A Multi-Functional Cellular Neural Network Circuit Using Pulse Modulation Signals for Image Recognition

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1 A MultFuctoal Cellula Neual Netwok Ccut Usg Pulse Modulato Sgals fo Image Recogto Takash Moe, Makoto Myake, Sech Nshjma, Makoto Nagata, ad Atsush Iwata Faculty of Egeeg, Hoshma Uvesty HgashHoshma, Japa Abstact Ths pape poposes a multfuctoal cellula eual etwok (CNN) ccut based o abtay olea fucto geeato usg pulse modulato sgals. The poposed ccut mplemets dscetetme cotuousstate CNN dyamcs, ad pefoms umecal calculatos based o aalog epesetatos usg pulse wdths. We peset a cell ccut that ca mplemet a esstvefuse etwok ad a CNNbased Gabotype flte, whch ae useful fo mage segmetato ad featue extacto. We have desged a oedmesoal esstvefuse etwok ad a Gabotype flte ccut usg the cell ccut based o.6µm CMOS techology, ad have vefed the opeato by usg HSPICE smulato. Itoducto Cellula eual etwoks o cellula olea etwoks (CNN) povde a attactve paadgm fo vey lagescale tegated (LSI) ccut achtectue applcatos devoted to pxelpaallel mage pocessg. The esstvefuse etwok s wellkow as a effectve model fo mage segmetato, ad some aalog ccuts mplemetg ths model have bee poposed []. Gabo flteg s a effectve method fo extactg the featues of mages, ad t s kow that such flteg s used the huma vso system. A flexble face ecogto techque usg ths method has also bee poposed [2]. To mplemet Gabotype flteg usg aalog ccuts, CNN models have bee poposed, ad aalog ccuts fo them have bee desged [3, 4]. Sce the aalog appoach mplemets cotuoustme ad cotuousstate dyamcs, t acheves fast covegece. It also leads to the small ccut sze, thus massvelypaallel pocessg ca be pefomed. Howeve, a pactcal desg fo pxelpaallel aalog CNN ccuts coespodg to eal mage szes (moe tha ) s vey dffcult to ealze because of uexpected paastc compoets ad vaous dstubace such as ose, tefeece, ad devce paamete msmatch. I addto, t s dffcult fo the aalog appoach to acheve abtay olea tasfomato, thus vaous types of CNN models caot be mplemeted by the same ccut. A pulsewdth modulato appoach s oe techque fo achevg tmedoma aalog fomato pocessg usg pulse sgals whch have dgtal values the voltage doma ad aalog values the tme doma. The PWM appoach s sutable fo the lagescale tegato of aalog pocessg ccuts because t matches the scalg ted S CMOS techology ad leads to low voltage opeato. It also has hgh cotollablty ad allows hghly effectve matchg wth oday dgtal systems. PWM ccuts ae stable ad obust agast vaous dstubaces asg eal LSI systems. We have aleady poposed a ccut pcple fo abtay olea tasfomato usg coveso fom a pulsewdth/pulsephase modulato (PWM/PPM) sgal to aalog voltage[5]. Ths pcple makes t possble to ealze abtay dscetetme cotuousstate olea dyamcal systems. O the bass of ths pcple, we desged ad fabcated a abtay chaos geeato ccut, ad tested ts pefomace [6]. We also desged a olea oscllato etwok ccut fo mage segmetato ad vefed ts opeato by usg HSPICE smulato [7]. I ths pape, we popose a CNN ccut wth abtay olea (omootoe) fuctos based o pulse modulato techques. I Sec. 2, we toduce pulse modulato ccut techques fo weghted summato ad abtay olea