Open Comput. Sci. 2015; 5:13–21 Research Article Open Access Pooneh Bagheri Zadeh*, Akbar Sheikh Akbari, and Tom Buggy DCT image codec using variance of sub-regions DOI 10.1515/comp-2015-0003 1 Introduction Received May 20, 2011; accepted July 21, 2015 Abstract: This paper presents a novel variance of sub- With advances in multimedia technologies and internet regions and discrete cosine transform based image-coding applications, demand for transmission and storage of vo- scheme. The proposed encoder divides the input image luminous amounts of multimedia data have dramatically into a number of non-overlapping blocks. The coecients increased. Over the past two decades much eort has been in each block are then transformed into their spatial fre- invested in developing ecient image compression tech- quencies using a discrete cosine transform. Coecients niques and has led to the development of many image with the same spatial frequency index at dierent blocks compression algorithms¹ [1, 2]. In recent years wavelet are put together generating a number of matrices, where based image coding schemes have achieved impressive each matrix contains coecients of a particular spatial success, mainly due to the novel approaches taken by frequency index. The matrix containing DC coecients is these schemes in data organization and representation losslessly coded to preserve its visually important infor- of wavelet-transformed coecients [1, 2]. Wavelet based mation. Matrices containing high frequency coecients methods oer very high compression eciency in terms are coded using a variance of sub-regions based encod- of PSNR. However, the high compression eciency in the ing algorithm proposed in this paper. Perceptual weights rate/distortion sense does not necessarily correspond to a are used to regulate the threshold value required in the similar degree of compression eciency in terms of visual coding process of the high frequency matrices. An exten- quality versus bitrates [3, 4]. Grgic et al. [5] has shown that sion of the system to the progressive image transmission Discrete Cosine Transform (DCT) produces slightly better is also developed. The proposed coding scheme, JPEG and results than wavelets especially at low compression ra- JPEG2000 were applied to a number of test images. Results tios while its computational complexity is less expensive show that the proposed coding scheme outperforms JPEG than that of wavelets. A comparative study on wavelets and JPEG2000 subjectively and objectively at low compres- and DCT, reported by Xiong et al. [6], shows that the sion ratios. Results also indicate that the proposed codec main factors to distinguish image compression schemes decoded images exhibit superior subjective quality at high are the way the transformed coecients are re-arranged, compression ratios compared to that of JPEG, while oer- quantized and coded rather than the dierence between ing satisfactory results to that of JPEG2000. the transforms used. Although wavelets appear to provide more exible space-frequency resolution tradeos than Keywords: discrete cosine transform; image compression; DCT, the latter has been successfully employed as the rst perceptual weights; quad-tree coding; variance of sub- step in several coding algorithms such as: JPEG¹, MEPG² regions and H.26x³ because of its compression capabilities and processing speeds. JPEG, the rst image compression standard¹, divides an image into blocks of 8x8. The resulting blocks are then decorrelated using a DCT. The transformed coecients are *Corresponding Author: Pooneh Bagheri Zadeh: Bagheri Zadeh School of Computer Science and Informatics, De Montfort Univer- sity, U.K., Email: [email protected] 1 Information Technology-JPEG-Digital Compression and Coding Akbar Sheikh Akbari: School of Computing, Creative Tech- of Continuous-Cone Still Image-Part 1: Req. and Guidelines, 1994. nology and Engineering, Faculty of Arts, Environment and ISO/IEC 10918-1 and ITU-T Recom. T.81. Technology, Leeds Beckett University, U.K., Email: a.sheikh- 2 ISO/IEC JTC1/SC29/WG11. MPEG-4 Overview, available from [email protected] http://mpeg.telecomitalialab.com/standards/mpeg-4/mpeg- Tom Buggy: Division of Communication, Network and Electronic 4.htm#E25E3, March 2001. Engineering, School of Engineering & Computing, Glasgow Caledo- 3 ITU-T Recommendation H.263, Video codec for Low bit rate commu- nian University, 70 Cowcaddens Road, Glasgow G4 0BA, UK E-mail: nication, Version 1, November 1995; Version 2, January 1998, Version [email protected] 3, November 2000. © 2015 P.B. Zadeh et al., licensee De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. The article is published with open access at www.degruyter.com. 14 Ë P.B. Zadeh et al. zigzag scanned, quantized and human coded. JPEG pro- frequency index at dierent DCT blocks are grouped to- vides good compression ratios, particularly when dealing gether