Abstract
Terrain representation is a basic topic in the field of interactive graphics. The amount of data required for good quality terrain representation offers an important challenge to developers of such systems. For users of these applications the accuracy of geographical data is less important than their natural visual appearance. This makes it possible to mantain a limited geographical data base for the system and to extend it generating synthetic data.
In this paper we combine fractal and wavelet theories to provide extra data which keeps the natural essence of actual information available. The new levels of detail(LOD) for the terrain are obtained applying an inverse Wavelet Transform (WT) to a set of values randomly generated, maintaining statistical properties coherence with original geographical data.
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M. F. Barnsley, R. L. Devaney, B. B. Mandelbrot, H. O. Peitgen, D. Saupe, and R. F. Voss. The Science of fractal images. Springer-Verlag, 1988. ISBN 0 387 96608 0.
I. Daubechies. Orthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math, 41:909–996, 1988.
C. E. Bolb F. K. Musgrave and R. S. Mace. The synthesis and renderin of eroded fractal terrains. In SIGGRAPH’89, Computer Graphics Proceedings, pages 41–50, 1989.
Patrick Flandrin. Wavelet analysis and synthesis of fractional brownian motion. IEEE Transactions on Information Theory, 38(2):910–917, 1992.
U. Frisch and G. Parisi. Fully developed turbulence and intermittency. In Int. Summer School on Turbulence and Predictability in GeoPysical Fluid Dynamics and Climate Dynamics, pages 84–88, 1985.
S. G. Mallat. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Patt. Anal. Machine Intell., 11:674–693, 1989.
B. B. Mandelbrot. Fractional brownian motion, fractional noises and applications. In SIAM Review 10, pages 422–437, 1968.
B. B. Mandelbrot. Intermittent turbulence in self similar cascades: Divergence of high moments and dimensionof the carrier. Fluid Mech., 62(3):331, 1974.
B. B. Mandelbrot. The Fractal Geometry of Nature. W. H. Freeman and Co., New York, 1982.
B. B. Mandelbrot. Fractals and scaling in Finance. Springer, New York, 1997.
B. B. Mandelbrot and C. J. Evertsz. Multifactility of the armonic measure on fractak aggregates and extended self-similarity. Physica, A 177:386–393, 1991.
Gregory W. Wornell. Wavelet-based representations for the 1/f family of fractal procesess. Proceedings of the IEEE, 81(10):1428–1450, 1993.
Gregory W. Wornell and Alan V. Oppenheim. Estimation of fractal signals from noisy measurements using wavelets. IEEE Transactions on Signal Prcess-ing, 40(3):785–800, 1992.
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© 2002 Springer-Verlag Berlin Heidelberg
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Perez, M., Fernandez, M., Lozano, M. (2002). Adding Synthetic Detail to Natural Terrain Using a Wavelet Approach. In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science — ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46080-2_3
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DOI: https://doi.org/10.1007/3-540-46080-2_3
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