tasfomato, whch ae basc fuctos equed fo eual etwoks. I Sec. 3, we peset a pulse modulato CNN ccut. I Sec. 4, as CNN models fo mage pocessg, esstvefuse ad Gabotype flte etwoks ae poposed, ad the smulato esults ae peseted. Fally, we povde the cocluso Sec Pulse Modulato Ccut Techques fo CNN 2. Weghted Summato Iputs to a PWM ccut ae PWM pulses. PWM put sgals havg pulsewdth W,( = ;2;3; ), dve the coespodg cuet souces, ad cuets I flow to capacto C dug peod W as show Fg.. The umbe of chages stoed the capacto, Q sum, ad the temal voltage of the capacto, sum, ae Q sum = I W ; ()

2 PWM sgals W ON OFF W 2 W 3 Swtched Cuet Souce (SCS) I 3 I I2 cuet (weght) sum C Wsum Wsum Fgue : Weghted summato usg PWM sgals. W P o C F(t) SW W P P F(W) F(W) P W W sum tme o tme Fgue 2: Pcple of abtay olea tasfomato usg a PWM sgal. sum = Q sum C = I W C ; espectvely. Thus, the weghted summato esult of the PWM data s obtaed the fom of the umbe of stoed chages o the temal voltage of a capacto. The, voltage sum s lealy tasfomed to a put PWM pulse wth a wdth of W sum by compag lealyamped efeece voltage l. I CNN dyamcs, postve ad egatve stateupdatg s equed. Such bpola updatg ca be acheved by chagg o dschagg the sgle capacto by usg postve ad egatve cuet souces. 2.2 Abtay Nolea Tasfomato The pcple of abtay olea tasfomato usg PWM sgals s oe of pulsevoltage coveso usg a sample ad hold opeato of a abtay olea voltage wavefom F(t) as show Fg. 2 [5]. The olea tasfomato fom PWM to PWM pulses poceeds as follows: Refeece voltage o whose wavefom tmedoma s gve by a abtay olea fucto F(t) s suppled to capacto C va swtch SW. The swtch s cotolled by put PWM pulse P, whee we assume o = F() at the leadg tal data put 2 I I O I CI CO SEL to othe cells PWM pulses fom othe cells ad bas pulses S_RE DIF s q RSFF N N2 DIF 2 S (H/L) S 2 2 W W2 N N2 N N2 Fgue 3: PWM CNN cell ccut. S C o C2 WW2 edge of P. Swtch SW s the ONstate dug peod W. Whe the swtch s tued off at the talg edge of P, the voltage of the capacto ode,, s kept at F(W ). Thus, we obta = F( ). oltage s lealy tasfomed to put PWM pulse P by compag lealyamped efeece voltage l.asa esult, the elatoshp betwee the pulse wdths of P ad P s gve by W = F(W ). Sce the PWMchagesPWM tasfomatos ae aalog opeatos, much atteto should be pad to the desg of the coespodg ccuts. Howeve, establshg the desg ctea the peset case s ease tha the pue aalog appoach because aalog pats PWM ccuts ae localzed. The easo ths appoach s useful s that t allows us to easly geeate F(t) by usg vaous oscllato ccuts o a combato of dgtal appoaches (lookup tables o fucto geeato) ad D/A covetes. I the latte case, basc wavefom data ae abtaly geeated by dgtal ccuts; addto, the wavefoms ca be chaged ealtme wth hgh cotollablty. Ths meas that the putput fuctos ca be chaged abtaly ad ealtme. Sce a D/A covete opeatg at moe tha MHz ca be fabcated usg submco CMOS techology [8], the olea tasfomato ccut ca opeate at moe tha MHz wth moe tha 6 bt pecso. Because commo wavefom geeatos ca be shaed by may tasfomato ccuts, the ovehead of wavefom geeato s mmzed. 3 A PWM CNN Ccut A PWM ccut seally mplemets the dscetetme dyamcs of CNN, although t spatally pefoms massvely paallel opeato. I cotast wth pue aalog ccut mplemetato, the PWM appoach e tme

