Fractals for Modelling and Analysing Geo-information

The high complexity of the remotely sensed images and measurements provided by the last generations of sensors demand new techniques for scene understanding and analysis. The similarity of fractal and real world objects was observed and intensively studied from the very beginning. The fractal geometry became a tool for computer graphics and data visualisation in the simulation of the real world. In order to perform visual analysis and comparisons between natural and synthetic scenes several techniques have been developed. After a period of qualitative experiments fractal geometry began to be used for objective and accurate purposes: modelling image formation processes, generation of geometrically and radiometrically accurate synthetic scenes and images, evaluation of the characteristics of the relief, determination of the surface roughness, analysis of textures. The techniques based on fractals show promising results in the field of image understanding and visualisation of high complexity data. In the aim to give an introduction to the theory of fractals the following topics will be summarised in this paper: the definition and analysis of fractals based on self-similarity and self-affinity behaviours, definitions for fractal dimension, fractal synthesis, the projection properties of fractal surfaces. The derived techniques with applications in geo-information processing and understanding will be underlined: synthetic DEMs generation, fractal resampling of actual DEMs, algorithms for computation of the fractal dimension, multiresolution analysis of fractal images, multiresolution analysis and fractal dimension estimation. The paper presents also several experiments done by the authors using fractals to generate accurate models for landforms and cover types, synthetic images generation for model based picture processing, and image processing techniques for remotely sensed images analysis and sensor fusion.