IMPROVED IMAGE COMPRESSION USING FRACTAL CONSTRUCTIONS

WE PROPOSE TO IMPROVE IMAGE COMPRESSION TECHNIQUES WHICH ARE BASED ON FRACTAL CONSTRUCTIONS. OUR APPROACH BUILDS ON A LINE OF RESEARCH BEGUN HUTCHINSON IN THE EARLY 1980'S. BARNSLEY AND HIS CO-WORKERS LATER APPLIED THESE IDEAS TO THE REPRESENTATION IMAGE DATA. BARNSLEY'S CONSTRUCTIONS ARE MAINLY BASED ON SYSTEMS OF AFFINE TRANSFORMATIONS (AFFINE ITERATED FUNCTION SYSTEMS). THE COORDINATES OF THE AFFINE TRANSFORMATION REPRESENT THE IMAGE DATA. THESE REPRESENTATIONS RESULT, IN THE CASE OF IMAGES DRAWN FROM NATURAL OBJECTS, IN A DATA COMPRESSION OF 10,000 TO 1, WITH GOOD PRESERVATION OF QUALITY IN THE RECONSTITUTED IMAGE. UNFORTUNATELY, CALCULATION OF THE TRANSFORMS IS COMPUTATION INTENSIVE. OUR RESEARCH IS AIMED AT REDUCING THE COMPUTATIONAL REQUIREMENTS, THROUGH A TRADE-OFF WITH COMPRESSION RATIOS. WE PROPOSE TO APPLY TECHNIQUES FROM FUNCTIONAL ANALYSIS AND HARMONIC ANALYSIS ON LIE GROUPS TO SPEED THE COMPUTATION OF AFFINE ITERATED FUNCTION SYSTEMS.