3 ques moe tme to each steady states, but t should have much hghe cotollablty because t umecally solves the dyamcs by usg aalog pulse wdths. A cell ccut of PWM CNN s show Fg. 3. The put ad put of cell ae deoted by I ad O, ad ae tempoaly stoed at capactos C I ad C O, espectvely. The put value I ad the tal value of O ae dowloaded fom the host compute, ad O s updated accodg to the followg dscetetme dyamcs. O (t ) O (t)= G jk (O j O k )F j (O j I ); j;k2n (2) whee N epesets eghbo cells of cludg cell tself, ad G jk ( ) ad F j ( ) ae abtay odd fuctos. The updatg pocess poceeds as follows:. Selecto SEL selects a set of sgals to be calculated, whch coespods to oe tem o the ght sde of Eq The absolute value ad the sg of the dffeece betwee the two sgals such as O O k o O I s calculated by ccut DIF. The absolute value ad the sg bt ae stoed by capacto C ad a flpflop (RSFF), espectvely. The sg bt detemes whethe the postve o egatve updatg of O s pefomed. 3. The voltage stoed capacto C s coveted to a PWM pulse, ad t swtches the voltage souce o whose voltage wavefom the tme doma s the same as the coespodg (olea) fucto (G jk ( ) o F j ( )). Thus, capacto C 2 holds the value of the coespodg tem Eq The voltage stoed capacto C 2 s aga coveted to a PWM pulse, ad t swtches the cuet souce I o I. Output O s thus updated by the coespodg tem. 5. Repeatg the above pocesses, O s updated by aothe tem. 4 CNN models fo mage pocessg 4. ResstveFuse Netwok Model The esstvefuse etwok s show Fg. 4. The steady state of the etwok s obtaed by mmzg the followg fucto E []: E = σ 2 Z O Ok k2n G()d (O I ) 2 ; (3) whee, σ s a costat, ad G( ) s the cuetvoltage chaactestc of the esstvefuse show Fg. 4(b). It s gve by» G()= exp( 2η(δ 2 2 )) R ; (4) esstvefuse (a) esstvefuse etwok G() δ δ O I σ aealg Ok η=. η=. η=. η=. (b) esstvefuse chaactestc Fgue 4: Resstvefuse etwok model. whee, η, δ ad R ae costats. Ths esstvefuse devce s cosdeed a lea essto whe η =, whle t s a complete esstvefuse whe η = ; the eghbog cells ae dscoected whe O O k > δ, ad edge detecto s pefomed, whle the esstace s lea whe O O k» δ, ad a smoothg pocess s pefomed. The PWM CNN ccut obtas the mmum of E by usg a steepest descet method: O (t ) = O (t) ν E O ; (5) E = O σ (O I ); (6) k2n G(O O k ) whee ν s a costat. To avod eachg local mma, the ccut pefoms a aealg pocess by chagg the shape of G( ),.e., by ceasg paamete η, as show Fg. 4(b). We have desged a D esstvefuse etwok ccut wth 2 cells. The esult of HSPICE smulato s show Fg. 5. It vefes that the PWM CNN ccut opeates as a esstvefuse etwok, ad t smultaeously pefoms edge detecto ad smoothg, thus mage segmetato s acheved. 4.2 CNNbased Gabotype Flteg A D CNN ccut pefomg Gabotype flteg s show Fg. 6 [3]. The cell cossts of two odes coespodg to eal ad magay pats. The covoluto keel ealzed ths ccut s h()= λ 2 e λjj e jω ; (7) Ik

