Performance requirements of the Mojette Transform for internet distributed databases and image processing

Transcription

1 Performance requrements the Mojette Transform for nternet dstrbuted databases and mage processng P. Serföző*, J. Vásárhely*, P.Szoboszla**, J. Turán*** * Unversty Mskolc, Department Automaton, Mskolc, Hungary ** Ercsson Hungary, Budapest, Hungary *** Department Electroncs and Multmeda Communcatons, Techncal Unversty Kosce, Slovaka Abstract In the last ten years there were ntensve researches to fnd new methods for handlng nternet dstrbuted databases and mage processng. One these methods s the Mojette transform (MOT). Ths transform s an exact dscrete Radon transform defned for a set specfc projectons. The MOT s used manly n mage processng applcatons. There were several mplementaton usng personal computers [8] and [9], but these applcaton were mplemented only for locally stored mages. There are some applcatons where real tme computng s a must, but the mplementatons before referred can not accomplsh ths requrement. The Mojette transforms mplemented under dfferent operatng systems and for dfferent processors presented below helps the performance analyses the MOT and also let to conclude the need for reconfgurable hardware mplementaton. There s also analyzed the mplementaton Mojette transform and Inverse Mojette transform (IMOT) the mplementaton n Feld Programmable Gate Arrays usng reconfgurable platform. The paper tres to conclude the necessty for hardware mplementaton for real tme processng. The paper outlne the development work n order to create an embedded reconfgurable hardware based on FPGA board. I. INTRODUCTION The word Mojette comes from France (Poters), where - n old French - t descrbes the class whte beans. These whte beans where used to teach chldren to start computng bascs arthmetc (addton and subtracton). Guédon named the transform Mojette after the analogy beans and bns. The bns contan the sum pxel values the respectve projecton lne [0]. Inscrbng nvsble marks (watermarkng) nto an mage has dfferent applcatons such as copyrght, steganography or data ntegrty checkng. Many dfferent technques have been employed for the last years n dfferent spaces (Fourer, wavelet, Mojette domans, etc.) [-0]. The applcatons come from dfferent feld such as computer tomography [], nternet dstrbuted data bases [4], encodng, multmeda error correcton [2], etc. Untl today the am the researches was stware mplementaton the Mojette and nverse Mojette transform. Ths knd mplementaton can be used only on stll mages, because they can not process the data n real-tme. Moton pctures, vdeo streams and dstrbuted data bases requre run-tme processng the frames. Only specalzed hardware or embedded systems wth real-tme operatng systems can ensure ths. II. DIRECT MOJETTE TRANSFORM The man dea behnd the Mojette transformaton (smlarly to the Radon transformaton) s to calculate a group projectons on an mage block. [3]. The Mojette transform (MOT) (see [5], [6] and []) projects the orgnal dgtal 2D mage: F { F(,j);,, N; j,, M} (.) onto a set K dscrete D projectons wth: M { M k (l); k,, K; l,, l K } (2.) MOT s an exact dscrete Radon transform defned for a set S {(p k, q k ), k,, K} specfc projectons angles: M K () l proj( pk, qk, bl ) F(, j) δ ( bl (, j) L q k jp ) k (3.) where proj (p k, q k, b l ) defnes the projecton lnes p k, q k ;δ(x) s the Drac delta wth the form: and ( ), f _ x 0 δ x { (4.) 0, f _ x L {(, j); b q jp 0} (5.) l k k s a dgtal bn n the drecton θ k and on set b l. So the projecton operator sums up all pxels value whch centers are ntersected by the dscrete projecton lne l. The restrcton angle θ k leads both to a dfferent samplng and to a dfferent number bns n each projecton (p k, q k ).

