In the paper a frequency method of filtering airborne laser data is presented. A number of algorithms developed to remove objects above a terrain (buildings, vegetation etc.) in order to obtain the terrain surface were presented in literature. Those all methods published are based on geometrical criteria, i.e. on a specific threshold of elevation differences between two neighbouring points or groups of points. In other words, topographical surface is described in a spatial domain. The proposed algorithm operates on topographical surface described in a frequency domain. Two major tools, i.e. Fast Fourier Transform (FFT) and digital filters are used. The principal assumption is based on the idea that low frequencies are responsible for a terrain surface, while high frequencies are connected to objects above the terrain. The general guidelines of this method were for the first time presented at (Marmol and Jachimski, 2004). Due to the fact that the preliminary results showed some limitations, two-stage filtering algorithm has been introduced. The frequency filter was modified in such a manner that different filter parameters are used to detect buildings than those to recognize vegetation. In the first stage of data processing the filtering concerning elimination of points connected with urban areas was applied. The low-pass filter with parameters determined for urban area was used for the whole tested terrain in that stage. The purpose of the second stage was to eliminate vegetation by using the filter for forest areas. The presented method was tested by using data sets obtained in the ISPRS test on extracting DTM from point clouds. The results of using the two-stage algorithm were com- pared with both reference data and with filtering results of eight method reported to ISPRS test. A numerical comparison of the filter output with a reference data set shows that the filter generates DTM of a satisfactory quality. The accuracy of DTM produced by the frequency algorithm fits the average accuracy of eight methods reported in the ISPRS test.

In the recent years three-dimensional buildings modelling based on an raw air- borne laser scanning point clouds, became an important issue. A significant step towards 3D modelling is buildings segmentation in laser scanning data. For this purpose an algorithm, based on the multi-resolution analysis in wavelet domain, is proposed in the paper. The proposed method concentrates only on buildings, which have to be segmented. All other objects and terrain surface have to be removed. The algorithm works on gridded data. The wavelet-based segmentation proceeds in the following main steps: wavelet decomposition up to appropriately chosen level, thresholding on the chosen and adjacent levels, removal of all coefficients in the so-called influence pyramid and wavelet reconstruction. If buildings on several scaling spaces have to be segmented, the procedure should be applied iteratively. The wavelet approach makes the procedure very fast. However, the limitation of the proposed procedure is its scale-based distinction between objects to be segmented and the rest.