Box counting

About: Box counting is a research topic. Over the lifetime, 1028 publications have been published within this topic receiving 19710 citations.

Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes

Abstract: We argue that the basic properties of rain and cloud fields (particularly their scaling and intermittency) are best understood in terms of coupled (anisotropic and scaling) cascade processes. We show how such cascades provide a framework not only for theoretically and empirically investigating these fields, but also for constructing physically based stochastic models. This physical basis is provided by cascade scaling and intermittency, which is of broadly the same sort as that specified by the dynamical (nonlinear, partial differential) equations. Theoretically, we clarify the links between the divergence of high-order statistical moments, the multiple scaling and dimensions of the fields, and the multiplicative and anisotropic nature of the cascade processes themselves. We show how such fields can be modeled by fractional integration of the product of appropriate powers of conserved but highly intermittent fluxes. We also empirically test these ideas by exploiting high-resolution radar rain reflectivities. The divergence of moments is established by direct use of probability distributions, whereas the multiple scaling and dimensions required the development of new empirical techniques. The first of these estimates the "trace moments" of rain reflectivities, which are used to determine a moment-dependent exponent governing the variation of the various statistical moments with scale. This exponent function in turn is used to estimate the dimension function of the moments. A second technique called "functional box counting," is a generalization of a method first developed for investigating strange sets and permits the direct evaluation of another dimension function, this time associated with the increasingly intense regions. We further show how the different intensities are related to singularities of different orders in the field. This technique provides the basis for another new technique, called "elliptical dimensional sampling," which permits the elliptical dimension rain (describing its stratification) to be directly estimated: it yields del =2.22+0.07, which is less than that of an isotropic rain field (del =3), but significantly greater than that of a completely flat (stratified) two-dimensional field (de1-2).

An efficient differential box-counting approach to compute fractal dimension of image

Abstract: Fractal dimension is an interesting feature proposed to characterize roughness and self-similarity in a picture. This feature has been used in texture segmentation and classification, shape analysis and other problems. An efficient differential box-counting approach to estimate fractal dimension is proposed in this note. By comparison with four other methods, it has been shown that the authors, method is both efficient and accurate. Practical results on artificial and natural textured images are presented. >

Texture description and segmentation through fractal geometry

Abstract: Fractal geometry is receiving increased attention as a model for natural phenomena In this paper we first present a new method for estimating the fractal dimension from image surfaces and show that it performs better at describing and segmenting generated fractal sets Since the fractal dimension alone is not sufficient to characterize natural textures, we define a new class of texture measures based on the concept of lacunarity and use them, together with the fractal dimension, to describe and segment natural texture images