2 For a projecton defned by θ, the number bns n can be calculated by: n ( N ) p + ( M ) q + (6.) The drect MOT s depcted for a 3x3 pxel mage and for 3x3 pxel unary mage n Fg.. a and b. The set three drectons S {(-, ), (, ), (, 0)}, gves the thrteen bns for nteger values (*.pgm fles Portable Grey Map format fle wth 256 grey tones) and unary mage. The MOT can be ether performed by drectly addton the mage grey values or by addto-modulus (to preserve the magntude the computed spectral coeffcents). For bnary mages operaton XOR may be used (see [5], [6] and []). III. INVERSE MOJETTE TRANSFORM The nverse Mojette transform (IMOT) back-projects the bns the dfferent projectons onto the reconstructed mage. That means a sngle pxel bn correspondence must be found at each teraton n order to reconstruct a pxel value. When t has been done, ths pxel value s subtracted from each projecton. The Inverse Mojette Transform means to terate ths process untl the mage s completely reconstructed. For the reconstructon one need two projecton sets, one s the MOT the mage and the other s the MOT a unary mage (each pxel value s ). Fg.. c and d shows the frst step the reconstructon process. A. The condton reconstructon The key the transform wth regard to the controlled redundancy s that the number computed projectons can be larger than one need for the reconstructon (nverse transform). Thus, we can control a frst step redundancy wth the number projectons. The queston s then to know how many projectons and whch projectons gve an adequate set to reconstruct the mage (compute the Inverse Mojette Transform). The result was gven by Katz n 99 for rectangular mage [5]. Accordng to Katz s lemma [5], an mage F dmenson NxM pxels can be reconstructed wth the set K projectons M {M k } f K N P K p k k K or M Q K q k k (.) where N x M s the mage sze, p k s the drecton coordnate x axs (N), q k s the drecton coordnate y axs (M). Ths means that for the reconstructon one need as many projectons as the sum the absolute value the projecton coordnates have to be equal or greater then the dmenson the mage n the same drecton. The order complexty the MOT s lnear both n the number projectons and the number pxels. In order to obtan the same complexty for the IMOT, a specfc lst sngle pxel-bn correspondence has to be created and managed [6, ]. There s no need that both sums satsfy the crtera, t s suffcent f one the sums does. The man characterstc the MOT s the redundancy, whch can be measured by the followng parameter: bns R pxels (8.) Due to the ll-posed nature the IMOT mportant degradaton occurs when the bns have been slghtly modfed durng the transfer (.e. before the IMOT process start). [5], [6] and []. IV. 5 p,q (,), (-,), (0,) a, b, c, d, Fg.. The drect Mojette transform for real valued (a) and unary (b) mage and the frst step the reconstructon process (c and d) MOTITIMOT CO-PROCESSOR IMPLEMENTATION HARDWARE NEEDS The MOTIMOT co-processor denotes the hardware mplementaton the drect and nverse Mojette transform as co-processng element an embedded processor. To estmate the hardware and stware needs for a MOTIMOT system there s necessary to map the resources what such a system should need. These resources are not lmted to the drect and nverse Mojette transformaton, but also posses embedded computer functons mplemented n an embedded system runnng a real tme operatng system. Snce the data are dstrbuted thru the nternet we suppose that the database elements or the mages are receved n real-tme thru an Ethernet connecton or from a dgtal camera connected to the platform and transmtted on the nternet after the mage are transformed wth the MOT. The MOT and IMOT functons are mplemented as separate hardware co-processors the man processor. For the moment the MOT has been mplemented n stware n order to be able to compare dfferent hardware platforms wth dfferent operatng systems. The Vrtex2P FPGA has and embedded Power PC, Ths processor wll execute the MOT transform and we can compare ts performance wth other platform performances. As stated n [5] real tme mage processng needs very hgh computng performances wth relatvely low power dsspaton, whch condton can not accomplshed by PC

