Pseudo line‐image coding and drawing method based on fractal theory

Abstract

AbstractThe fractal theory proposed by Mandelbrot is applied primarily to computer graphics and related problems as a means to generate a pseudo‐natural image. In contrast to those problems dealing with natural images, it is possible to apply the fractal theory as a means to approximate actual natural images. This paper considers such natural line‐images as a coastline and the contour of a mountain, and presents a method to generate an image with apparently high resolution by applying the fractal theory based on a small amount of information. A feature of this method is the use of an algorithm called squig to generate the fractal curve, which is also proposed by Mandelbrot. The method recursively partitions the original image and generates the fractal curve by determining the internal path. It has several advantages such as the property that self‐intersection is not produced in principle. In this paper, the properties of the squig are described first. Then the proposed algorithm is applied to the line‐image composed of a coastline, and the result is presented. As a result of experiment, it is seen that the data for the chain code is compressed to some 1/10, resulting in a visually natural image.