Enhanced AMBTC for Image Compression using Block Classification and Interpolation

Transcription

1 Internatonal Journal of Computer Applcatons ( ) Volume 5 No.0, August 0 Enhanced AMBTC for Image Compresson usng Block Classfcaton and Interpolaton S. Vmala Dept. of Comp. Scence Mother Teresa Women s Unversty Kodakanal 64 0 M. Sathya Dept. of Comp. Sc. Mother Teresa Women s Unversty Kodakanal 64 0 K. Kowsalya Dev Dept. of Comp. Sc. Mother Teresa Women s Unversty Kodakanal 64 0 ABSTRACT Block Truncaton Codng (BTC) s a fast moment preservng lossy mage compresson technque. Ths paper proposes a two-level compresson scheme. In the frst level of compresson, the blocks are categorzed nto hgh-detal blocks and low-detal blocks. The hgh detal blocks are stored or transmtted n the form of a bt plane (6 bts), and two statstcal moments; hgh mean and low mean (6 bts). Only the mean values are stored for low detaled blocks. In second level of compresson, the nterpolaton technque s ncorporated as part of the proposed method for further bt rate reducton. The performance of the method s tested wth standard mages Lena, Cameraman Boats, Brdge, Baboon and Kush. The proposed scheme acheves better codng effcency wth a slght degradaton n PSNR when compared to estng methods. General Terms Image Compresson Keywords mage compresson; hgh-detal block; low-detal block; nterpolaton; bpp; PSNR;. INTRODUCTION Generally mages occupy more storage space and take more tme to get transmtted across network. Image compresson technque s used to reduce the cost of storng, retrevng and transmsson of mages across a network []. One of the fundamental goals of mage compresson s to reduce the sze of data needed to represent the mage whle mantanng the necessary nformaton []. There are two types of Image compresson technques: lossless technques and lossy technques. A lossy compresson technque provdes much hgher compresson rato than lossless scheme. The performance of any compresson technque s measured n terms of.compresson rato.sgnal-to-nose Rato (qualty of the reconstructed mage) and.encodng and Decodng Speed []. In lossy mage compresson method, the redundant nformaton can be compressed [4]. One such lossy mage compresson technque s Block Truncaton codng (BTC) technque. BTC s one of the recent technques used to compress mage data. The computatonal complety s lee n terms of BTC when compared to other technques. A compresson rate of bpp s acheved wth BTC [5] & [6]. The compressed mage s only an appromaton of the orgnal mage. Though some data s removed, for Human Vsual System, there s no much dfference between the orgnal and the compressed mage. In encodng process, for each nput mage block of sze 44 pels, a bt plane s formed by replacng each pel value wth ether or 0. When the pel value s greater than mean, t s coded as, otherwse 0. Two statstcal moments of sze 6 bts are preserved along wth the bt plane [7]. The bt-rate acheved wth BTC can further be reduced by reducng the amount of data needed to represent the Btplane by droppng few bts. The dropped bts can be generated at the decodng stage by usng the Interpolaton technque [8]. By usng nterpolaton method, the sze of btplane s reduced from 6 bts to just 8 bts leadng to a btrate of.75 bpp reduced from bpp. The total number of bts s 4 for each block and the bt rate s reduced from to.5 bts/pel. In BTC, the statstcal overheads: the standard Mean and standard devaton are preserved for each nput block. The truncated block of the BTC s the one-bt output of the quantzer for every pel n the block. A smple varant of BTC called Absolute Moment Block Truncaton Codng (AMBTC) was presented by Lema and Mtchell, and t preserves the hgher mean and lower mean of the blocks [9]. The nterpolatve technques are used to code the compressed bt plane of BTC [0, ]. An algorthm for preservng moments whch results n less mean square error (MSE) was proposed n []. To reduce the btrate further, few adaptve Block Truncaton Codng technques have been evolved: A four level four level quantzer has been desgned n [] and an dea of Multlevel Quantzer has been proposed n [4]. The dfference between the orgnal mage and the reconstructed mage s called Mean Square Error (MSE) and s calculated usng the Eq. (). The Qualty of the reconstructed mage s measured usng Peak Sgnal to Nose Rato (PSNR) and s computed usng the Eq. (). PSNR s the nverse of MSE. 48

