Evolutive Image Coding

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1 1 (GP) JPEG H.64/AVC / () GP Evolutive Image Coding Seishi TAKAMURA 1 Evolutive methods based on genetic programming (GP) enable dynamic algorithm generation, and have been successfully applied to many areas such as plant control, robot control, and stock market prediction. However, conventional image/video coding methods such as JPEG and H.64/AVC all use fixed (non-dynamic) algorithms without exception. The evolutive coding enables an automatic generation of pixel prediction algorithm. It is a radical departure from conventional fixed algorithm, man-made algorithm and hand-made programming toward a new paradigm. In this article, we introduce a GP-based image predictor that is specifically evolved for each input image, which have been evolving day by day. We demonstrate its up-to-date performance as well as the investigation on predictor complexity versus prediction performance. We also report about speeding up the evolution process using parallelization by a factor of 100. Ultimate coding efficiency will also be touched upon. 1. ( ) 1). (genetic algorithm, GA) 1 (genetic programming, GP) GA, GP GA ),3) GA, GP 4).1 1 NTT NTT Cyber Space Labotratories, NTT Corporation, Y-517A, 1-1 Hikarino-oka, Yokosuka-shi, Japan 1 c 009 Information Processing Society of Japan

2 1 Table 1 Differences between evolutive image processing and evolutive image coding bloat I 10 I 07 I 05 I 08 I 11 I 06 Inw In Ine I 09 I 04 Iw p 1 p Fig. 1 Neighboring pixels of p. GP (bloat) 5) p ( Inw, In ) x x ( ˆx ) x ˆx JPEG-LS 6) MED C T (e.g., ) 3. GP MED GP ( ( )) minimal generation gap 7) T max, min, ave, abs, sqr, sqrt,,, ( ) sin, cos, tan arcsin, arccos, arctan sinh, cosh, tanh log, log 10, pow, pow (log x ) (pow(a, b) = sgn(a) a b, pow(a, b) = sgn(a) a b/10 ) add, sub, mul, div xor, or, and In, Ine, Iw, Inw, I 04...I 11 D GAP D = ( Iw Inw + In Inn + Ine Inne ) ( Iw Iww + In Inw + In Ine ) I I = (Iw + In)/ + (Ine Inw)/4 Igap, Imed, Ils, Ile1 GAP, MED, (4 ), (1 ) x, y (x, y) = ( 1, 1), (1, 1) ρ, θ (L1 ) ρ = 1, θ = π/4 3 (float) ( 1 ) (MED ) ( ) ( ) ( 3 ) ( ) () ( 4 ) ( ) H T H R (H T + H R, ) H T ( ) H R (CALIC 8) 8 ) CALIC error feedback/flipping c 009 Information Processing Society of Japan

3 if (Inw >= max(iw, In)) return min(iw, In); else if (Inw <= min(iw, In)) return max(iw, In); else return Iw + In - Inw; C MED Fig. C- and Tree- expressions of MED predictor 3 () Fig. 3 Evolution strategy (for single process) min, max,,,,,, p (x, y [ 1, 1]), 1 4 CALIC gradient-adjusted prediction (GAP) MED N = 49 3 bit (C float ) P num = 0.15 n dc C(8 ) d C (= ) N C C 3 : (H T + H R [bpp]) (H T [bits]) : (1 ) Table 3 Top table: Residual entropy (overhead inclusive) of the predictors (H T + H R [bpp]), their increment ( incr. in percentage) against EP1, as well as their H T [bits]. Numbers next to the predictors mean the number of reference pixels. Lower table: proposed predictor (with 1 pixels) s generic prediction performance (H T + H R [bpp]). Lena Baboon Airplane Peppers [%] LS(4) LS(1) LE(4) LE(1) GAP MED Proposed(4) H T [bits] Proposed(1) H T [bits] Lena (4.45) Baboon (5.334) Airplane (3.486) Peppers (4.96) H T, H R : log H T = P num + 3 (n ) [bits] (1) log n (1 P num ) + log N (n ) n dc H R = n dc log [bits] () N C C n dc (Global Best Individual, GBI) (Local Best Individual, LBI) LBI GBI GBI 5 3 c 009 Information Processing Society of Japan

4 "!$#&% "! #%$& Z(['\^]^_ `ba'ced frgihj '( ) * + )-,/ :; k^lm'npoq ] hr s 657 8%9 // <= '( B CEDF PRQTS UVEW % > B GHIJ%K 4 Fig. 4 Modification for parallel processing 5 Fig. 5 An image of asynchronous parallel evolution X QYS UV W L( > B ( M%NO OS 1 ( 10 ) ( ) () I/O load 100% ')( 4. Lena, Baboon, Airplane, Peppers 4 ( bpp, ) ( (LS) (LE) GAP( ) MED ( 3 ) LE LS ( =)5 ( 1+1=13 ) Powell H R 4.1 Lena 6 Peppers (LS(4), LE(4) (3 5 =)160, LS(1), LE(1) 416, GAP, MED 0, H T bits) H T H T bits GAP, MED ( H T 349.5, bits. 0 ) Peppers Lena Baboon bpp Peppers Lena 4.3 Core Extreme QX9775 (3.GHz, 4GB Memory, MS Windows Vista Ultimate (3bit) SP1) Core Quad Q6600 (.4GHz, GB Memory, MS Windows XP Professional x64 Ed. Ver. 003 SP) 30 ( 10 ) 4 c 009 Information Processing Society of Japan

