=Paper=
{{Paper
|id=Vol-2081/paper10
|storemode=property
|title=Correction of Digital Images Distortion
|pdfUrl=https://ceur-ws.org/Vol-2081/paper10.pdf
|volume=Vol-2081
|authors=Tatiana Ts. Damdinova,Liubov D. Zhimbueva,Innokentii T. Bubeev,Nasak N. Dampilov
}}
==Correction of Digital Images Distortion==
https://ceur-ws.org/Vol-2081/paper10.pdf
Correction of Digital Images Distortion
Tatiana Ts. Damdinova, Liubov D. Zhimbueva, Innokentii T. Bubeev and Nasak N. Dampilov
Engineering and Computer Graphics Department
East-Siberia State University of Technology and Management
Ulan-Ude, Russian Federation
dtatyanac@mail.ru, zhimbueva@mail.ru, it_bubeev@mail.ru, office@esstu.ru
Abstract —The problem of digital images distortion is which are actively used and developed. All of them are based
considered in the article. Authors investigated the factors that on obtaining information on the basis of optical systems,
influence on digital image aberrations. These appear mainly due which, as a rule, have hardware errors .
to the optical system errors. The image acquisition conditions
were investigated as well. To determine values of distortion as a The resulting images may have a radial or tangential
test object square grid is used. The focus distance of camera distortion. Methods and algorithms for images improving are
affects on distortion value. To determine the value of distortion relevant and continue to develop actively [6]. Algorithm to
the program has been developed. Using this program it was automatically correct wide-angle lens distortion is described in
found out that for every camera the optimal focus distance with article [7], in article [8] image quality improved using contour
minimal distortion can be determined. The distortions correction stencils.
techniques are developed on base of well-known image processing
methods and on methods worked out by the authors. To find
II. DEFINITION AND CORRECTION OF DISTORTION OF
coordinates of grid nodes authors worked out the technique using
DIGITAL IMAGES.
information of the central part of test object’s image. The
common case of mutual position of camera lens and object plane As a rule, to determine the distortion of optical systems,
is solved using method of projective geometry based on the specially created objects of known shape are used, analyzing
harmonic properties of the full quadrangle. When they are that images values of distortion are determined [9, 10]. As the
parallel to each other, coordinates of nodes are determined using object to determine the distortion, we chose a square grid, the
method of line detection developed by authors. image of which was obtained by means of different input
devices and processed by developed software [11].
Keywords— digital image processing; distortion of digital
images; optical aberrations; camera calibration; line The main difficulty of processing the grid image was to
detection, edges detection. determine the points of the grid nodes. There are many well-
known techniques and algorithms of edges detection [12]. This
problem continues developing and improving [13-15].
After stage of computational experiments, an algorithm
I. INTRODUCTION
has been developed. The main advantage of this algorithm is
Processing of digital images is the basis of many tasks of that user can obtain ordered set of points. The results of this
modern complexes equipped with technical vision. The algorithm are the determined values of total distortion and new
relevance of image processing techniques, development of coordinates of nodes after correction (Fig. 1). To determine
methods improving their accuracy is continued with new way nodes of grid we consider two variants. The first variant when
to obtain visual information. Increasing speed of data optical axis of lens is perpendicular to image plane (Fig.2A).
processing and expanding of digital images usage affects also. Another one is when there is some angle between lens axis
In information security biometric identification and and object plane (Fig.2B). For both of them methods to
authentication systems are based on human physiological compute coordinates of grid nodes have been worked out.
characteristics and used as protection of unauthorized access
[1, 2]. The central part of the image has minimal distortion.
Based on the coordinates of the central quadrilateral of grid,
Appearance and possibility to use inexpensive photo and the coordinates of the ideal grid are calculated. For the first
video systems as a part of security access systems [3-5] case coordinates of nodes are determined as point of
increase the demand for them. This is one of factors for intersection of approximated lines. In the second case the
accumulation of visual information for further analysis. A new coordinates of grid are determined on the basis of the
source of visual information is unmanned aerial vehicles
45
harmonic properties of the complete quadrangle located in the Vertexes of the central quadrangle are calculated, and the
central part of the image. points of intersection of the line KL and the diagonal BD is
the point F (Fig. 3).
This method allows finding all intersection points of lines,
Image and then the program chooses points belonging to frame of
acquisition image which is shown as blue rectangle in Fig.3.
Comparing the coordinates of the ideal and real grids,
distortion values are determined.
Image
Based on the obtained data on distortion values, a
preprocessing mathematical model of the error surface is created, which
makes it possible to automate the correction and significantly
reduce the distortion in digital images (Fig. 4).
Determining of coordinates of central
quadrangle node points
A
Calculation of coordinates of
“perfect” grid nodes
Is optical axis
of lens perpendicular
to image plane?
B
Calculation of grid Calculation grid nodes
nodes by the methods of using the difference on
projective geometry neighboring pixels
Calculation of the value of
distortion (Δx, Δy)
Fig. 2. Images on different position of camera lens and object plane
Calculation of error surface
coefficients (approximation Δx, Δy)
Correcting the nodes of the
original image
Fig. 1. Algorithm of distortion correction
46
A
A
B
B
C
Fig. 3. A - Computing of central quadrangle vertexes
B – Computing coordinates of other nodes
Fig. 4. Lines of square grid on diferent kinds of distortions:
A - distortion of barrel shape with a focus of 5.2 mm,
B - the distortion is minimal at a focus of 7.1 mm,
C - distortion of the cushion shape at a focus of 12.9 mm.
Red lines - lines of the real grid
Blue lines - grid lines after correction
47
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