3 and fxed pont DSP. Whle usng FPGA the advantage s usng embedded on-chp processors wth on-chp memory and on chp system bus. For ths reason and for the flexblty was chosen Vrtex FPGA based platforms. These boards are Xlnx embedded system boards and for detals see [3] and [20]. The man advantage usng FPGAs s the flexblty development tools, the hardware-stware co-desgn soluton, and hardware n the loop smulaton. Also as the result ths mplementaton the MOT and IMOT mplemented by parallel functons nstead sequental ones s much faster then the stware mplementaton. For tests was chosen a 256x256 pxel szed grayscale mage, whch requres 64KB memory for storage. The bn vectors are stored n the memory n a so called MOT memory fle. The dmenson the MOT memory fle s gven by the product between the mage slces, the number bns n (see eq. 6.) and the maxmum sze a bn, whch s gven below: λ mn( N mod p, M mod q ) (9.) bn _ sze max[{ λ, w] (0.) max( bt _ nr) C + ( bn _ szemod2 + x) (.) where mem x fle _ sze + 0 f bn _ sze 2k, k Z f bn _ sze 2k +, k Z n n max( bt _ nr), (2.) + slces where N, M, p, q were specfed n eq. (6), λ s the maxmum number pxels contaned by a bn n the th projecton lne, w s the number projecton lnes, C s the color depth the orgnal mage (8 bts for a *.pgm), bn_sze s the maxmum number pxels contaned by a bn for any projecton lne, n s the number bns n the projecton lne and n slces s the number mage slces. An mage slce s obtaned by the dvson the mage by an even number. The dvson the orgnal mage n slces s motvated by the fact that durng the transmsson the MOT fle ths can be corrupted. From the corrupted MOT fle the mage can not be reconstructed wthout damaged area. Whle applyng the Mojette transform to slces the effect the MOT corrupton s dmnshed. Also the memory necessary to calculate the MOT and IMOT s smaller n the case slces. Processng the whole mage would result n the need for reconfguraton n order to calculate all the projectons, because to load the 256x256 mage n the embedded memory need 256KB only for 4 projecton lnes [2]. For ths reason the 256x256 pxel mage s dvded n 4 slces (28x28). Whle processng the IMOT (for the same mage sze) one needs to read the MOT memory fle from the external memory and to reconstruct the mage. For the reconstructon one need to generate the MOT fle the same sze unary mage wth the same projecton lnes. From eq. (0) the bn_sze means the maxmum pxel numbers contaned by a bn and also defnes the number bts needed for the unary bns the unary MOT fle. Durng the back projecton (IMOT) the bns whch contan only one pxel value are substtuted to ther correspondng poston. These pxel values contaned by other bns (n other projectons) also and those bn values have to be decreased wth the current pxel value. To calculate the postons the bns n the projectons and to calculate the correspondence n the mage a sngle pxel bn the unary mage s needed. It results when the value a sngle pxel bn s substtuted and the other bn values are decreased, the changes also have to be valdated n the unary MOT fle. The unary MOT fle contan unary bns. These bns contan not only the current pxel number contaned by the bn n the MOT fle but the correspondng poston n the mage these pxels to. Snce there s no need to process at the same tme the MOT and the IMOT there s the possblty to actvate only one co-processor at a tme by usng partal run-tme reconfguraton. The reconfguraton s actvated by the embedded Power PC processor usng the ICAP nterface. The proposed MOT/IMOT hardware s strongly dependent by the board structure gven n [3] or [20]. Ths dependency constran only the communcaton channels to the devces from whch the mages are receved, but do not mpose lmts to the co-processor mplementatons. A. The IMOT mplementaton Fg. 2 shows the nternal block schema a MOT/IMOT computng hardware wth the IMOT coprocessor actve. In the fgure the MOT/IMOT s represented as a sngle block, snce the mplementaton area needed for one them wll be used to mplement the other one, ths may explan why partal reconfguraton s needed. Fg. 2 summarzes only the man parts the mage processng system. Ths are: the PowerPC as the man processng unt and the IMOT unt. The IMOT coprocessor s connected to the