Fractal geometry is becoming increasingly more important in the study of image characteristics. There are numerous methods available to estimate parameters from images of fractal surfaces. A very general technique to calculate numerous fractal features involves the estimation of the mass density function by box counting. The authors analyze the box-counting method, establish a lower bound for the box size, and indicate how algorithms can be improved to give better estimates of fractal features of images. This provides a theoretical basis for a heuristic approach used by C.A. Pickover and A.L. Khorasani (1986).>

Many objects in images of natural scenes are so complex and erratic, that describing them by the familiar models of classical geometry is inadequate. In this paper, we exploit the power of fractal geometry to generate global characteristics of natural scenes. In particular we are concerned with the following two questions: 1) Can we develop a measure which can distinguish between different global backgrounds (e.g., mountains and trees)? and 2) Can we develop a measure that is sensitive to change in distance (or scale)? We present a model based on fractional Brownian motion which will allow us to recover two characteristics related to the fractal dimension from silhouettes. The first characteristic is an estimate of the fractal dimension based on a least squares linear fit. We show that this feature is stable under a variety of real image conditions and use it to distinguish silhouettes of trees from silhouettes of mountains. Next we introduce a new theoretical concept called the average Holder constant and relate it mathematically to the fractal dimension. It is shown that this measurement is sensitive to scale in a predictable manner, and hence, provides the potential for use as a range indicator. Corroborating experimental results are presented.