to make a number of matrices. The matrix contain- with natural images. However, the decoded image using ing the DC coecients is losslessly coded. The matrices JPEG suers from blocking artifacts especially in smooth containing high frequency coecients are coded using a regions, and the Gibbs phenomenon, which causes rip- novel variance of sub-regions based encoding algorithm. ples or oscillations around sharp edges at high compres- The proposed encoder applies a hierarchical estimation sion ratios [7]. Recent DCT-based encoders with novel ap- algorithm to code the coecients in each matrix. The hi- proaches to data organization and representation of DCT erarchical estimation algorithm assumes that the distri- coecients have obtained higher compression eciency butions of the coecients in the matrices are Gaussian compared to JPEG [4, 8, 9]. A DCT-based embedded im- in some regions. A threshold on the variance of the coef- age coding (EZDCT) algorithm was proposed by Xiong cients is used to determine if it is possible to estimate et al. [8], which like JPEG, divides an image into blocks the coecients in the input matrix with a single Gaus- of 8x8 and performs DCT on each block. Each resulting sian distribution or if it needs further dividing into four DCT block is viewed as wavelet decomposition with a uni- sub-blocks. This hierarchal algorithm is repeated until the form 8x8 subband decomposition. The DCT coecients distribution of the coecients in all sub-blocks fulls the are then rearranged into a 3-level wavelet pyramidal struc- above criteria. Finally, the mean value of the Gaussian dis- ture and the re-arranged coecients are coded using em- tribution of each block is taken as an estimation value for bedded zerotree coding scheme. Another DCT-based im- all coecients in that block. During the encoding process age codec that uses the morphological representation of a quadtree-like binary map is generated to save a record DCT coecients (MRDCT) was presented by Debin et al. of the hierarchical operation, which is used in decoding [4]. It re-arranges DCT coecients like the EZDCT and then process. The application of the codec to progressive im- uses a morphological dilation to represent the re-arranged age transmission is also investigated. The rest of the pa- DCT coecients. An Embedded Quadtree DCT based im- per is organized as follows: in Section 2 the proposed cod- age compression scheme (EQDCT) was suggested by Xing- ing scheme is discussed; Section 3 explains the progressive Song et al. [9]. It re-arranges the DCT coecients in a simi- mode of operation. Section 4 presents comparative exper- lar manner to the EZDCT scheme and then uses an adaptive imental results; nally Section 5 concludes the paper. quadtree splitting algorithm, which is similar to the quad tree coding strategy of EZBC in wavelet domain, to code the signicant DCT coecients. They reported superior perfor- 2 Variance of sub-regions and DCT mance to that of EZDCT, MRDCT and JPEG at high compres- sion ratios. based image encoder Variance of the image data have been used in a num- ber of image compression techniques and oers promis- A block diagram of the Variance of Sub-regions and Dis- ing visual quality especially at high compression ratios crete Cosine Transform (VSDCT) based image encoder is [10, 11], while the application of variance of the trans- illustrated in Figure 1. A gray scale image is input to the formed image data in image compression has been less re- encoder. The encoder divides the input image into a num- ported in the literature. In progressive image transmission, ber of 8x8 non-overlapping pixel blocks called B11 to Bnn an image is transmitted in two or more stages. A coarse but as shown in Figure 1(a). The coecients in each block are recognizable image with basic quality is rst transmitted then transformed into the frequency domain using a dis- to the receiver. The transmission of further details is made crete cosine transform as shown in Figure 1 (b) where A0−ij at the later stages upon the request of the viewer. Some im- to A63−ij are DCT transformed coecients in the Bij block. age coding schemes, e.g. JPEG, JPEG2000, SPIHT and EZW, The transformed coecients with the same frequency in- are very suitable for progressive image transmission due dex at dierent blocks are then grouped together generat- to the good energy compaction properties of their trans- ing 64 matrices called M0 to M63, where M0 contains the forms, i.e. Wavelets and DCT [12]. DC coecients and M1 to M63 contain the AC coecients In this paper, a novel Variance of Sub-regions and DCT from the lowest to the highest frequency, respectively. (VSDCT) based image-coding scheme is presented. The Figure 1(c) shows one of these matrices (Mk), where proposed coding scheme divides the input image into a Ak−11 to Ak−nn in this matrix represent coecients with the number of non-overlapping blocks.