|dc.description.abstract||Increase in technological advancements in fields of telecommunications, computers and
television have prompted the need to exchange video, image and audio files between people.
Transmission of such files finds numerous multimedia applications such as, internet multimedia,
video conferencing, videophone, etc. However, the transmission and rece-ption of these files are
limited by the available bandwidth as well as storage capacities of systems. Thus there is a need
to develop compression systems, such that required multimedia applications can operate within
these limited capacities.
This dissertation presents two well established coding approaches that are used in modern' image
and video compression systems. These are the wavelet and fractal methods. The wavelet based
coder, which adopts the transform coding paradigm, performs the discrete wavelet transform on
an image before any compression algorithms are implemented. The wavelet transform provides
good energy compaction and decorrelating properties that make it suited for compression.
Fractal compression systems on the other hand differ from the traditional transform coders.
These algorithms are based on the theory of iterated function systems and take advantage of
local self-similarities present in images. In this dissertation, we first review the theoretical
foundations of both wavelet and fractal coders. Thereafter we evaluate different wavelet and
fractal based compression algorithms, and assess the strengths and weakness in each case.
Due to the short-comings of fractal based compression schemes, such as the tiling effect
appearing in reconstructed images, a wavelet based analysis of fractal image compression is
presented. This is the link that produces fractal coding in the wavelet domain, and presents a
hybrid coding scheme called fractal-wavelet coders. We show that by using smooth wavelet
basis in computing the wavelet transform, the tiling effect of fractal systems can be removed.
The few wavelet-fractal coders that have been proposed in literature are discussed, showing
advantages over the traditional fractal coders.
This dissertation will present a new low-bit rate video compression system that is based on
fractal coding in the wavelet domain. This coder makes use of the advantages of both the
wavelet and fractal coders discussed in their review. The self-similarity property of fractal
coders exploits the high spatial and temporal correlation between video frames. Thus the fractal
coding step gives an approximate representation of the coded frame, while the wavelet
technique adds detail to the frame. In this proposed scheme, each frame is decomposed using
the pyramidal multi-resolution wavelet transform. Thereafter a motion detection operation is used in which the subtrees are partitioned into motion and non-motion subtrees. The nonmotion
subtrees are easily coded by a binary decision, whereas the moving ones are coded using
the combination of the wavelet SPIHT and fractal variable subtree size coding scheme. All
intra-frame compression is performed using the SPIHT compression algorithm and inter-frame
using the fractal-wavelet method described above.
The proposed coder is then compared to current low bit-rate video coding standards such as the
H.263+ and MPEG-4 coders through analysis and simulations. Results show that the proposed
coder is competitive with the current standards, with a performance improvement been shown in
video sequences that do not posses large global motion. Finally, a real-time implementation of
the proposed algorithm is performed on a digital signal processor. This illustrates the suitability
of the proposed coder being applied to numerous multimedia applications.||en