Fractal image coding using SSIM

Abstract

Since Jacquin proposed original fractal image compression technique in 1990, fractal coding method has been developed into various schemes. Traditionally, fractal coding uses mean square error (MSE) to evaluate similarity of image blocks, but the similarity evaluated by MSE usually differs from human visual system (HVS). Compared with MSE, structural similarity (SSIM) is an image measure index which is more appropriate for the HVS. This paper proposes a new fractal coding scheme which uses structural similarity to measure the similarity between image blocks and compute these blocks' coefficients. The experiment results show that the proposed method generates higher quality images for the HVS than MSE scheme.

A Novel Fractal Image Compression Scheme With Block Classification and Sorting Based on Pearson's Correlation Coefficient

“…(1) by the least-squares method, we can obtain the values of parameters s, o, and the simplified energy function H as follows [23]:…”

“…If σ R = 0 and σ D = 0, it has been proved in some papers [22], [23] that the affine similarity between two image blocks in FIC is equivalent to the absolute value of the Pearson's correlation coefficient (APCC) between them whether the image measurement is MSE or SSIM [25], [26]. In fact, as in Eq.…”

“…This scheme is based on the fact that the affine similarity between two image blocks is equivalent to the absolute value of Pearson's correlation coefficient (APCC) between them [22], [23]. Firstly, all the domain blocks are classified into 3 classes according to the classification method proposed by Fisher in 1992 [15].…”

Use of fractals to measure anisotropy in point patterns extracted with the DPT of an image

“…In the past, the fractal dimension has been investigated in image analysis, specifically texture analysis. The theoretical development has increased as computing grows (Chen et al, 1993;Ida and Sambonsugi, 1998;Kisan et al, 2016;Lam and Li, 2010;Liu, 2008;Melnikov, 2007;Rigaut et al, 1998;Rosen, 1995;Wang et al, 2011;Zhao and Liu, 2005). It has been used in remote sensing (Al-Saidi and Abdul-Wahed, 2018;Berizzi et al, 2001;Chenoweth et al, 1995;Lam, 1990;Zhu and Yang, 2010;Di Martino et al, 2010;Riccio et al, 2014;Sawada et al, 2001), image inpainting (Xiu-hong and Bao-long, 2009;Bai et al, 2011), image matching with texture (Dolez and Vincent, 2007), denoising (Ghazel et al, 2003;Malviya, 2008), restoration (Hamano et al, 1996), segmentation (Ida and Sambonsugi, 1998), compression (Ismail et al, 2010;Jiang, 1995), shape classification and segmentation (Kisan et al, 2016;Nayak et al, 2015), interpolation (Shi et al, 2008), classification (Shih, 2008), superresolution (Wee and Shin, 2010), medical imaging (Hong and Huidong, 2012;Priya et al, 2011;Qi et al, 2009;Tang and Wang, 2006) and specifically in texture analysis (Avadhanam and Mitra, 1994;Costa et al, 2012;…”