PowerPC va the nternal PLB bus. The co-processor read and wrtes data to the dual memory, whch s the nterface memory when the perpherals were generated n the Embedded Development Kt (EDK) Fg. 3 represents the detaled block dagram the IMOT co-processor. The IMOT fle s sent n quarter mage fragments by the man processor va the PLB (processor local bus). In Fg. 3 the co-processor reads the IMOT from memory va the PLB n drect memory access mode (DMA), the bns are wrtten n the reconstructon blocks (P, P2, P3, P4) together wth ther ndex. The pxel ndex s computed from the bn ndex by the pxel ndex computng sub-block. The pxel ndex s wrtten to the pxel value storage regster the correspondng drecton (qs*8bt). In parallel to ths the other blocks (P2, P3, and P4) receve the bn value and the pxel ndex. From the receved pxel ndex every block computes the correspondng bn ndex and decreases ther bn value wth the receved bn value and valdates the changes n the correspondng dual memory

4 block. The co-processor block s synchronzed by an IMOT fnte state machne not represented n Fg. 3. motherboard, processor PowerPC 405, CPU frequency 00 MHz; processor local and on chp perpheral bus frequency PLB/OPB/OCM: 00 MHz; DDR: 00 MHz, 32-bt;, 256MB DDR DIMM, System ACE CF controller, 52 MB Compact Flash card, onboard 0/00 Ethernet network nterface card. In the frst step the FPGA mplementaton ML30 the operatng system used for platform support was Lnux. Fg. 2. MOTIMOT block schema wth the IMOT co-processor. Two dfferent types FPGA boards were consdered n the development phase because the hardware resources the two dfferent FPGAs (Vrtex4 and Vrtex2P) are dfferent and also the board characterstcs are dfferent. B. The MOT mplementaton In order to have benchmark tests the Drect Mojette transform and the nverse transform also was mplemented n stware usng C programmng language. For the performance test were used dfferent hardware platforms wth dfferent operatng systems and dfferent system confguratons. In ths paper we analyze the performance test for the followng platforms: - PC: The frst platform was an Intel the P4/3.4GHz processor based boar wth GByte DDR DIMM RAM/400MHz, 0/00 Ethernet network nterface card, 300GByte Wnchester; operatng system: Wndows XP. - PCL: The second platform s a Lnux based server wth the followng confguraton: number processors: 2. Processor 0 s: AuthentcAMD cpu famly: 5 model3 model name: AMD Opteron(tm) Processor 250, steppng:, MHz cache sze: 024 KB, floatng pont unt (fpu): yes fpu_excepton: yes, cpud level: wp : yes, bogomps: TLB sze: 024 4K pages clflush sze: 64 cache_algnment: 64 address szes: 40 bts physcal, 48 bts vrtual; Processor s: vendor_d: AuthentcAMD, cpu famly: 5, model: 3, model name: AMD Opteron(tm) Processor 250, steppng:, cpu: MHz, cache sze: 024 KB fpu: yes, fpu_excepton: yes cpud level :, wp: yes, bogomps: TLB, sze: 024 4K pages, clflush sze: 64, cache_algnment : 64, address szes: 40 bts physcal,. - ML30: The thrd platform s an FPGA based board, whch can be characterzed as follows: Vrtex-II Pro XC2VP30 FPGA, ATX form factor Fg. 3. IMOT detaled block dagram The MOT computng stware was run for 0 tmes n each platform and n the followng condtons: The processed mages had the followng dmensons: 52x52, 256x256, 28x96 pxel values and were dvded n 32x32 pxel slces; there were 3 knd tests as follows: a. Compute one frame 52x52 pxel dvded n 32x32 pxel slces; b. Compute 6 frame 52x52 pxel dvded n 32x32 pxel slces; c. Compute 24 frame 52x52 pxel dvded n 32x32 pxel slces; There were also consdered the same tests for the 52x52 pxel mages wth 6x6 pxel sze wndow, 256x256 pxel mages wth 6x6, 32x32 pxel sze wndow and 28x96 pxel mages wth 6x6 pxels sze wndow. The 28x96 pxel mages were consdered because the moble applcatons have general LCD graphc dsplay wth the mentoned dmenson. Table I. contans the mnmum and maxmum test results for the PC, PCL and ML30 platforms. From the table result that for the PC platform the average computng tmes are the longest compared to the other platforms. In Table I. one frame s one stll mage. Whle 24 frames represent one second an uncompressed moton pcture, the 6 frames represent one second a compressed vdeo.

