Toward visual microprocessors

Towa d Visual Mic op ocesso s TAMÁS ROSKA, FELLOW, IEEE, AND ÁNGEL RODRÍGUEZ-VÁZQUEZ, FELLOW, IEEE In i ed Pape This pape ou lines mo i a ions and models unde lying he design o isual mic op ocesso s based on he cellula neu al ne wo k uni e sal machine. We also o e iew he s a e o he a ega ding he ealiza ion o hese mic op ocesso s in he o m o e y la ge-scale in eg a ion chips. Examples co esponding o measu emen s ealized on hese chips a e enclosed o illus a ion pu poses. Keywo ds—Analogic cellula supe compu ing, cellula neu al ne wo ks, CNN echnology, isual mic op ocesso s. I. INTRODUCTION Fo mo e han 100 yea s, he li ing isual sys em o mam- mals has been in ensi ely s udied by neu oscien is s and bio- physicis s alike. Recen ly, compu e enginee s ha e been ac- i e c ea ing machine ision sys ems. S ill, al hough many ideasha ebeenp oposedandimplemen edinsilicon[1]–[3], including esis i e g id “silicon e inas,” p og ammable cel- lula neu al/nonlinea ne wo k (CNN)1models o he isual pa hway, as well as many “sma op ical senso s,” no com- ple e neu omo phic model o he opog aphic pa s o he i- sual pa hway has been made a ailable. The eason is simple: he lack o unde s anding o he de ailed ope a ion o many key componen s loca ed a he on -end o he isual sys em, no ably, he e ina and he la e al genicula e nucleus (LGN). Hence, he ep esen a ion o he isual scene om he inpu o he highe laye s has been unknown. O he many exci ing Manusc ip ecei ed May 31, 2001; e ised Feb ua y 15, 2002. This wo k was suppo ed by g an s om he Hunga ian Academy o Sciences, he Spanish MCyT (P ojec TIC1999-0826), he Na ional Resea ch Fund o Hunga y (OTKA), he CEE (P ojec IST-1999-19007), and he O ice o Na al Resea ch (P ojec s N00014-00-C-0295, N68171 97-C- 9038 and N68171 98-C-9004). T. Roska is wi h he Analogic and Neu al Compu ing Labo a o y, MTA- SzTaki(Hunga ianAcademyo Science)andPázmányUni e si y,Budapes H-1111, Hunga y (e-mail: [email p o ec ed]). Á. Rod íguez-Vázquez is wi h he Depa men o Analog and Mixed-Signal Ci cui Design, IMSE/CNM, 41012 Se illa, Spain (e-mail: [email p o ec ed]). Publishe I em Iden i ie 10.1109/JPROC.2002.801453. 1Cellula neu al/nonlinea ne wo k (CNN) models we e in oduced by Chua and Yang in 1988 [5], and hen gene alized and used as a model o bionic eyes by Chua, Roska, and We blin [6]–[8]. Thei p inciples and ap- plica ions o isual p ocessing a e co e ed in [9]. pa ial esul s ela ed o he isualpa hway,some ecen ind- ings (see, o ins ance, [4]) sugges a ew sound p inciples. • Sensing and p ocessing a e in e ac i e p ocesses, and he p ocessing is mainly analog, combined wi h masks o bina y (yes/no) maps. • The basic s uc u e is composed o se e al s acks o laye s o neu ons connec ed by local ecep i e ield o - ganiza ions wi h di e en spa ial dis ibu ions and ime cons an s. • The p ocessing s a egy is a kind o “mul isc een he- a e ”; namely, om a gi en isual scene, se e al pa - allel maps a e gene a ed and hen u he p ocessed. This is ue e en in he mammalian e ina [4] whe e abou a dozen pa allel channels a e o ganized. To implemen neu omo phic isual models on silicon, we ha e wo ways: • Pick up a speci ic ask and i s model and implemen i on silicon. This is he usual way, leading o e y use ul, ask-speci ic sma senso s. • Make mixed-signal2 isual mic op ocesso s. Tha is, p ocesso s which combine op ical sensing wi h analog cellula spa ial- empo al dynamics and some o m o logic ( hey a e called analogic p ocesso s because hey combineanalogandlogicp ocessings uc u es),which ha e ecep i e ields like elemen a y ins uc ions, and he possibili y o s o