5 I 08 max min(in,0.5 (Ine+Imed)) ( Ile 1,Igap and(min(inw, I cosh arcsin arcsin cos( 04 max(θ+and(ile 1, min(cosh( log 10 (I 06 ) + Igap ), log sinh sinh 4 arcsin sinh tanh( ) Ile 1 )+sinh sinh arctan sinh(max(0.5 (Inw+,I 09 ),I 05 )) sinh sinh log 10 (cosh log 10 (Ine)) (I 09 +Ine) max(i 04,I 10 ) ) max(imed, In)), I 09 ) Ile 1 )), or(min( sinh tan y+max(imed,i 05) Iw Ine,, log( 8 y arctan arctan log 10 (Iw) 0 D I05 ) Ils+Ile sin 8 sin arctan arctan tanh 4 log 10 (Ile 1 ) max 4 1, 0.5 (0.5 (I 09+Inw)+max(and(or(Imed, I 05), Inw (Ine,I ) cos 8 sin ( x 1 x ) (Inw I 09) 8 In xor(d, cos tan( ))), 0.5 (Iw+In)+0.5 (Ine Inw), log Inw+Imed 10 (I 08)+ arcsin tan sinh x +0.5 (Inw+Ils)))+ arccos( max(igap,iw) I 04 ) 1 In 4 4 +θ), min(max( max(inw, I 06, I 07 )+and(ile 1, log sinh(0.5 ( xor(d, cos cosh( 1 ))+ Inw + Igap) + sinh sinh(0.5 (arcsin sinh tan y + θ)) sinh arccos arcsin x)) + max(ile 1, min(max(imed, In), sinh D )), tanh tanh sin(0.5 (Iw + In) (Ine Inw) Ile 1 ) + Igap), max(0.5 (Iw + In) (Ine Inw), 1.818(I (I 05 + Ine)))))) 6 Lena ( bits) Fig. 6 Generated predictor for Lena (tree size=150.4 bits) if D then Igap else if D then ( xor(min(max(ine, Iw), I 05 max(min(ine, Inw), and(i 10, Ine) I 06 + θ + Ils + Ile 1 I 08 I 07 ρ + max(inw, if x 0 then y else min(imed, I 11 I 10 ))) In ), Igap) + Igap) else if I 10 I 04 I 10 Iw I 10 Ile 1 + θ max(inw, I 07 and(ile 1, I 09 ) + max(ine, max( or(i 07,Inw) I 04 sinh ρ Inw Imed, or(i 10, I 07 )))) + min(or(min(min(ils, I 08 ), I 06, I 09 ), D Ils Ine ), I 05 ) then (3 ( ( ( sin tan( 1 Ine ) I 09+ sin cos θ I 04 Iw Ils Inw+max(xor(xor( Ine, Ine), I 11 ), I 05 + Iw + Ils) ( I 07 I 04 + Ine Inw + Ine) + xor ( , tan cos y )) + sin( In) else tan sin tan( Ile 1 ) 1 Ile 1 I 07 arctan θ Iw+In Iw Inw Ine Inw 4 +min(max(min(min(ine,inw),i 04,I 09 ), θ+min(sinh Iw, I 06 + Iw+In +and(inw,ine)+ Ine Inw 4 )+Ile 1 I 08 ),max(iw,i 09 )) +Igap ) I tan sin tan( Ile I Ine) Iw Ine Ine) + )+1 1 Ile 1 7 Peppers ( bits) Fig. 7 Generated predictor for Peppers (tree size=199.1 bits) or(i 05,I 09 ) 1 4 Lena 8 5 Peppers H T (H R + H T ) 1bit 8.5bit ( 7.5bit ) 9 Lena (H T ) (H R + H T ) 1, y = x y = x ( x = H T, y = H R + H T ) H R 0, H T 0 H R [bpp]( 1) [bpp]( ) 5. GAP 5 c 009 Information Processing Society of Japan

6 total info (H R + H T ) [bits] tree info (H T ) [bits] total info (H R + H T ) [bits]-1.148e+6 tree info (H T ) [bits]* /13 04/14 04/15 04/16 04/17 04/18 04/19 04/0 04/1 04/ 04/3 total information (H R + H T ) [bits] 1.17e e e e e+06 trial bits/tree slope trial -13 bits/tree slope 1.145e tree information (H T ) [bits] 8 (H R + H T ) (H T 7.5) ( ). : Lena, Fig. 8 Transitions of total information (H R + H T ) and tree information (H T 7.5), after parallelization. Horizontal axis means the date. Image: Lena, trial: 1. 9 (H T ) (H R + H T ). : Lena Fig. 9 Tree information (H T ) vs. total information (H R + H T ) and their trends. (LE 3.0 %, GAP 3.4 %) GPU 9) Genetic Network Programming 10) 1),, :,, vol. 108, no. 45, IE008-10, pp , Feb. (009) ),,, :, D-II, vol. J83-D-II, no. 5, pp , May (000). 3),,, :, D-II vol. J83-D-II, no. 6, pp , June (000). 4), : GP GA PT-ACTIT,, vol. 59, no. 11, pp , Nov. (005). 5), :, 30, Mar. (003). 6) ISO/IEC : Lossless and near-lossless compression of continuous tone still images (000). 7),, :,, vol. 1, no. 5, pp , Sep. (1997). 8) Wu, X. and Memon, N.: Context-based, adaptive, lossless image coding, IEEE Trans. Commun., vol. 45, no. 4, pp , Apr. (1997). 9), : GPU,. MPS,, vol. 85, pp , Sep. (008). 10),,,, : Genetic Network Programming Genetic Programming, C vol. 11, no. 6, pp (001). 6 c 009 Information Processing Society of Japan

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