프랙탈 기법을 이용한 자연지형의 고도 보간

Abstract

Digital surface representation from a set of 3D samples is one of important issues of computer graphics that has had many applications to the areas of engineering, geology, geography, meteorology, etc. The digital terrain model allows important information to be stored and analyzed without the necessity of working directly with terrain surface. In addition, we can integrate products from digital terrain model(DTM) and other data in a geospatial information system(GIS) environment.

One of the most popular stochastic models which represent curves and surfaces is based on fractal concept. A fractal is a geometrical or physical structure having an irregular of fragmented shape at all scales of measurement. In addition, a fractal is based on self-similarity concept indicating that each part of its structure is similar to the whole. The fractional Brownian motion(fBm), derived from Brownian motion, can be used to simulate topographic surfaces. fBm provides a method of generating irregular, self-similar surfaces that resemble topography and that have a known fractional dimension.

In this thesis, despite the many applications of fractals in geosciences, the problem of inconsistent results derived from different fractal calculation algorithms remains. It have been found that the triangular prism method is one of accurate algorithms for calculating the fractal dimension of complex surfaces such as remote sensing images. This thesis introduces a method for enhancing the performance of the conventional triangular prism method(TPSM) and interpolating TBD areas using both extracted information and a fractal-based technique. The proposed method is tested using simulated and real DTMs.