Application Of Improved Fractal Encoding In Image Compression

In natural world, all objects can be divided into two classes. Objects in one class are called classic objects, which can be described by classic Euclid geometry and its generalized theory. Usually, objects in this class have smooth, regular edge, which can be described by continuous function. Objects in the other class are called non-classic objects, which have fuzzy, discontinuous edge. The edge can notdepicted by continuous function. As we known, classic geometry can not process those objects whose natural form is rough or irregular. This objects are mostly have elaborate structure or self-similarproperties, whichcan not be described by classic geometry. So they are called fractal objects and fractal geometry is constructed to study the fractal objects. Fractal theory is a novel theory which is constructed by the self-similarity of objects. Soon, it becomes a novel subject. The fractal objects contain many natural objects, such as coastline, hill shape, stream, plant, lightning, and so on. Furthermore, many structures in microcosm and macrocosm are also fractal objects.Recently, with the rapid improvement of the combine of fractal theory and computer technology, fractal science becomes a new subject is constructed in nonlinear area. Fractal science soon applies in many other subjects. Its theoretical study and real application is applied deeply in many areas.Today, multimedia technology is improved with the improvement of computer technology. However, the large multimedia makes network flow very crowd. So, multimedia compression becomes a new highlight. Meanwhile, image compression is basis of multimedia compression. Then, it is admittedly that fractal image coding is an effective coding method without resolutionin the multimedia encoding technology. The effectiveness is because of the high compressing ratio of fractal image coding.But the computational complexity of this coding method is so high that it needs long encoding time. In this paper, a novel fast fractal coding method is constructed to decrease the coding time by the capture of primary additional error values. This method is a universal algorithm, which is independent of image types. However, it decreases compressing time with the similar compressing ratio.In this case, main content of this thesis is shown as follows.1) First, because classic fractal encoding method is a loss compression method, we abstract the additional error values by difference betweenoriginal image and decoding file.2) Then, we present anabstraction method to abstract the primary error values of encoding method with a given rule of weight. This is because the importance of error values in encoding method is different from the error values in difference between original image and decoding file. In other words, some error values seems more important than others since their distribution in images. We have the ’real’ error values of all points by applied weighted computation which is driven by the neighbors of the points with error values.3) Moreover, the classic encoding and decoding methods are reformed based on the new weights of all additional error points which are weighted computed by the given weighted rules. The spare encoding space is distributed to those points with higher weighted additional error values. Meantime, the decoding method is also reformed to adapt the encoding method. Moreover, for the novel encoding and decoding method, we present theorems to compute the compression rate and rate of compressing time between the proposed method and classic method.4) Finally, experimental results show the improved fractal image coding method has higher compressing ratio and better effectiveness (signal to noise ratio) than the classic algorithm. Experimental results also verify the theorems we proposed.