ing and execu ing use -selec able sequences o ins uc ions (p og ams). Clea ly, he second app oach is mo e demanding in e ms o a chi ec u e, e y la ge-scale in eg a ion (VLSI) chip design, and compu a ional in as uc u e, leading o a new ype o ha dwa e/so wa e sys em design. This pape ocuses on he second app oach. Namely, we will b ie ly e iew he analogic cellula compu e a chi ec- u e,someCMOSp o o ypechips ela ed o ha a chi ec u e, and he accompanying compu a ional in as uc u e. Some examples measu ed om he so-called ACE4K chip [10] and he CACE1K chip [11] a e included o illus a ion pu poses. The o me has a one-laye a chi ec u e, while he la e has a h ee-laye a chi ec u e inspi ed by he CNN model o he 2Mixed-signal means ha analog and digi al signal ep esen a ions a e combined, and hence analog and digi al signal p ocessing. 0018-9219/02$17.00 © 2002 IEEE 1244 PROCEEDINGS OF THE IEEE, VOL. 90, NO. 7, JULY 2002 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 15,2020 a 14:17:43 UTC om IEEE Xplo e. Res ic ions apply. mammalian e ina p oposed in [12] based on he disco e ies abou he unc ionali y o he inne pa o his e ina as e- po ed in [4]. II. CNN-BASED VISUAL MICROPROCESSORS Back in he 1960s, he building blocks o logic design had been he a ious logic ci cui s (mic omodules) imple- men ing di e en “sma ” logic asks. These had also been used o make digi al compu e s. The digi al compu e has a key a ibu e due o J. Von Neumann, namely s o ed p o- g ammabili y. I means ha he same co e a chi ec u e, ia algo i hms coded in so wa e, can be used o a my iad o asks. O , o pu i in ano he way, he a chi ec u e is open o he human in ellec o millions o algo i hmic inno a ions. This is he unc ional sec e behind he success o he digi al mic op ocesso , i s made in he ea ly 70s. Visual mic op o- cesso s aim o mimic his unc ional sec e . Howe e , hey a emixed-signalde iceswhich ealizeanalog-and-logicspa- ial/ empo al p ocessing asks (wa e p ocessing), and hence equi e qui e di e en building blocks [3]. The on -end “de ices” encoun e ed in na u al ision sys- emsa ecapableo acqui ingandp ocessingimagesinacon- cu en manne . The e ina con ains pho o ecep o s and dy- namicallycoupledp ocessingcellso di e en ypes.Among many o he asks, he ea ly p ocessing ealized a he e ina se es oex ac impo an ea u es om he awsenso yda a and, hus, o educe he amoun o in o ma ion ansmi ed o subsequen p ocessing. In con as o ha , image acqui- si ion and p ocessing a e usually sepa a ed in con en ional a i icial ision sys ems. One key aspec o isual mic op o- cesso sis hein eg a iono sensingands o edp og ammable p ocessing (SPP) a he analog signal a ay le el— he in e- g a ed SPP p inciple. Among many o he hings, his allows us o une he senso s dynamically, pixel by pixel, depending on he con en and e en on he con ex o he changing scene. Some o he key a chi ec u al aspec s ha e been discussed in [13]. Some ea u es which make he isual mic op ocesso s ad- d essed in his pape di e en om o he opog aphic sma senso s [1], [2] include he ollowing. • They use a co e analog p ocessing a ay (a CNN [5]–[7]) wi h unable in e ac ion weigh pa e ns and embedded pixel-wise da a memo ies. • This p og ammable and econ igu able a ay is em- bedded in a compu e a chi ec u e esul ing in he so-called CNN uni esal machine (CNN-UM). • The CNN-UM is s o ed p og ammable and capable o implemen ing analogic spa ial– empo al algo i hms h ough he sma syne gy o ha dwa e and so wa e. All he signal a iables a e con inuous, excep o he dis- c e eness in space (pixels o oxels). A he same ime, isual mic op ocesso s e ain he ex ao dina y s eng h o digi