4 oltage (I, O) [] O I Pulse wdth [a.u.] Real pat Imagay pat Cell () Fgue 5: HSPICE smulato esult of a esstvefuse etwok usg the PWM CNN ccut Cell () Fgue 7: HSPICE smulato esult of a D Gabotype flte usg the PWM CNN ccut. The put s oly gve at the sxth cell. λ = :7;ω = π=4. G G G By usg wdths of PWM sgals, W, stead of voltages v Eq. 8, we obta the followg dscetetme dyamcs fo ou PWM CNN ccut: G G G λ 2 I() Fgue 6: D CNN ccut pefomg Gabotype flteg, whee G = 2 λ 2 2cosω sω, = cosω, = sω. whee λ s a costat, ad ω s a fequecy. The dyamcs of ths ccut ae expessed by two ode voltages v ad v fo each cell:» v v» = cosω sω sω cosω» 2λ 2 2 λ 2 cosω sω» sω cosω» λ 2 I» v v» v v» v v : (8) I ode to mplemet these dyamcs ou PWM CNN ccut, ths equato s modfed so that each tem s expessed by a dffeece betwee two vaables (o betwee a vaable ad a costat). Sce vaables v ad v ca be postve o egatve, we defe W as the pulse wdth coespodg to zeo value, ad epeset egatve value by a PWM pulse wth a wdth less tha W. W W (t ) W (t) = λ 2 (I W ) cosω (W W ) cosω (W W ) sω (W W ) (2λ 2 )(W W ); W W (t ) W (t) = cosω (W W ) cosω (W W ) sω (W W ) (2λ 2 )(W W ): (9) We have desged a D Gabotype flte ccut wth cells, each of whch cossts of two PWM CNN cell ccuts. The esult of HSPICE smulato s show Fg. 7. It vefes that the PWM CNN ccut opeates as a Gabotype flte ccut. 5 Cocluso We poposed a multfuctoal CNN ccut based o abtay olea fucto geeato usg PWM sgals. Ths PWM ccut seally mplemets the dscetetme dyamcs of the CNN whle t spatally pefoms massvelypaallel opeato. Although the PWM appoach eques moe tme to each steady states tha does the pue aalog appoach, t should povde much geate cotollablty ad obustess because t umecally solves the dyamcs by usg aalog pulse wdths. By usg the basc cell ccut, we desged a D esstvefuse etwok ad a Gabotype flte ccut based o.6µm CMOS techology, ad vefed the opeato by usg HSPICE smulato.

5 ACKNOWLEDGMENT Ths wok was suppoted by a Gatad fo Scetfc Reseach fom the Msty of Educato, Scece ad Cultue of Japa. Refeeces [] J. Has, C. Koch, ad J. Luo, Resstve Fuses: Aalog Hadwae fo Detectg Dscotutes Ealy so, C. Mead ad M. Ismal, edtos, Aalog LSI Implemetato of Neual Systems, pp Kluwe Academc Publshes, 989. [2] M. Lades, J. C. obügge, J. Buhma, J. Lage, C. v.d. Malsbug, R. P. Wütz, ad W. Koe, Dstoto Ivaat Object Recogto the Dyamc Lk Achtectue, IEEE Tas. Comput., vol. 42, o. 3, pp. 3 3, 993. [3] B. E. Sh, GaboType Flteg Space ad Tme wth Cellula Neual Netwoks, IEEE Tas. Ccuts & Syst. I, vol. 45, pp. 2 32, 998. [4] B. E. Sh, 2D Focal Plae Steeable ad Scalable Cotal Fltes, Poc. It. Cof. o Mcoelectocs fo Neual, Fuzzy ad Bosped Systems (McoNeuo), pp , 999. [5] T. Moe, S. Sakabayash, H. Ado, M. Nagata, ad A. Iwata, Pulse Modulato Ccut Techques fo Nolea Dyamcal Systems, Poc. It. Symp. o Nolea Theoy ad ts Applcato (NOLTA 98), pp , CasMotaa, Sept [6] K. Muakosh, T. Moe, M. Nagata, ad A. Iwata, A Abtay Chaos Geeato Coe Ccut Usg PWM/PPM Sgals, Asa ad Sh Pacfc Desg Automato Cofeece (ASDDAC2), pp., Tokyo, Ja. 2. [7] H. Ado, M. Myake, T. Moe, M. Nagata, ad A. Iwata, A Nolea Oscllato Netwok fo Gaylevel Image Segmetato ad PWM/PPM Ccuts fo Its LSI Implemetato, IEICE Tas. Fudametals., vol. E83A, o. 2, pp , 2. [8] J. M. Foue ad P. Se, A 3MHz 8b CMOS deo DAC fo HDT Applcatos, IEEE J. SoldState Ccuts, vol. 26, o. 7, pp , 99.

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