5 TABLE I. TEST RESULT OF MOJETTE TRANSFROM ON 3 PLATFORMS Mn. max-mn P IV MHz W AMD Opteron 2x2400MHz W PowerPC MHz mW Table II. contans the speed rato the embedded PPC405 (platform ML30) compared to the other two mcroprocessors (platform PC and PCL). One can say that the embedded ML30 platform processng speed s just only ~0-2 tmes slower compared to the PC, and ~46 tmes slower compared to the PCL platform; whle the system clock frequency the PC s 34 tmes faster and the PCL system clock frequency s 24 tmes faster then the ML30 platform clock (00MHz). TABLE II. SPEED RATION OF EMBEDDED PPC405 COMPARED TO OTHER PROCESSORS PIV AMD Opt. PPC405 PIV PPC405 AMD Opt In Table III. are presented the test results the PPC405 mcroprocessor wth 32x32 pxel wndow for the MOT transform and for dfferent mage szes. One can conclude from the table that the computatonal tme s not growng parallel wth the mage sze. Another notceable result s the decreasng standard devaton when the computatonal tme ncrease (wth the mage sze). TABLE III. MOT COMPUTING PERFORMANCES FOR ML30 PLTAFROM Wndow: 32x32 28x96 256x256 52x52 Mn. maxmn Aganst the low power dsspaton the ML30 platform the mplemented stware soluton s unusable when real-tme computaton data s needed. One can conclude that hardware realzaton s necessary for the MOT dependng on the applcaton. Table IV presents the test results for the stware mplementaton the IMOT for dfferent sze mages wth 6x6 pxel sze wndow. The long processng tme for vdeo fles s not acceptable. Whle the data after the MOT s stored n a data storage devce, the reconstructed data (output the IMOT) s processed by an applcaton. The long computatonal tme requre a relatve large data buffer between the IMOT and the applcaton. TABLE IV. IMOT COMPUTING PERFORMANCES FOR ML30 PLTAFROM Wndow: 6x6 28x96 256x256 Mn. maxmn Today the portable devces are very popular and there s a real demand to ntegrate dfferent devces (telephone, mp3 player, TV) n one applance. An average LCD dsplay a normal moble phone have approxmately a dsplay sze 28x96 pxels. Test result MOT and IMOT on ML30 for ths sze mage (28x96 pxels) s represented n Table V. The man dea usng the ML30 and ts embedded PowerPC processor to compute MOT and IMOT s ts very low power consumpton. Unfortunately ths platform wth a Lnux kernel s not powerful enough for real-tme computaton n the case stware mplementaton the algorthm. As t s shown n the table computng the IMOT s more tme-wastng then computng the MOT data fle. However n the targeted applcaton (nternet dstrbuted vdeo data base) the IMOT computng s tme crtcal. Ths s another motvaton to mplement the MOT-IMOT n hardware. Wndow: 6x6 28x96 (MoT) 28x96 (IMoT) TABLE V. IMOT COMPUTATION PERFORMANCES Mn. max-mn The mnmum, maxmum and average computatonal tmes for the MOT n the case 28x96 pxel sze mage and dfferent wndow szes (6x6:, 2 and 3; 32x32: 4, 5 and 6)

6 are depcted n Fg. 4. tce that the stware mplementaton the algorthm s faster when 32x32 pxel sze wndow s used. Probably t s caused by the less overhead (n tme) the process creaton. tme [sec] Test results MoT computng mn dt [sec] max dt [sec] avg dt [sec] Fg. 4. The mnmum, maxmum and average computatonal tmes for the MOT for dfferent wndow szes From the test result t can be concluded that the ML30 platform runnng on 00MHz clock frequency t s just 5-6 tmes slower then the other two platforms runnng wth 34 and 24 tmes faster clock, but the computaton tmes s not slower as 34/24 tmes as expected. Analyzng the power dsspaton durng the computaton the MOT t can be fgured that the less power was dsspated by the ML30 platform consumng just around 00mW whle the PC platform dsspated between W, and for the PCL platform the dsspated power was even larger W. V. CONCLUSIONS There was mplemented n stware the MOT and IMOT for three dfferent platforms wth dfferent operatng systems. The mplementaton was motvated by the fact that the Mojette transforms wll be mplemented n hardware