Introduction
In the performance measurements of digital images using computers is
essential automated methods. One of the most important tasks of automation of
photogrammetric measurements is to find corresponding (identical) points to the pictures.
This task is to mark the spatial position on the surface of the model position
marks on the left and right stereo pair of pictures in identical points.
If we look at several pictures, then this problem reduces to the relevant provisions
of the measured points in all images.
There are several algorithms for solving this problem. However, when choosing an
optimal method should take into account not only the accuracy of the method, but also the
effectiveness of the method, simplicity of computation and its implementation in certain
circumstances.
As an optimal criterion for the identification of points for all methods is the
correlation coefficient of the optical density plots of images.
Theme urgency
Currently, information technology is largely replacing traditional. So to replace
the traditional photogrammetry is digital photogrammetry. Digital photogrammetry, in
contrast to the use of natural images on glass, foil or paper, handles images in digital
form in a computer. This photographic image is converted to digital form by scanning and
digitalization. Images can also be obtained in digital form directly with a special camera
mounted on different media.
The main task of digital photogrammetry is the image dimension and continue building
a digital terrain model.
Measurement of images is done by specifying the identical points of stereo pair
images. Thus, in performing the task of measuring image search automation of identical
points. Consequently, the task is urgent.
Relationship of academic programs, plans and themes
Specialty «Geoinformation Technology» implies the introduction of information
technology in the geodetic measurements and processing of measurement results. One of the
disciplines of the department of Geoinformatics and Geodesy is photogrammetry. The theme
of the master's work is one of the tasks of digital photogrammetry. Hence, the theme of
the master's work could be related to academic programs, plans and themes.
The purpose and research problems
The purpose of work: an analysis of existing methods of identical points
on the image and choose the best method of corresponding points, making the most effective
to recognize the identical point on the pictures.
The idea of work: improving the current best technology to date,
recognition of corresponding points on images and their further automation.
The main objectives of development and research :
1) to investigate the existing methods of recognition of the respective points in the images;
2) to justify the optimal method of identical points on the images;
3) to develop a software product that allows to realize the automation of the optimal method.
The subject of development and research is a method of recognizing the respective points in the images.
Method of research : an analysis of existing methods of corresponding points on images.
The amount of development and research: The current method of corresponding
points on images, performed the best way to justify the search of identical points, the
software is under development.
Scientific novelty à:ÏGetting a new software product to effectively recognize
the identical point shots.
The practical significance of the results:
1) automation of the optimal method of corresponding points on images;
2) reduction of labor to perform the measurements.
Testing of work: The research results reported at the scientific student conference in 2009.
Survey of research and developments
Local review:
1) Mogilny, S.G., Belikov, I.L., Ahonina L.I., Brezhnev D.V. Photogrammetry. - Kiev.: Higher School, 1985.-278 pp.
Global review:
1) Pratt W. Digital image processing / Per. England. Ed. Ph.D. Lebedev DS - M.: Mir, 1982. - 790 pp.
2) Duda R., Hart P. Pattern recognition and scene analysis / Per. England. Ed. Stefanyuk V.L. M.: Mir, 1976.
3) Tu J., Gonzales R. Principles of pattern recognition. M.: Mir. 1978.
4) Lobanov A.K., Zhurkin I.G. Automating photogrammetric processes. M.: Nedra, 1980.
National review:
1) Chopenko E.F. Ergonomic aspects of stereoscopic observation in automated systems and complexes. - Lviv: the National University t "Lviv Polytechnic", 2001.
2) Gnatushenko V.V. Identification and analysis of multi-image projection fotogrammetrichnih nature. - Simferopol, 2002.
3) Ivanov, L.I, Egorov O.I. Basics of Photogrammetry - Kiev. KNUBA.-2002.-155 pp.
The main content of work
Digital images is locality thumbnail area, represented in digital form,
that is recorded on computer media. Digital photo, which used in photogrammetry are
different so that there are images of points with known coordinates or the so-called
control points. The task of recognizing identical points is to establish an identical
situation stamps bearing points on the measured images [2].
