Breaking the Time Complexity of Fractal Image Compression
: In fractal image compression the encoding step is computationally expensive. A large number of sequential searches through a list of domains (portions of the image) are carried out while trying to find a best match for another image portion. We show that this step can be replaced by multi-dimensional nearest neighbor search which runs in logarithmic time instead of linear time required for the common sequential search. Keywords: Image compression, multi-dimensional search, nearest neighbors, fractals. 1 Introduction With the ever increasing demand for images, sound, video sequences, computer animations and volume visualization, data compression remains a critical issue regarding the cost of data storage and transmission times. While JPEG currently provides the industry standard for still image compression there is ongoing research in alternative methods. Fractal image compression is one of them. JPEG can be termed symmetric in the sense that the encoding and decoding phases require ..