In the present paper, we are describing a methodology for the determination of the complete set of parameters associated with the Weierstrass-Mandelbrot (W-M) function that can describe a fractal scalar field distribution defined by measured or computed data distributed on a surface or in a volume. Our effort is motivated not only by the need for accurate fractal surface and volume reconstruction but also by the need to be able to describe analytically a scalar field quantity distribution on a surface or in a volume that corresponds to various material properties distributions for engineering and science applications. Our method involves utilizing a refactoring of the W-M function that permits defining the characterization problem as a high dimensional inverse problem solved by singular value decomposition for the so-called phases of the function. Coupled with this process is a second level exhaustive search that enables the determination of the density of the frequencies involved in defining the trigonometric functions participating in the definition of the W-M function. Numerical applications of the proposed method on both synthetic and actual surface and volume data, validate the efficiency and the accuracy of the proposed approach. This approach constitutes a radical departure from the traditional fractal dimension characterization studies and opens the road for a very large number of applications.
Complete High Dimensional Inverse Characterization of Fractal Surfaces and Volumes
Center of Computational Material Science,
Naval Research Laboratory,
Washington, DC 20375
Fairfax, VA 22030
Contributed by the Computers and Information Division of ASME for publication in the Journal of Computers and Information Division in Engineering. Manuscript received October 17, 2012; final manuscript received October 25, 2012; published online December 19, 2012. Assoc. Editor: Bahram Ravani.
- Views Icon Views
- Share Icon Share
- Cite Icon Cite
- Search Site
Michopoulos, J. G., and Iliopoulos, A. (December 19, 2012). "Complete High Dimensional Inverse Characterization of Fractal Surfaces and Volumes." ASME. J. Comput. Inf. Sci. Eng. March 2013; 13(1): 011001. https://doi.org/10.1115/1.4007987
Download citation file:
- Ris (Zotero)
- Reference Manager