Figure 1 - Search corresponding points on the images
(6 frames, the interval between frames 100 ms, the number of cycles of repetition 7, volume 95 KB)
Depending on the algorithm for identification of corresponding points are produced,
the following methods for solving this problem:
1. The analytical method for finding corresponding points on images. This method
is a mathematical model for solving this problem using the coordinates of points depending
on the image and the coordinates of points on the ground. The disadvantage of this method
is the need for knowledge of the elements of orientation of images[5].
2. The method of estimation of contrasts. Based on the replacement of the
correlation functions and the polar relay correlation functions. This is done replacing
the original signal clipping signal, ire the alternating signal of constant amplitude.
The advantage of this method is the use of different search criteria identical points for
different types of circuits of control points. The disadvantage of this method is the
appearance of the methodical error caused by the low degree of similarity, and replaced
the original signal[8].
3.The method of assessing the shapes of points. The basis of this method is based
on the notion of an shape that is part of the basic snapshot. The algorithm aims at finding
the parameters that satisfy the criterion of identity, which is called the alphabet set of
shapes. The advantage of this method is the possibility of identification of several pairs
of corresponding points at the same time. The disadvantage of this method is the need for
computing the coefficient of correlation for all the shapes included in the alphabet[1].
The best method is the method of assessing the shapes of points because it does not
require information on the measured images, such as elements of orientation of images or
types of units of control points, as well as its implementation is not a methodological
errors associated with the use of superseded signal.
To implement this method, a digital photograph is seen as a set of optical densities
corresponding to each pixel image. For a snapshot of the solution of the problem is divided
into a fixed number of sites, called the shapes of the photo[3].
Thus, a digital photo is a collection of shapes, each of which consists of more
than simple, basic shapes with a known optical density [4].
Next is considered the implementation of this method on an example pair of images.
With the identification of corresponding points should select the reference image, a
snapshot that will set the reference point for the search. As a reference set to the
left picture.
If denote by  the
optical density of one pixel of the image, the shape of the image can be described by the
following expression:
For the left image:
 (1)
And for the right image:
 (2)
where ð – the dimension of the image.
Figure 2 - Scheme of the identification of corresponding points
Identification of identical stereo pair of points is reduced to finding the minimum
Euclidean distance between two vectors RL and RP, respectively, characterizing the images
of the left and right stereo pair of images that can be expressed as follows[9]:
 (3)
By substitution of expression (3) as the Rë and Rï Expressions (1) and (2) accordingly,
the expression (3) takes the form:
 (4)
Since the beginning of the vectors RL and RP do not overlap, it is necessary to bring
them to a top. Thus, the expression (4) using a central values of these vectors, and as a
result of some kind of transformation will gain [7]:
 (5)
where 
- the average optical density of points respectively for the left and right shapes of images
calculated by the formula:
 (6)
On the basis of formulas (5) are calculated every correlation coefficient corresponding
to each of the right shape. That shape, which corresponds maximum value from all calculated
correlation coefficients, is identical to the reference.
Simplification of the task is performed by forming the alphabet of shapes, consisting
of the parameters of an shape in which the correlation coefficient maximum [6].
The total count of shapes for which the calculated correlation coefficients calculated by the formula:
 (7)
where 
— the alphabet of shapes, consisting of rows of points of the right image;
— changes identifiable image
— the count of rows within the image on the right picture.
Count of shapes in the alphabet
determined by the count of partitions the area of the right image and is calculated as
follows:
 (8)
where 
— the maximum count of elements, which may consist of a basic right shape;
ð — the dimension of the shape.
Parameters and primarily
depend on the terrain shown in the pictures and can be calculated by the formula [10]:
 (9)
where 
— a field of view angle of the image along the line;
— angle characterizing the increment of height between the two areas defined by the formula:
 (10)
where  — the
increment of the coordinates along the X axis between the two areas;
f — focal length of the camera.
Figure 3 - Dependence of the position of a point on the image of the terrain
Thus, the rate of identification of identical points depends on the number of shapes
included in the alphabet n. Consequently, the smaller the n, the less time for identification.