2 Internatonal Journal of Computer Applcatons ( ) Volume 5 No.0, August 0 N MSE y N Where y s the reconstructed pel value, s the orgnal pel value and N s the number of Pels n an mage. PSNR 0log 0 55 MSE The performance of an mage compresson technque s measured n terms of the PSNR and bpp. The PSNR must be hgh and bpp must be low... Standard BTC In BTC Algorthm, the mage s dvded n to non-overlappng blocks of sze 4 4 pels. The mean s computed usng Eq. () for each block. n n Bt-plane Generaton: Each pel value n the block s compared aganst. If the value s greater than or equal to the mean value, t s coded as otherwse 0. The standard devaton s computed usng the Eq. (4) to generate the statstcal moments. n n Where represents the th pel value of the mage block and n s the total number of pels n that block []. The two statstcal moments H and L are computed usng the Eq. (5) and Eq. (6). H L Where p and q are the number of 0 s and s n the compressed bt plane respectvely. In the decoder, an mage block s reconstructed by replacng s n the bt plane wth H and the 0s wth L. p q q p () (4) (5) (6) () ().. Absolute Moment Block Truncaton Codng (AMBTC) Lema and Mtchell presented a smple and fast varant of BTC named Absolute Moment Block Truncaton Codng (AMBTC). In ths method, the hgher mean h and lower mean l are preserved nstead of the mean and standard devaton values. Pels n an mage block are then classfed nto two groups of values. One group (hgher range) comprsng of gray levels whch are greater than or equal to the mean ( ) and the remanng gray levels are brought nto another group (lower range). The mean h of hgher range and l of the lower range are calculated usng the Eq. (7) and Eq. (8). l m q q h (8) where q s the number of pels whose gray levels are greater than or equal to. Then a two level quantzaton s performed for all the pels n that block to form a bt plane of s and 0 s. The encoder generates l, h and bt plane for each block, thus leadng to bpp lke BTC. AMBTC nvolves less number of computatons, when compared to BTC as standard devaton nvolves more multplcatons. AMBTC yelds hgh qualty of reconstructed mages... Interpolatve Technque The boldfaced components as n Fg. are dropped and the sze of the bt plane s 8=8 bts rather than 6 bts [4] Fg. The pattern of droppng bts (7) 49

3 Internatonal Journal of Computer Applcatons ( ) Volume 5 No.0, August 0 The estng 8bts are transformed nto gray levels based on the quantzers n decodng phase. The dropped bts are recovered by takng the arthmetc mean of the adjacent pel values as gven n Eq. (9) for for for for for 5 4 for for 7,0. PROPOSED TECHNIQUE The proposed method s based on AMBTC technque for generatng the bt plane and the statstcal moments, hghmean and low-mean. The compresson s done n two levels. In frst level of compresson, block classfcaton s done. In second level of compresson, the nterpolaton method s used. At the frst level of compresson, each nput block s categorzed nto ether a hgh detal block or a low detal block. To categorze, the mean of each block s computed usng Eq. (). The sum of dfferences between the mean and the ndvdual pel value of each block s computed usng Eq. (0). Dff m abs (0) If the dfference s greater than a threshold value, the block s categorzed as hgh detal block otherwse low detal block. In low detal block, the pel values are closer to each other. Hence for a low detal block, only the mean value s preserved. But for a hgh detal block, a bt plane (6 bts) and two statstcal moments: hmean and lmean are stored as the dfference between the pel values s hgh. Therefore the number of bts requred to store a hgh detal block s hgh and s low for a low detal block. Encodng Algorthm Level Step: Input the mage of sze m m pels. Step: Splt the mage nto blocks of sze 4 4 pels. Step: For each block, perform the followng. (a) Compute the mean usng Eq. (). (b) Compute the sum of dfferences usng Eq. (0). (c) f Dff >= Threshold, declare t as a hgh detal block else (9) t s a low detal block (d) f hgh detal block. generate the bt plane. compute h usng Eq. (7) and usng Eq. (8).. store/transmt the set {bt plane, and l }. l (e) f low detal block, store and transmt only the mean. At the second level of compresson, the nterpolaton method s ncorporated as part of the proposed method. Certan elements of bt plane as shown n fg. are dropped leadng to bt rate reducton. Level Step: For each hgh detal block, perform the followng (a) Drop the elements of the bt plane as n Fg.. The compressed mage s ether stored or transmtted n the form of compressed bt plane (8 bts), hgh mean (8 bts) and low mean (8 bts) for hgh detal blocks and, only the blockmean values are stored for the low detal block. The compressed mage s reconstructed (decoded) at the recevng end as follows: For hgh detal blocks, the s and 0 s n the bt plane are replaced wth h and l respectvely. Then the dropped elements are regenerated usng the Eq. (). The low detal blocks are reconstructed only wth the mean values. Decodng Algorthm Step: Reconstruct the mage as follows: Step: f hgh detal block, (a) replace all s n the bt plane wth wth l. h h and 0 s (b) nterpolate the dropped elements usng the Eq. (). Step: f low detal block, generate a block of 4 4 pels wth mean for all pel values. for,5 for,8 for,5 for 9, () By categorzng the blocks nto hgh detal block or low detal block, the codng effcency can be mproved. In BTC / 50

