A Systematic Multichimera Transform for Color Image Representation

Abstract

Mathematically representing an image with only a small number of coefficients has been attempted a few times. These attempts represent initial steps to achieve this goal and showed promising results by either working on a small image block size or utilizing a codebook built using a complex operation. The use of the codebook complicated the entire transformation process. In this work, we overcome these difficulties by developing a new scheme called systematic multichimera transform (SMCT). This transform employs simple mathematical functions called fractal half functions to independently build a codebook of image contents and size. These functions satisfy the symmetry under fractal form while breaking the orthogonality condition. The transform can deal with different image block sizes such as 8×8, 16×16, and 32×32. The encoding process is conducted by repetitively finding the similarity between image blocks and codebook blocks to achieve data reduction and preserve important information. The coefficients of the matching process are then employed in the decoding process to reconstruct the image. SMCT produced the highest structural similarity index (SSIM) and a competitive Peak Signal to Noise Ratio (PSNR) over the standard discrete wavelet transform (DWT) and discrete cosine transform (DCT) without degrading important image content.