This algorithm is the most common and it developed the following methods:
1) depending on the number of shapes included in the alphabet:
à) shear - the number of shapes belonging to the alphabet, is a linear function of
the number of shifts needed to find the first shape;
á) code - the number of shapes in the alphabet is equal to the total number of shapes
compared in the identification process;
â) code-shear - the number of shapes included in the alphabet is defined as a function of
the total number of shapes and the number of shifts.
2) depending on the type of search points:
à) linery - to search for the relevant points is carried out along the only one
selected by each of the stereo pair of shapes;
á) square algorithm - the search of the points is performed on basic sites, containing
multiple rows of shapes stereopair;
â) the synthesis of area and line methods.
Conclusions
The main problem in solving the problem of recognition of corresponding points is that
when searching for corresponding points to one point of reference image, there are several
points in the other pictures, which are approximately equal correlation coefficients. At
the highest correlation coefficient can have on the way, are not identical to the reference
image of the shape, which greatly reduces the accuracy of all methods.
Also one of the problems is the large amount of time spent on the computation of
correlation coefficient for all the shapes to other images. Especially this problem in
finding outlets for several pairs of images.
The main sources of these problems are:
1) the criteria selected for the identification of identical points;
2) the parameters of mathematical model identification;
3) discretization step pictures along the axes of the image;
4) the accuracy of calculating the correlation coefficient of optical densities;
5) the availability of various types of noises;
6) the nature of the terrain shown in the picture.
The most common methods are finding corresponding points, based on the calculation of
the coefficient of correlation of the shapes of images.
These methods are fairly labor-intensive because it requires computation of a large
number of coefficients of correlation. To simplify this task allows for more precise search
points in the search image. Refinement is realized through a job field overlapping shapes
or analytical tasks of relief, is depicted in pictures. In this case, the methods become
more effective and easily implementable.
When writing the abstract of the Master's work is not yet complete. The final completion
- December 2009. Full text of the work and materials on the topic can be obtained from the
author or his scientific adviser after that date.
References:
1. Lobanov A.K., Zhurkin I.G. Automation of photogrammetric processes. M.: Nedra, 1980.
2. Mogilny S.G., Belikov I.L., Ahonina L.I., Brezhnev D.V. Photogrammetry. - Kiev.: Higher School, 1985.-278 pp.
3. Pratt W. Digital image processing / Per. England. Ed. Ph.D. Lebedev D.S. - M.: Mir, 1982. - 790 pp.
4. Mikhailov A.P. Model stereo pair of digital images for the testing of automatic identification of corresponding points [electronic resource] / Geoiformatsionny portal GIS Association, - http://www.gisa.ru/3810.html .
5. Dmitriev V.G., Sunyaev S.I. The analytical task areas to automatically search for the respective points in the images / / Proceedings of the universities. Geodesy and aerial photography. - 1990. - ¹ 2. p. 104-113.
6. Dunayev A.A., Lobiv I.V., Murzin F.A., Polovinko O.N. Algorithms for quick search of fragments of photographic images [electronic resource] / Institute of Informatics Systems. Ershov A.P., SB RAS, - http://www.iis.nsk.su/preprints/articles/pdf/sbor_kas_10_murzin_polovinko_lobiv.pdf
7. Bykov L.V., Essin A.S., Makarov A.P. Investigation of algorithms for automatic identification of points on a pair videopictures. [Electronic resource] / Omsk branch FKTS «Earth». Articles, reports, - http://www.sibrcc.ru/info/article.php?show_art=yes&id_article=15 .
8. Akulova L.V., Zdanovich V.V., Pivovarov V.T. Automation stereomeasurement on the basis of correlation analysis / / Process automation control and information processing. - Lviv, 1980. - p. 83-88.
9. Sharovatov G.L., Selyaninova T.N., Borisov E.A. Automation of photogrammetric measurement of coordinates of points marked with / / Geodesy and Photogrammetry. - Rostov na Donu, 1984. - p. 61-66.
10. Krasnov V.I. The method of automatic identification of identical points of stereo / / Proceedings of the universities. Geodesy and aerial photography. - 1981. - ¹ 12.- p. 40-46.
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