4 Internatonal Journal of Computer Applcatons ( ) Volume 5 No.0, August 0 AMBTC, each block requres bts (6 for bt plane, 6 for two statstcal moments). The bpp acheved s / 6 = bpp, where a block contans 6 elements. In the proposed method, the hgh detal blocks are stored n the form of bt plane and two statstcal moments. Only the mean value s stored for the low detal block. The bpp acheved for a low detal block s 8/6, whch s just 0.5. The bpp vares for each mage dependng on the number of hgh and low detal blocks. If n s the number of hgh detal blocks and n s the number of low detal blocks, the average bpp s computed usng the Eq. (). bpp = ((n * ) + (n * 6)) / (56 * 56) () where 56 * 56 s the number of pels n an mage. The bt rate s further reduced when nterpolaton method s used. For the cameraman mage, Number of hgh detal blocks, n = 587 Number of low detal blocks, n = 509 The average bpp s computed as follows, The total number of bts after level (block classfcaton): n = (587 * ) + (509 * 8) = bpp = / (56 * 56) = 0.7 bpp. The total number of bts after level (nterpolaton): N = (587 * 4) + (509 * 8) = 460 bpp = 460 / (56 * 56) = 0.64 bpp. Smlarly, the bpp s calculated for dfferent mages wth dfferent dstrbuton of gray shades. The average bpp for the entre mage depends on the number of low and hgh detal blocks and s dfferent for each mage.. RESULTS AND DISCUSSION The proposed method s tested wth Lena, Cameraman, Boats, Brdge, Baboon and Kush mages. The nput mages taken for the study are gven n Fg.. The results obtaned n terms of PSNR and bpp wth the proposed method are compared wth that of the BTC and AMBTC methods n Table.. The results are generated for three dfferent threshold values. (a) Lena (b) Cameraman (c) Boats (d) Brdge (e) Baboon (f) Kush Fg.. Input mages taken for the study The results n Table. show that there s a sgnfcant mprovement n the codng effcency,.e. from to 0.7, 0.5 and 0.48 for Lena mage at the cost of PSNR. A mnmum of 0.70 bpp s acheved for Lena mage wth the threshold value f 50. It s observed that the reducton n bpp s due to less number of hgh detal blocks n any mage. Number of hgh detal blocks s hgh n Boats mage and the bpp obtaned s., whch s a mamum value. The bpp s reduced further when the threshold values are rased from 50 to 00 and 50. The number of hgh detal blocks wll be less when the threshold values are ncreased. The bpp wll also be decreased f the number of hgh detal blocks decreases. A mnmum of 0.40 bpp s acheved for Baboon mage wth the threshold value of 50, whch s a sgnfcant mprovement. The reconstructed mages are gven n Fg.. 5

