9 Partitioned Fractal Interpolation

The word fractal is chosen by Mandelbrot [46 ] to describe the field of study of rough or fragmented geometric shapes that can be subdivided in parts, each of which is (at least approximately) a size reduced copy of the whole. This might be because “fract,” the Latin root of the word fractal, means broken. The main idea that stands behind fractal is the concept of “self‐similarity.” Fractal found applications in image processing with great success. This is attributed to the fact that objects in natural images are generally observed to be self‐similar. There was great deal of hope and excitement over the application of fractal to compress natural images when it was first introduced in the 1980s. At that period of time, fractal has spurred considerable amount of research activities. Although fractal image coding is no longer considered to be a competitive method to compress images because the compression ratio is not good enough, it is worthy to study it as an alternate type of image interpolation scheme because of the natural‐looking interpolation results. In this chapter, we shall study the application of fractal image coding to interpolate images. Fractal image coding considers images to be “self‐similar.” In other words, images are modeled as deterministic fractal objects, such that parts of an image are approximated by different parts of the same image, a direct result of the image being self‐similar. As a consequence of the self‐similarity, ...

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