Relative orientation with constraints for invariant geometric elements

To eliminate uncertainties in relative orientation, sometimes it becomes advantageous to include additional information on geometrical structures, which remain invariant under changes in camera calibration and viewing positions. Such structures may be lines, circles, etc. Combined with robust estimation of the orientation parameters, we can substantially reduce the effects of outliers

Relative orientations of images taken by non-metric cameras using 2D projective transformations and robust estimation

The paper deals with the robust estimation of relative orientation parameters without making use of interior orientations. 2D projective transformations are used to produce rectified stereo-pair images

Solution of the intersection problem by the Sylvester-resultant and a comparison of two solutions of the 2D similarity transformation

In a basic problem of geodesy the directions from points with known coordinates to an unknown (new) point are measured, and then the resulting angles are used to compute the coordinates of the new point. The relations between angles and lengths lead to a system of nonlinear equations of the form fi =0(i = 1, 2, 3), where each fi is a second degree polynomial of the unknown distances x1, x2, x3. Two different direct (non-iterative) solutions are discussed: one is based on the Sylvesterdeterminant of the resultant (this is a new result), the other on the Gr¨obner-bases. We show that in the general case both methods lead to the same equations in one variable and of fourth degree, but in a special case the equations obtained from Sylvester-determinant are of second degree. As a numerical example, three known points and an unknown point were selected in the city of Sopron. The required space angles were used to make the computations yielding the X, Y, Z coordinates of the unknown point. We show that the direct solution of the 2D similarity transformation leads to the same result as applying the Gr¨obner-bases

Preliminary analysis of the connection between ocean dynamics and the noise of gravity tide observed at the Sopronbánfalva Geodynamical Observatory, Hungary

An experimental development of a computer controlled photoelectric ocular system applied for the LaCoste and Romberg G949 gravimeter made the continuous observation of time variation of gravity possible. The system was operated for half a year in the Sopronbánfalva Geodynamical Observatory to test its capabilities. The primary aim of this development was to provide an alternative and self-manageable solution for the standard electronic (Capacitive Position Indicator) reading of this type of gravimeter and use it for the monitoring of Earth tide. It, however, turned out that this system is sensitive enough to observe the effect of variable seismic noise (microseisms) due to the changes of ocean weather in the North Atlantic and North Sea regions at microGal level (1 μGal = 10−8 m/s2). Up to now not much attention was paid to its influence on the quality and accuracy of gravity observations because of the large distance (>1000 km) between the observation place (generally the Carpathian–Pannonian basin) and the locations (centres of storm zones of the northern hydrosphere) of triggering events. Based on an elementary harmonic surface deformation model the noise level of gravity observations was compared to the spectral characteristics of seismic time series recorded at the same time in the observatory. Although the sampling rate of gravity records was 120 s the daily variation of gravity noise level showed significant correlation with the variation of spectral amplitude distribution of the analysed high pass filtered (cut-off frequency = 0.005 Hz) seismograms up to 10 Hz. Also available daily maps of ocean weather parameters were used to support both the correlation analysis and the parameterization of the triggering events of microseisms for further statistical investigations. These maps, which were processed by standard image processing algorithms, provide numerical data about geometrical (distance and azimuth of the storm centres relative to the observation point) and physical (mass of swelling water) quantities. The information can be applied for characterizing the state of ocean weather at a given day which may help the prediction of its influence on gravity measurements in the future. Probably it is the first attempt to analyse quantitatively the effect of ocean weather on gravity observations in this specific area of the Carpathian–Pannonian region

Research in mathematical geodesy

In the Mathematical Geodesy Division of the Geodetic and Geophysical Research Institute of the Hungarian Academy of Sciences research has been done mainly in two areas: theoretical foundation of the evaluation of geodetic measurements and the practical application of theoretical results. These include interpolation methods, robust estimation, time-series analysis. Results of the research have been applied in areas such as photogrammetry, digital terrain model, polar motion, geodynamics