5 Internatonal Journal of Computer Applcatons ( ) Volume 5 No.0, August 0 Table. The PSNR and the bpp values obtaned wth respect to BTC, AMBTC and the proposed method for dfferent Threshold Values. Images BTC AMBTC Threshold 50 Threshold 00 Threshold 50 PSNR bpp PSNR bpp PSNR Bpp PSNR bpp PSNR bpp Lena Cameraman Boats Brdge Baboon Kush Orgnal Threshold 50 Threshold 00 Threshold 50 (bpp : 8.00) (bpp: 0.78) (bpp : 0.47) (bpp: 0.78) Orgnal Threshold 50 Threshold 00 Threshold 50 (bpp : 8.00) (bpp : 0..7) (bpp : 0.5) (bpp : 0.45) Fg. Reconstructed mages obtaned wth dfferent Threshold values 50,00 and 50. 5

6 Internatonal Journal of Computer Applcatons ( ) Volume 5 No.0, August 0 4. CONCLUSION A two-stage compresson s acheved wth the proposed method. In the frst stage, the bt rate s reduced by categorzng the blocks nto hgh detal and low detal blocks. The nterpolaton technque s used n the second stage to reduce the bt-rate further. 75% of compresson s acheved wth the estng methods BTC and AMBTC. A compresson rate of 95% s acheved wth the proposed method, whch s a sgnfcant mprovement. The qualty of reconstructed mages depends on the selecton of threshold values. Ths technque s best sutable for hand-held devces and may also be etended to color mages. 5. REFERENCES [] K.Somasundram and P.Sumtra, RGB & Gray Scale Component on MPQ-BTC n mage Compresson, Internatonal Journal on Computer Scence and Engneerng, Vol., No. 4, Aprl 0. [] K.Somasundaram and S.Vmala, Codebook Generaton for vector Quantzaton wth Edge features, CT, Internatonal Journal of Dgtal Image Processng, 00. [] Sonal and DneshKumar, A Study of varous mage compresson technque, Natonal Conference on Challenges and Opportuntes n Informaton Technology, Hsar, 007. [4] Pham, D.Premkumar, A. Madakumar, Error Detecton and Correcton n Communcaton Channels Usng Inverse Gray RSNS Codes, IEEE Transacton on Communcatons. [5] S.Vmala, P.Uma, B.Abdha, Improved Adaptve Block Truncaton Codng for Image Compresson, Internatonal Journal of Computer Applcatons, Vol.9- No.7, Aprl 0. [6] Adtya Kumar and Pradeep Sngh, Enhanced Block Truncaton codng for Gray Scale Image, Internatonal Journal of Computer Technology and Applcaton,Vol (), [7] Doaa Mohammed, Fatma Abou-Chad, Image compresson usng Block Truncaton Codng, Multdscplnary journals n scence and Technology, JSAT, February 0. [8] Elghana.M. Rhoma, Abdosllam.M. Abobaker, Mean Square Error Mnmzaton Usng Interpolatve Block Truncaton Codng Algorthms, Proceedngs of the nd Internatonal Conference on Educaton Technology and Computer, Vol.5, 00. [9] Lema, M.D. and O.R. Mtchell, Absolute Moment Block Truncaton Codng and ts Applcaton to Color Images, IEEE Trans. On Communcatons, pp: 48-57, 984. [0] K.Somasundaram and I.Kaspar Raj, A New Predctve and Interpolatve Image Compresson Scheme Based on Block Truncaton Codng, Internatonal Journal of Soft Computng, Vol., No., 007. [] Hengfu Yang and Janpng Yn, An Adaptve Block Truncaton Codng Algorthm Based on Data Hdng, Informaton Technology Journal (5): , 0. [] Halverson D.R., A generalzed BTC Algorthm for Image Compresson, IEEE Transactons on Acoustcs, Speech, Sgnal Processng, Vol. ASSP-, pp , 984. [] Lucas Hu, An Adaptve Block Truncaton Codng for Image Compresson, IEEE Transactons, CH847-, pp. -6, 990. [4] Madhu Shandlya and Rajesh Shandlya, Implementaton of Absolute Moment Block Truncaton Codng Scheme Based on Mean Square Error Crteron, Proceedngs of the SDR 0 Techncal Conference and Product Eposton, 00. 5