Spatial scaling and information fractal dimension of surface parameters used in quantitative remote sensing

Abstract

In this paper, a general formula has been modified, proving that the scaling difference of a surface parameter depends not only on the variance of the surface parameter itself but also on the function structure of the surface parameter. Through quantitatively describing the relationship between scaling differences and measuring scale, in terms of the concept of information fractal dimension and topological dimension, a definition of information fractal dimension used in remote sensing was proposed. By computing the information fractal dimension of Leaf Area Index and surface temperature, we found that the method describes not only the information on spatial texture and spatial structure of remotely sensed data as the traditional methods did, but also illustrates the connection between the scaling difference and measuring scale. Where the information fractal dimension of a surface parameter in some areas is known, the scaling difference can be obtained according to the measuring scale, then it can be eliminated and more accurate results could be achieved after scaling transform. At last, the problems about the relativity of true values of surface parameters were discussed.

Acknowledgments

This work was supported by the National Natural Science Foundation of China under grants 40371089, 40425012, 40471099, 4042501 and the ‘Hundred Talent’ program of the Chinese Academy of Science.