### Cite Details

Brendt Wohlberg and Gerhard de Jager, "On the reduction of fractal image compression encoding time", in

*IEEE South African Symposium on Communications and Signal Processing (COMSIG '94)*, (Stellenbosch, South Africa), doi:

10.1109/COMSIG.1994.512455, pp. 158--161, Oct 1994

### Abstract

Lossy image coding by Partitioned Iterated Function Systems,
popularly known as Fractal Image Compression, has recently
become an active area of research. An image is coded as a set
of contractive transformations in a complete metric space. As
a result of a well known theorem in metric space theory, the
set of contractive transformations (subject to a few
constraints) is guaranteed to produce an approximation to the
original image, when iteratively applied to
*any* initial image. While rapid
decompression algorithms exist, the compression process is
extremely time consuming; an exhaustive search for the
optimum mappings is
*O(n*^{4}) for an *n
× n* image. The most common solution involves
classification of domain and range blocks according to
features such as the presence of edges, after which matches
across class boundaries are excluded. We propose a geometric
construction, allowing clustering, as well as providing upper
and lower bounds for the best match between domain and range
blocks, allowing blocks to be excluded from the
computationally costly matching process.

### BibTeX Entry

@inproceedings{wohlberg-1994-reduction,

author = {Brendt Wohlberg and Gerhard de Jager},

title = {On the reduction of fractal image compression encoding time},

year = {1994},

month = Oct,

urlpdf = {http://brendt.wohlberg.net/publications/pdf/wohlberg-1994-reduction.pdf},

booktitle = {IEEE South African Symposium on Communications and Signal Processing (COMSIG '94)},

address = {Stellenbosch, South Africa},

doi = {10.1109/COMSIG.1994.512455},

pages = {158--161}

}