-The problem of digital images distortion is considered in the article. Authors investigated the factors that influence on digital image aberrations. These appear mainly due to the optical system errors. The image acquisition conditions were investigated as well. To determine values of distortion as a test object square grid is used. The focus distance of camera affects on distortion value. To determine the value of distortion the program has been developed. Using this program it was found out that for every camera the optimal focus distance with minimal distortion can be determined. The distortions correction techniques are developed on base of well-known image processing methods and on methods worked out by the authors. To find coordinates of grid nodes authors worked out the technique using information of the central part of test object's image. The common case of mutual position of camera lens and object plane is solved using method of projective geometry based on the harmonic properties of the full quadrangle. When they are parallel to each other, coordinates of nodes are determined using method of line detection developed by authors.
INTRODUCTION
Processing of digital images is the basis of many tasks of
modern complexes equipped with technical vision. The
relevance of image processing techniques, development of
methods improving their accuracy is continued with new way
to obtain visual information. Increasing speed of data
processing and expanding of digital images usage affects also.
In information security biometric identification and
authentication systems are based on human physiological
characteristics and used as protection of unauthorized access
[
Appearance and possibility to use inexpensive photo and
video systems as a part of security access systems [
The resulting images may have a radial or tangential
distortion. Methods and algorithms for images improving are
relevant and continue to develop actively [
II.
DEFINITION AND CORRECTION OF DISTORTION OF
DIGITAL IMAGES.
As a rule, to determine the distortion of optical systems,
specially created objects of known shape are used, analyzing
that images values of distortion are determined [
The main difficulty of processing the grid image was to
determine the points of the grid nodes. There are many
wellknown techniques and algorithms of edges detection [
After stage of computational experiments, an algorithm has been developed. The main advantage of this algorithm is that user can obtain ordered set of points. The results of this algorithm are the determined values of total distortion and new coordinates of nodes after correction (Fig. 1). To determine nodes of grid we consider two variants. The first variant when optical axis of lens is perpendicular to image plane (Fig.2A). Another one is when there is some angle between lens axis and object plane (Fig.2B). For both of them methods to compute coordinates of grid nodes have been worked out.
The central part of the image has minimal distortion. Based on the coordinates of the central quadrilateral of grid, the coordinates of the ideal grid are calculated. For the first case coordinates of nodes are determined as point of intersection of approximated lines. In the second case the coordinates of grid are determined on the basis of the harmonic properties of the complete quadrangle located in the central part of the image.
“perfect” grid nodes
Is optical axis of lens perpendicular to image plane?
Calculation of grid nodes by the methods of projective geometry Calculation grid nodes using the difference on neighboring pixels Calculation of the value of distortion (Δx, Δy)
Vertexes of the central quadrangle are calculated, and the 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, and then the program chooses points belonging to frame of image which is shown as blue rectangle in Fig.3.
Comparing the coordinates of the ideal and real grids, distortion values are determined.
Based on the obtained data on distortion values, a 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).
As a result of the experiments [
The fact that the focal length is significantly affected on of optical aberrations is confirmed. In addition, the processing of experimental data by the developed program made it possible to reveal that for each input device it is possible to determine the optimum value of the focal length at which the distortion is minimal.
This is due to the fact that the change of the focal length affects on distortion: from the "barrel" shape at small values the focal length distance to the "pincushion" shape with increasing the value of the focal length.
To solve the problem of determining the grid nodes, image
processing methods, methods of projective geometry and
approximation were used [
The proposed algorithm and methods for determining grid nodes, correcting distortions developed by the authors allow improving the quality of digital images, accuracy of determining lines and other characteristics for more efficient use in recognition systems and geometric modeling.