A Class Of Fractal Interpolation Function With Multi-parameters And Its Surface Fitting

Since Mandelbrot established the fractal geometry theory framework, the fractal geometry has a very wide range of applications in the area of image processing. Specifically,in1986Barnsley put forward the concept of fractal interpolation function, it became a new and important theoretical tool of data fitting, approximation of function and image processing. With the development of the collage theorem and random iteration technology, the fractal image compression has been got some of the better results, later, Jacquin put forward the compression coding algorithm make the image compression with fractal enter a new development stage. But the traditional research focus on the linear function and the iterated function system with a small number of parameters, in this paper, a class of nonlinear and multi-parameter iterated function system is constructed and the effect of image compression by the function will be discussed. The main research works described in this article are as follows: In the introduction of this paper, we introduce the history of the fractal geometry and the current situation of fractal interpolation function system, furthermore the major content of the article is summarized.In chapter1, we mainly introduced the basic knowledge of the fractal theory.Including the fractal space and the definition of the iterated function system.In chapter2,we constructed a class of multi-parameter iterated function system, and introduced the way to get the parameters.In chapter3,we discussed the properties of iterated function system and it’s attractor,including the uniqueness and the image of the attractor.