A New Scramblng Evaluaton Scheme based on Spatal Dstrbuton Entropy and Centrod Dfference of Bt-plane Lang Zhao *, Avshek Adhkar Kouch Sakura * * Graduate School of Informaton Scence and Electrcal Engneerng, Kyushu Unversty, Japan College of Computer Scence, Chongqng Unversty, Chna Department of Pure Mathematcs, Unversty of Calcutta, Inda Ths research s supported by The Strategc Japanese-Indan Cooperatve Programme on Multdscplnary Research Feld, whch combnes Informaton and Communcatons wth Other Felds Supported by Japan Scence and Technology Agency and Department of Scence and Technology of the Government of Inda, and The Governmental Scholarshp From Chna Scholarshp Councl (CSC).
Outlne Research Background Features of Bt-plane and Reason Why It Can Be Used Detals Informaton of Scramblng Scheme Smulaton Experments on Proposed Scheme 1/24
Research Background Reason: the fast development of computer scence and network technque many mage protecton methods whch are sutable for all knds of dgtal mage (1) an elegant one-dmensonal scramblng scheme based on the dscrete prolate spherodal sequences.(wyner, IEEE transacton on nformaton theory) (2) extended the above mage scramblng algorthm to two-dmenson. (Van De Vle et al., IEEE transacton on CS for vdeo technology) (3) a chaotc mage scramblng scheme makng use of S-DES system.(yu et al., Journal of Physcs) (4) chaos theory and sortng transformaton for desgn a mage scramblng scheme.(lu et al., Internatonal Journal of Computer Scence and Network Securty) 2/24
Research Background Typcal mage scramblng method: Arnold cat map Baker map Fbonacc transformaton sub-affne transformaton Generalzed Arnold cat map 3/24
Research Background Prevous work L presents a measure for mage scramblng degree whch takes advantage of grey level dfference and nformaton entropy Yu et al. use the correlaton of pxels to analyze and evaluate the mage scramblng 4/24
Research Background Present Challenges Pxel values and pxel postons Evaluaton results can reflect the character of mage scramblng scheme The scramblng degree should be ndependent of the plan mage Less mage data can reflect the correspondng scramblng degree 5/24
Features of Bt-plane For any sze of uncompressed dgtal mage, f one pxel s located at the poston of (x, y), the correspondng value of t can be denoted as P(x, y). As the computer can only dsplay dscrete number accordng to ts representaton precson for gray scale mage, the pxel value s dvded nto 256 for the nterval [0, 255]. As the computer only deal wth bnary number, every pxel value s represented by 8 bts bnary: P(x, y)=bt(7) bt(6) bt(5) bt(4) bt(3) bt(2) bt(1) bt(0) bt(0) 1+ bt(1) 2+ bt(2) 2 2+ + bt(7) 2 2 6/24
Features of Bt-plane 8 bt-planes from most sgnfcant bt-plane(msb-p) to least sgnfcant btplane(lsb-p): Bt-planes(0) Bt-planes(7) orgnal mage For every bt-plan, there s a dfferent contrbuton to orgnal gray mage. The mpact can ncrease when the bt-plane s from LSB-P to MSB-P. 7/24
Features of Bt-plane another mportant fact s that the relaton between two adjacent btplanes s also ncrease for the hgher bt-planes. The relatonshp between bt-plane(6) and bt-plane(7) 8/24
Features of Bt-plane for obtanng the relatonshp between gray-scale mage and the correspondng bt-planes, such a test s done: CS()=Ibt()/255 Ibt() {128, 64, 1} 9/24
Why Bt-plan Can Be Used (1) Each bt-plane has an effect to orgnal dgtal mage. However, the mpact of the bt-plane s dfferent. (2) For the bt-plane, only 0 or 1 n each poston of pxel. It can decrease the calculated amount, and the bt-plane s easy to deal wth. 10/24
