enhancement can be consideosd sa a procedure of impaoving the image, as after its applicaeion ate image becomes more pleating to tiie eye, and tee areatment cf blurred images by usee of corresponding inverse procedures should be rnfereed to tiee set of tools oo image recoeeny.
To cany out the simulation ooimage renonstruciiona[lgoaitlim t!tene wot used mathematical package MATLAB, whech mdudes IPT library (Image Processmg Tootex) which contains the functions of digital msne procesting. Let us consider tfie basic approach uaed tn the development of algorilhma foe the si mulation of distortion and image rec oveey.
The deterioration of the image is modeled using the distortion function, which together with the additive noise creates a di stortion of the «<blurring» ty pe . T his functio n c an b e w ritten as (1):
o1x, y) = H[f(x,y)] + t;x,y)l (1)
weere g (x,y) - image function, H - distorting operator, £ (x, y) - additive noise, f (x, y) - initial spatial image function.
Formula (1) can be rewritten to the spatial domain as [2]:
g(x,y) = hfry) * e(x,y) + ?(x,y)i (2)
where h (x, y) - space representation of distorting operator, «<*» symbol - denotes convolution.
As it is known, convolution in the spatial domain is equivalent to multiplicarinn in the frequency domain. Fourier transforms of these functions, so the abone equation (2) of distortion model can be written in an equivalent representation in the frequency domain:
G(u,v) = H(u,v) + N(u,v), (3)
where capital letters denote the corretponding Fourier tranrforms of functions of the convolution equation (2).
The function H (u, v) is often referred to as optical transfer function (OTF, Optical Transfer Function). The term is derived from Fourier analysis of optical systems [2]. In the spatial domain function h (x, y) is called the spread of points (PSF, Point Spread Function). This term occurs when the function h (x, y) reacts on the light points to produce distortion characteristics for various types of input data. Functions h (x, y) and H (u, v) transform into each other under the influence of forward and reverse Fourier transforms, so there are two M-function otf2psf and psf2otf for these actions in the MATLAB package.
In this paper the following algorithm to simulate the distorting function was used. Point Spread Function PSF was set by means of the operator fspecial IPT library as follows: PSF = fspecial ('motion', len, theta). Fspecial operator allows to simulate the effect of a linear movement of the camera relative to the fixed object, thereby allowing distortion of «blurring» type. Len parameter specifies the number of pixels that the camera was moving to, theta - is the angle parameter measured in degrees, and it is measured from the positive horizontal semi-axis counterclockwise. Motion parameter gives the transfer characteristic of the spatial filter, which, being folded with the image, approximates linear movement (camcorder with respect to the image) by len pixels. The direction of movement is defined by the value of theta angle.
To carry out the simulation of distortion of the «blurring» type the following parameters were used: len = 45, theta = 45. With using imfilter function there was developed the filter with transfer function given by PSF function. The filter allows to achieve the effect of blurring the image with a linear motion of objects. Further there was simulated the process of adding the additive Gaussian noise interference by IPT imnoise library functions. Gaussian noise has the following characteristics: zero mean value and variance equal to 0.01. Fig. 1 and 2 show the result of the model image distortion.
From Fig. 2 it is seen that such an image from a video camera is not suitable for further processing in the optoelectronic system for measuring distance, as the object itself and its borders are not distinguishable.
Let us consider the process of restoring the image after distortion shown in Fig. 2. The first step in recovery algorithm is a high-frequency filter that improves the image brightness and contrast. HF filter is projected with the help of prototype LF filter and has the following transfer characteristic h: h = ((—* 1,2. Where hi - transfer characteristic of the LF filter, which is HFF prototype.
The formula was obtained experimentally by the best image quality criteria, perceived visually. Next there was designed the filter to improve the image borders, based on the calculation of «counter harmonious average.» Further information connecting with such filtering techniques can be found in paper [2].
For the implementation of «counter harmonious average» filter IPT library function spfilt corresponds performing spatial filtering.
The final stage of restoring the image shown on Fig. 2 is the implementation of Lucy-Richardson algorithm giving [he biggest effect in case of distortions discussed in this paper. Lucy-Richardson recovery algorithm is the algorithm of non-lineaf iterative reconstruction [2]. Let us consider the algorithm. Lucy Richardson algorithm is based on a maximum likelihood method, in which an image is formed usifg the Poisson statistics [2]. Maximizotioo od the likelihood function model leads to an equation that has a solution [or the nsxt iteration of convergence, as in formula (4):
Fig. 1. The original image
v W* . To± Mm Yvi-
J J .■ lj " S ii У. ■
a □ и a a
Fig. 2. The result ofthe model introducing distortion
fk+1(x,y) = fk(x,y) [h(-x,-y)* (4)
where tlie symbol «*» denotes convolution, fk - k - approximation t((nted image and functions f, g are identified.
IPT librasy hax thi) (lgorithm perforated by doconvlucy function with the foilow(ng syntax: deconviucy (g, PFS, NUMIT, DAMPAR, WEIGHT), where g - distorted image, PFS - spresd function points, NUMIT - the number of iterations, DAMPAR - a scalar that specifies the dtviation limit of the received image of g. Iterationr stop for pixels which dtviation from the initial values does not exceed
t 1 LÎUTïM l^i&flE!
I— 1* - — 1—1 1 44H M4 -
|jr U i ti \ . ■ S V À' 1 □ = : ■ □
Fig. 3. The result of Lucy-Richardson algorithm
this limit. This prevents the generation of noise in such pixels preserving necessary details. While default DAMPAR = 0 (no limit stop), WEIGHT - an array with the dimension of g, which assigns each pixel some weight that reflecfs its quality0.
For example eebad» pixels derived from the defective area on the image ean be excluded from consideration giving them zeuo weight.
To implemenf Lucy-Richardson algorithm there weee taken the following parameters: NUMIT = 80 (the number of iterations is chosen experimentally for the case) DAMPAR = 0 (no limit stops), the parameter WEIGHT - set default. The result of the final stage of recovery after arithmetic average is showo in Fig. 3.
Fig.3 shows the reeult ot image reconstruction ysing algorithms proposed by the authors in the paper and it is acceptable for further processing in the optoelectronic system ranging [1], as the reconstructed image has clear borders and it is possible to identify the object itself. Using the above said algorithms the authors of the paper created iterative model program.
The result will be useful in the development of electronic identification systems and range finders both in military industry and civil sectors: m televisron, robotics and autometion industry. The disadvantage ft this algorithm is relatively large processing time, so the authors are continuing the research to reduce the processing time and to study the possibilities of morphological features of image processing algorithms.
References
[1] Zubar A.V. // Omsk Scientific Bulletin, 2013. N 3 (123). P. 273-277.
[2] Gonzalez P., Woods R., Eddins S. Digital image processing environment MATLAB, Moscow: Technosphere, 2006. 616 p.
