Natalia Moskal
GENERALIZED MATHEMATICAL MODEL OF PRECISE PHOTOGRAMMETRY RECONSTRUCTION OF THE
OBJECTS.
Natalia MOSKAL , Alexander DOROZHYNSKYY
State University “L’vivska Politechnika”, Ukraine
Chair of Photogrammetry
moskal@ polynet.lviv.ua
aldorozh@ polynet.lviv.ua
KEY WORDS : Photogrammetry , Mathematical models , Measurement , Reconstruction , Algorithms , GPS
ABSTRACT
The research presents analysis of photogrammetry data and adjustment methods, the classification scheme of
mathematic processing of data in photogrammetry. The authors shaped generalized mathematic model which is universal
for photogrammetry problems. Here is enlighted the theoretical solution of joint adjustment of measured quantities, their
functions and control data. There are some examples of partial cases proceeding from generalized mathematical model,
The authors proves that the notion of the function of loses provides with the possibility to process series of
measurement with the errors division different from Gaussian law. The article provides with the generalized model of
phototheodolite survey and the theoretical solution of the adjustment task when control points and linear elements of
exterior orientation are known with high and almost equal accuracy (as in case with the use of GPS observation). The
presented mathematical models may be used to create new algorithms, software, for extension of functional abilities of
software for analytical photogrammetric equipment and digital stations.
INTRODUCTIONS
The integration of data received from various GIS sources causes the importance of fundamental task of
photogrammetry, namely the reconstruction of objects and measuring its metric parameters by its photoimage. Various
methods and techniques are applied to process images received in the result of stereophotogrammetric survey. The
methods of the digital photogrammetry on the stage of geometrical construction of model and analyzing results of
measuring apply in full the apparatus of analytical photogrammetry. Thus nowdays it still significant to elaborate
research the models and algorithms for mathematical processing of photogrammetric data.
The authors have already elaborated a set of such models [3-8]. In this research the following problems are put for the
discussion: Classification scheme of methods of mathematical data processing in photogrammetry, Generalized
mathematical model of adjustment in photogrammetry, some partial mathematical models, mathematical model of
adjustment in phototheodolite survey.
Let us discuss in detail the problems mentioned above.
1. CLASSIFICATION OF METHODS OF MATHEMATICAL PROCESSING IN PHOTOGRAMMETRY PROBLRMS
The analysis of photogrammetry data and methods of adjustment permits to make a scheme containing main
characteristics of series of measured quantities, extra data and geometrical conditions that appear in differen
photogrammetry tasks (Fig.l).
We are going to concentrate on some explanation of this scheme, putting aside the classical points that do not need
discussion.
624 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
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