on the ML30 and ML403 platform. From the stware mplementatons result the followng conclusons: The expected computaton speed per workng frequency for the ML30 platform was not as bad as expected. te that the ML30 platform workng frequency s 00MHz, whle the other platforms run wth 2.4 and 3.4 GHz. The drect MOT transformaton s not so tme crtcal, but n some applcatons hardware mplementaton would be recommended. The IMOT for moble applcatons t should be mplemented n hardware snce the transformaton s tme crtcal for vdeo on demand applcatons. The dsspated power should be consdered n the case moble applcatons. In the paper were mentoned two dfferent FPGA hardware platforms. The man reason to consder these platforms s that the two platforms contan two dfferent types FPGAs. The ML 30 board s a PC form factor board platform contanng the Vrtex 2P FPGA wth the PC board possbltes (PCI, Ethernet, etc.), whle the ML30 board s small form factor board as powerful as the prevous one wth a Vrtex 4 FPGA chp. REFERENCES [] Hartung, F., Kutter, M.: Multmeda Watermarkng Technques, Proc. IEEE, vol. 8,, 999. [2] Turán, J.: Fast Translaton Invarant Transforms and Ther Applcatons, ELFA, Kosce, 999. [3] rmand, N., Guedon, J. P.: La transformee Mojette: une representaton recordante pour l mage, Comptes Rendus Academe des Scences de Pars, Theoretcal Comp. SCI. Secton, 998, pp [4] Guedon, J. P., Parren, B., rmand, N.: Internet Dstrbuted Image Databases. Int. Comp. Aded Eng., Vol. 8, 200, pp [5] Katz, M.: Questons unqueness and resoluton n reconstructon from projectons. Lecture tes n Bomathematcs, (Vol. 26), Sprnger-Verlag, Berln, 99. [6] Autrusseau, F., Guedon, J. P.: Image Watermarkng for Copyrght Protecton and Data Hdng va the Mojette Transform, Proceedngs SPIE, VOL. 465, 2002, pp [] Turán, J., Ovsenk, L., Benca, M., Turán, J. Jr: Implementaton CT and IHT Processors for nvarant Object Recognton System, Radoengneerng, Vol. 3, dec. page 65- [8] Autrusseau F.: Modélsaton psychovsuelle pour le tatouage des mages, Ph. D. Dssertaton, Nantes, France, 2002., pp. [9] Szoboszla P.: Dgtal Watermarkng wth Mojette and Wawelet transforms, Dploma work, Unversty Mskolc, Department Automaton, 2006, pp. 58. [0] Guédon J-P., rmand N.: The Mojette Transform: The Frst Ten Years, Proceedngs DGCI 2005, LNCS 3429, 2005, pp [] Guédon J-P., rmand N.: Splne Mojette Transform Applcaton n tomography and communcaton, In EUSIPCO, sep [2] Parren B., rmand N., Guédon J-P.: Multmeda Forward Error Correctng Codes For Wreless Lan, Annals Telecommuncatons (3-4) March-Aprl, [3] Xlnx, ML403 User Gude, [4] Bobda C., Huebner M., Nyonkuru A, Blodget B., Majer M., Ahmadna A.,: Desgnng Partal and Dynamcally Reconfgurable Applcatons on Xlnx Vrtex-II FPGAs usng Handel-C, /default.asp, pp. 6. [5] Amlcar do Carmo L., Hethecker S., Rolf E., FlexFlm An Image Processor for Dgtal Flm Processng, Dagstuhl Semnar on Dynamcally Reconfgurable Archtectures, [6] Hethecker S., Rolf E., FlexFlm: A Qualty Servce Capable Schedulng SDRAM Controller, Dagstuhl Semnar on Dynamcally Reconfgurable Archtectures, [] G. Eason, B. ble, and I. N. Sneddon, On certan ntegrals Lpschtz-Hankel type nvolvng products Bessel functons, Phl. Trans. Roy. Soc. London, vol. A24, pp , Aprl 955. [8] I. S. Jacobs and C. P. Bean, Fne partcles, thn flms and exchange ansotropy, n Magnetsm, vol. III, G. T. Rado and H. Suhl, Eds. New York: Academc, 963, pp [9] Y. Yorozu, M. Hrano, K. Oka, and Y. Tagawa, Electron spectroscopy studes on magneto-optcal meda and plastc substrate nterface, IEEE Transl. J. Magn. Japan, vol. 2, pp. 40 4, August 98 [Dgests 9 th Annual Conf. Magnetcs Japan, p. 30, 982]. [20] Xlnx, ML30 User Gude, [2] P. Serfőző, J. Vásárhely, Analyss Mojette Transform Implementaton on Feld Programmable Gate Array, Proceedngs the th Internatonal Symposum Hugaran Researchers on Computatonal Intellgence, Budapest, pp , ISBN X ACKNOWLEDGMENT The authors gratefully acknowledge the donatons Xlnx Inc. and Celoxca Inc.