Image compression

The classic methods in indexing image and video databases are either using keywords or analysis of color distribution. In the recent year, there is a new standard in image and video compression standard called JPEG and MPEG respectively. One of the basic operations of JPEG and MPEG is Discrete Cosine Transform (DCT). The human visual system is known to be very dependent on spatial frequency. The DCT has capability to provide a good approximation of the images' spatial frequency that is sensitive to human eyes. We take this advantage of DCT in indexing image and video databases. However, the two-dimensional DCT can give us 64 coefficients per block of 8 x 8 pixels. These numbers are too many to calculate to receive fast indexing results. We use only first coefficient of DCT called DC coefficient to represent an 8 x 8 block of transformed data. This representation yields satisfactory indexing results.

In this thesis we applied wavelet transforms to image and video coding. First, a survey of various wavelets and their features is presented, including continuous, discrete, and orthogonal wavelets. Theories and concepts underlying one and two-dimensional wavelet transforms are introduced and compared to Fourier transform and sub-band coding. The core of the thesis is the implementation of two-dimensional and three-dimensional codec architectures and their application to coding images and videos, respectively. We studied performance of the wavelet codec by comparing it to DCT and JPEG coding techniques. We applied these techniques for compression of a variety of test images and videos. We also analyzed the adaptability and scalability of 2D and 3D codec. Experimental results, presented in the thesis, illustrate the superior performance of wavelets compared to other coding techniques.

The main objective of the research is to develop computationally efficient hybrid coding schemes for the low bit implementations of image frames and image sequences. The basic fractal block coding can compress a relatively low resolution image efficiently without blocky artifacts, but it does not converge well at the high frequency edges. This research proposes a hybrid multi-resolution scheme which combines the advantages of fractal and DCT coding schemes. The fractal coding is applied to get a lower resolution, quarter size output image and DCT is then used to encode the error residual between original full bandwidth image signal and the fractal decoded image signal. At the decoder side, the full resolution, full size reproduced image is generated by adding decoded error image to the decoded fractal image. Also, the lower resolution, quarter size output image is automatically given by the iteration function scheme without having to spend extra effort. Other advantages of the scheme are that the high resolution layer is generated by error image which covers the bandwidth loss of the lower resolution layer as well as the coding error of the lower resolution layer, and that it does not need a sophisticated classification procedure. A series of computer simulation experiments are conducted and their results are presented to illustrate the merit of the scheme. The hybrid fractal coding method is then extended to process motion sequences as well. A new scheme is proposed for motion vector detection and motion compensation, by judiciously combining the techniques of fractal compression and block matching. The advantage of this scheme is that it improves the performance of the motion compensation, while keeping the overall computational complexity low for each frame. The simulation results on realistic video conference image sequences support the superiority of the proposed method in terms of reproduced picture quality and compression ratio.