Fractal Image Coding And Its Applications To Digital Watermarking

Image compressions are essentially important for the development of various multimedia services and telecommunication applications. Recent publications show a substantial increase in this field, in which many new ideas have been proposed. Fractal image coding opens up a refreshing new view to image compression and has become one of the most remarkable compression techniques. Although it has mainly been exploited for the purpose of image compression over the past decade, fractal coding is recently investigated for watermarking.Based on the research interests of the fractal coding and its applications, this dissertation is mainly concentrated on the study of two aspects: fast coding algorithms and applications to watermarking.First, a fast fractal coding algorithm is proposed. The excellent visual quality and high compression rate of fractal image coding have the limited applications due to exhaustive inherent encoding time. The time is mostly spent on searching for the best-matched block to an input range block in a usually large domain pool; therefore, a fast algorithm is proposed to limit the search space. It is an improvement of the algorithm based on cross trace proposed by my supervisor [Fast fractal image coding based on local cross trace, Chinese Journal of Computers, 2005, no.10]; in detail, the newly-defined cross trace of image block (i.e., the sum of absolute intensities of normalized block along the main and sub-principal diagonal pixels), which is a modification of original one, is utilized to confine efficiently the search space to the vicinity of the initial-matched block (i.e., the domain block having the closest new cross trace to that of the input range block being encoded). Moreover, an error threshold is also used to control the search neighborhood around the initial-matched block. The proposed algorithm has been compared with the fast algorithm based on cross-trace experimentally, showing it performs better in terms of encoding time and image quality.Then, a fractal watermarking algorithm is proposed. A watermarking algorithm proposed by Pi et al [A novel fractal image watermarking, IEEE Transactions on Multimedia, 2006, no.3] is improved in order to embed a binary copyright symbol into a host image. In detail, the host image is first divided into non-overlapping range blocks of fixed size, which are encoded by fractal coding (using orthogonal fractal coding method). The range blocks are then sorted by collage errors to become a descending range sequence. The range sequence is partitioned into three subsequences according to the content of the host image. Next, the watermark, which is first scrambled using Arnold transform, is embedded into the quantized means of distinct range blocks in the three range subsequences by a new quantization-based embedding formula with different quantized steps, followed by fractal decoding. The experimental results show that this algorithm really achieves good perceptual invisibility and is also very robust against some image processing such as cropping, scribbling, adding noise, filtering, and JPEG compression.