Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Fractals method (FM) <s> Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. However, many are statistically "selfsimilar," meaning that each portion can be considered a reduced-scale image of the whole. In that case, the degree of complication can be described by a quantity D that has many properties of a "dimension," though it is fractional; that is, it exceeds the value unity associated with the ordinary, rectifiable, curves. <s> BIB001 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Fractals method (FM) <s> Scale and resolution have long been key issues in geography. The rapid development of analytical cartography, GIS, and remote sensing (the mapping sciences) in the last decade has forced the issues of scale and resolution to be treated formally and better defined. This paper addresses the problem of scale and resolution in geographical studies, with special reference to the mapping sciences. The fractal concept is introduced, and its use in identifying the scale and resolution problem is discussed. The implications of the scale and resolution problem on studies of global change and modeling are also explored. <s> BIB002
The term "fractals", first proposed by Mandelbrot BIB001 , is now widely used in different science domains, such as biology, physics, chemistry, geography and so on. The reason why fractals attract more and more attention is that the real world is too regular to be measured or simulated by traditional methods BIB002 . Many curves or surfaces in the world may be statistically made up of copies of itself at a reduced scale. This statistical self-similar property is the key point to understanding the concept of fractals. In classical geometry, the dimension of a point is zero, a line is 1, a plane is 2, and a cube is 3. While, in fractal geometry, the fractal dimension D of an object can be any non-integer dimension  . For example, the fractal dimension of a curve can be any value between 1 and 2. The fractal dimension of a surface can be any value between 2 and 3. Empirical studies indicate that true fractals with strict self-similarity do not exist. However, the information that fractal dimensions provide with scale can be used to indicate the optimum measurement scale. There are many ways to determine fractal dimensions. Xia and Clarke  introduced several frequently used definitions of fractal dimension, which could be used to find the process scale. The turning points of fractal dimension may contain some important information. For example, they should be those where new patterns may emerge or resolutions approach dominant operational scales. Generally speaking, the more irregular an object, the bigger the fractal dimension. The fractal dimension of an image is expected to be lower as the resolution becomes coarser due to coarser resolution corresponding to lower variability and vice versa. Therefore, the scale at which the highest fractal dimension is measured may be the scale at which most processes operate BIB002 . Although no agreement has been reached on the definition of fractal dimension, it is a promising research direction. Table 2 summarizes the advantages and disadvantages of the above mentioned methods. 