Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2015, Vol. 12, No. 3, pp. 36-51
Mathematical model of stereo images and terrain reconstruction algorithm based on it
M.Yu. Zagorskii
1 , V.L. Bogdanov
1 , V.V. Garmanov
1 , V.P. Koroleva
1 , Yu.V. Ryabov
2 1 St. Petersburg State University, St. Petersburg, Russia
2 St. Petersburg Scientific Research Centre for Ecological Safety RAS, St. Petersburg, Russia
A mathematical model of images that make up a stereo pair is presented. The model links the coordinates of points of images showing some scene (usually terrain) from different angles with the distribution of brightness caused by simultaneous photographic recording of all points of the scene. The paper gives a mathematical relationship of three objects, each being a function of two variables (the distribution function of brightness on the left and right stereo pair images and the distribution function of the relief of the terrain), and states that for any pair of objects selected from these three the third object can be constructed.
We propose a piecewise linear approximation of the relief in the basal plane, we show how the task of building the relief in the form of a function of two variables is reduced to a set of tasks of constructing a function of one variable and we explain how to find the parameters of the relief.
The above procedure is universal and can be used for restoring a nonlinearly defined functional dependence. For example, it can be used to construct non-linear regression equations or determine parameters of regression equation based on the method of least modules. It is noted that this procedure can be generalized also to the case of recovery of two or more functional dependencies, whose treatment depends on the problem to be solved.
Keywords: stereo model, algorithm determining the relief, relief reconstruction, automation of stereo measurements
Full textReferences:
- Gimel'farb G.L., Marchenko V.B., Rybak V.I., Algoritm avtomaticheskogo otozhdestvleniya identichnykh uchastkov na snimkakh stereopary (The algorithm of automatic identification of identical areas of the image stereo pair), Kibernetika, 1972, No. 2, pp. 41-43.
- Gimel'farb G.L., Marchenko V.B., Rybak V.I., Avtomaticheskoe otozhdestvlenie identichnykh tochek stereosnimkov s uchetom neravnomernykh fotometricheskikh iskazhenii signalov (Automatic identification of identical points of stereo images with the non-uniform photometric distortion signals), Kibernetika, 1976, No. 4, pp. 107-113.
- Gimel'farb G.L., Simmetrizovannyi podkhod k resheniyu zadachi avtomatizatsii stereoizmerenii v fotogrammetrii (Symmetrized approach to the problem of automation stereo measurements in photogrammetry), Kibernetika, 1979, No. 2, pp. 73-82.
- Zagorskii M.Yu., Algoritm avtomaticheskogo vospriyatiya ob"ema ob"ekta po ego opticheskim izobrazheniyam (The algorithm of automatic perceptions of the object in its optical images), III konferentsiya dokladov molodykh spetsialistov Dzerzhinskogo raiona g. Leningrada (3rd Conf. of young specialists of the Dzerzhinskij district of Leningrad), Book of Abstracts, Leningrad, 1972, pp. 108-110.
- Zagorskii M.Yu., Algoritm vychisleniya funktsii, vkhodyashchei v poleznyi signal additivno s argumentom (The algorithm for computing functions in a useful signal additively with the argument), In: Elektricheskie mashiny i sistemy upravleniya (Electrical devices and control systems), Leningrad: VNIIJelektromash, 1973, pp. 51-55.
- Zagorskii M.Yu., Zdanovich V.V., Pivovarov V.T., Sposob avtomaticheskogo opredeleniya rel'efa (A method for automatically determining the relief), Russian Federation State Patent 462077, 1973.
- Zagorskii M.Yu., Zdanovich V.V., Krivopustov A.I., Filimonov E.V. Vybor razmerov izobrazheniya dlya korrelyatsionno-ekstremal'nogo metoda sovmeshcheniya pri raznomasshtabnosti izobrazhenii (Selecting the image size for correlation-extreme methods of combining images at different scales), In: Avtomaticheskie i avtomatizirovannye sistemy upravleniya (Automatic and automated control systems), Leningrad: VNIIJeletromash, 1976, pp. 141-146.
- Zagorskii M.Yu., Zdanovich V.V., Krylov O.D., Pivovarov V.T. Avtomaticheskii metod otozhdestvleniya identichnykh uchastkov snimkov (Automatic identification method of identical portions of images), In: Avtomaticheskie i avtomatizirovannye sistemy upravleniya (Automatic and automated control systems), Leningrad: VNIIJeletromash, 1976, pp. 147-150.
- Zagorskii M.Yu., Zdanovich V.V. Uchet yarkostnykh iskazhenii snimkov stereopary pri avtomaticheskikh stereoizmereniyakh (Accounting of distortion of brightness of images of stereo pair in the automatic stereo measurements), In: Avtomatizatsiya protsessov upravleniya i obrabotki informatsii (Automating data management and processing), Leningrad: VNIIJeletromash, 1977, pp. 148-152.
- Zagorskii M.Yu., Zhuravlev G.A., Krivopustov A.I., Pivovarov V.A. Algoritmy postroeniya tsifrovoi modeli rel'efa, porozhdaemye apparatom dinamicheskogo programmirovaniya (Algorithms for constructing a digital terrain model generated by the apparatus of dynamic programming), In: Obrabotka videoinformatsii i distantsionnye issledovaniya (Visible data processing and remote sensing), Novosibirsk: Nauka, 1983, pp. 41-47.
- Komissarov D.V., Issledovanie tochnosti algoritmov avtomaticheskoi identifikatsii tochek snimkov (Investigation of accuracy of algorithms for automatic identification of points shots), In: Sbornik nauchnyh trudov aspirantov i molodyh uchenyh (Collection of research papers of postdoc and young scientists), Novosibirsk: SSGA, 2003, pp. 9-15.
- Mikhailov A.P., Chibuntsev A.G., http://www.racurs.ru/wiki/index.php/Kurs_lektsii_po_fotogrammetrii_MIIGAiK.