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Author(s) Kopilovic, I.
Title Progressiveness and preprocessing in image compression
Abstract The recent developments in the multimedia communication technology made it necessary to provide image compression standards with a number of functionalities such as the capability of progressive transmission of the code and more conformity with the human visual perception. The general purpose still image compression standard JPEG2000 for example, incorporates many such functionalities. This thesis contributes to the improvement of these functionalities by considering two special aspects: progressive transmission and preprocessing to improve the visual quality of the compressed images. In progressive transmission, the code for the image is sent in packets. The user attempting to view the image will be shown a sequence of "previews" that approximate the nal reconstruction with increasing quality, based on the incoming packets. This allows the user to terminate the decoding at an arbitrary point and quickly browse among a large number of images. Though many practical methods use optimisation for progressive transmission, a good understanding of the progressive behaviour and the optimality in this process has not been given yet. We give formal de nitions of the progressiveness and the optimality in the progressive transmission here. Since we show that there are di erent possibilities to de ne progressiveness, we are going to give and prove sucient conditions that imply the di erent progressive properties. The linear transform-based compression will be considered separately, where further sucient conditions for progressiveness are given. We use this framework to analyse the underlying optimisation procedures in existing wavelet compression schemes. Our results can help the design of progressive compression systems. In most of the image compression standards, the images are described as linear combinations of given basis elements. Lossy compression is achieved by using an incomplete description. There are however compression methods that use a di erent kind of description. In fractal compression, the image is partitioned into a number of regions, each of which is approximated by some appropriate part of the same image. If we start with an arbitrary image and iterate these approximation steps, this procedure will converge to an approximation of the original image. Since the above description method is not necessarily perfect, its parameters constitute a lossy compression of the image. We give an optimal progressive transmission method for the fractal compression, which is the rst result of this kind. In lossy compression, various kinds of error patterns can appear on the decompressed image. For example, the images compressed with JPEG su er from blocking artefacts. There is also a iv ringing artefact observable along the edges in JPEG or JPEG2000 compressed images at high compression ratios. One way of alleviating these e ects is to preprocess the image before compression. We shall consider a previously proposed preprocessing method here, which is based on edge-adaptive ltering. The ltering is achieved with non-linear di usion processes. The previous results did not give a complete understanding of the underlying processes and they did not give an analysis of the di erent parameter choices. A visual testing of the method was also missing. We complete the analysis by proposing di usion methods that are appropriate for preprocessing. We consider methods for adjusting the parameters for these di usion processes. We show that they reduce the artifacts, help in preserving the edges, and that they can improve the visual quality. However, diculties can arise when preprocessing images with highly irregular texture. Due to visual phenomena, the visibility of artefacts is low in this case. Preprocessing may yield a visible blur for such images and an inferior visual quality when compared to the compression without preprocessing. This research was supported by the Grant Sa449/8 of the German Research Foundation (DFG). I am grateful to Professor Dietmar Saupe and to Professor Kenneth Rose for carefully reading my thesis and giving helpful suggestions in their reviews.
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