Detals Informaton of Scramblng Scheme The Spatal Dstrbuton Entropy of Dgtal Image the dstrbuton of 0 and 1 > the uncertanty of pxel values Sun et al. proposed spatal dstrbuton entropy. (Sun J, Dng Z, Zhou L. Image Retreval Based on Image Entropy And Spatal Dstrbuton Entropy. J. Infrared Mllm. Waves. 24: 135-139, 2005) on the assumpton that there are N knd of pxel values B 1, B 2, B 3,, B N, S q ={(x, y) (x, y) U, p(x, y) = B q, q [1, N] }. calculate the centrod of S q, and ensure some rng cycles accordng to centrod and radus whch produced by segmentaton wth equal dstance or unequal dstance. 11/24
Detals Informaton of Scramblng Scheme Fnally, for the pxel value B q, the spatal dstrbuton entropy can be expressed as: E s q k j1 where k s the number of rng cycles, p qj = R qj / R, whch s the probablty densty of B q n rng cycle j. R s the number of B q n S q, R qj s the number of B q n rng cycle j. p qj ( log 2 p qj ) 12/24
Detals Informaton of Scramblng Scheme In our scheme s cut: Such as: Ths average partton s appled n the bt-plane: {0,1,2,3,4,5,6,7} or {4,5,6,7} 13/24
Detals Informaton of Scramblng Scheme The Centrod Dfference n Bt-plane Centrod whch s a math tool s always used n engneerng applcaton feld, such as mechancal manufacturng, archtecture desgn, computer graphcs and so on. X m k 1 k 1 M M X ; Y m For the bt-plane, we can suppose that each pxel has qualty -0 or 1.That s to say, for every block, the correspondng Centrod can be h h calculated as: X rg m X k 1 k 1 M Y M 1 rg 1 ; Y h m h n 1 1 (X m, Y m ) s the correspondng centrod. Y n M s the qualty of M (x,y) (X, Y ) s the locaton 14/24
The Centrod of whole mage s acqured by the followng: Therefore, the Centrod dfference s express as: Detals Informaton of Scramblng Scheme r t t h r t t rg m h g m r t t h r t t rg m h g m n n Y Y n X n X 1 1 1 1 1 1 1 1 ) ( ) ( ; ) ( ) ( 2 2 ) ( ) ( g c g m g c g m g Y Y X X dffva 15/24
Detals Informaton of Scramblng Scheme The scramblng degree s based on the above Spatal Dstrbuton Entropy and Centrod dfference. The fnal value of scramblng degree(scraderee) s calculated as followng: g scraval Spatal Dstrbuton Entropy Centrod dfference 7 g scraderee w( g) scraval ; g {0,1,2,3,4,5,6,7} g0/ 4 16/24
Detals Informaton of Scramblng Scheme w(g) s the correspondng weght for scraderee: (1) For 8-bt plane: CS() s the weght. {0,1,2,3,4,5,6,7} (2) For 4-bt plane: 17/24
Smulaton Experments on Proposed Scheme Two typcal scramblng map: Arnold cat map Generalzed Gray code 18/24
Smulaton Experments on Proposed Scheme The followng four mages are used n the proposed scheme: Baboon, Boat, Internetgrl and Landscape. 19/24
Smulaton Experments on Proposed Scheme The scramblng degree under one perod: (16 16) The max values half-perod phenomenon 20/24
Smulaton Experments on Proposed Scheme The scramblng degree under one perod: (32 32) The max values half-perod phenomenon 21/24
Smulaton Experments on Proposed Scheme Some phenomenon are presented: 1. The max and mn scramblng degree to demonstrate the teraton number. 2. Half-perod phenomenon n the scramblng transformaton wth a long perod. 3. The scramblng degree n 4-bt planes and 8-bt planes. 22/24
Conclusons One scramblng evaluaton scheme s gven 8 bt-planes or 4 bt-plans are used n our evaluaton system. The scramblng degree can be the same for some gray-scale mage The spatal dstrbuton entropy of dgtal mage and centrod dfference n bt-plane are used for textng the scramblng degree 23/24
Thank you very much, every researcher 24/24