al compu e s, hei uncons ained a iabili y ia p og amming o so wa e. Ob iously, such so wa e and ela ed algo i hms a e di e en om con en ional ones. Below we summa ize he main a chi ec u al and algo i hmic ideas unde lying CNN-based isual mic op o- cesso s. I is wo h men ioning ha al hough mos o hei p esen -day applica ions a e ela ed o ision, many o he Fig. 1. A ypical simple CNN s uc u e. Fig. 2. The s anda d ou pu nonlinea i y. opog aphic p oblems ( ac ile and audi o y), including opo- g aphic op imiza ion, a e among he eme ging applica ions. A. CNN Dynamics CNNs can be ei he single-laye o mul ilaye . Conside i s a single laye consis ing o a wo-dimensional (2-D), egula g id o cells , whe e and a e he ow and column coo dina es. The opog aphy o such a s uc u e is shown in Fig. 1. Assume each cell hos s a p ocesso wi h i s eal- alued inpu , s a e(s), and ou pu signals, , and , espec i ely. In such a 2-D laye , each cell p ocesso is con- nec ed o i s neighbo s (in a 3 3o 5 5, e c., neighbo - hood o sphe e o in luence), deno ed by . The sim- ples i s -o de cell s a e dynamics is gi en by3 (1) whe e is called he h eshold o he cell and a e called he eedback and eed- o wa d synap ic ope a o s o empla es; in case o a 3 3 neighbo hood o adius 1, hey a e 3 3 ma ices. The s a e and he ou pu signals o each cell a e ypically ela ed h ough he ollowing nonlinea ou pu equa ion: (2) depic ed in Fig. 2. Howe e , he nonlinea i y could be o se e al ypes and i could also be included in a simple dynamic equa ion o m. Namely, he s anda d nonlinea i y 3The ime is scaled in he ela i e ime uni  which is he ime con- s an o he simple i s -o de cell dyanmics. ROSKA AND RODRÍGUEZ-VÁZQUEZ: TOWARDS VISUAL MICROPROCESSORS 1245 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 15,2020 a 14:17:43 UTC om IEEE Xplo e. Res ic ions apply. Fig. 3. The ini ial pic u e and he di used pic u e using a di usion empla e de ined by gene G . in (2) and he cell-s a e dynamics ep esen ed by (1), he so-called Chua–Yang model, could be eplaced by he ull- ange model which means ha , and ha he i s e m in (1) is eplaced by a nonlinea unc ion whose shape is he in e se o ha used o he s anda d nonlinea i y [14]. Once he cell dynamics is ixed, he in e ac ion pa e ns and and he o se alue de ine he unc ionali y o he CNN laye . Gi en an inpu signal a ay o , de ined as a pic u e wi h pixel alues , he se o alues de e mines he ou come o he CNN dynamic p ocess. This se is called a cloning empla e o a gene. In he space-in a ian case, he empla es a e 3 3 (o 5 5o 7 7) ma ices. This means ha a CNN a ay can be de ined by he cell dynamics and he 19 (o 51 o 99) numbe s o he empla es and he o se . The inpu image could be ei he s a ic o dynamic; hence, a CNN laye plays he ole o an image p ocesso . The peculia p ope y o con olling he unc ionali y o a whole a ay o in e connec ed cells by means o jus a ew in e connec ion weigh s (e.g., 19 numbe s) is e y amilia o neu obiologis s. Indeed, he cloning empla e is no mo e han a ecep i e ield o ganiza ion in he e ino opic pa o he isual pa hway [8]. On he o he hand, he CNN pa a- digm is well sui ed o ep esen ing many opog aphic sen- so y modali ies ia hei ecep i e ield o ganiza ions. The i s a emp s [15] ha e been ollowed by many o he use ul esul s. In a non i ial case, he CNN dynamics is a wa e ac ing o a ini e ime . Fo example, o a di usion empla e o gene we ha e (3) Fig. 3 shows he ini ial s a e and he ou pu image (a elapsed ime). The e exis s a e y wide ca alog o empla es co e ing a my iad o applica ions. Also, because hese em- pla esa ep og ammablebyde ini ion,lea ning canbeinco - po a ed o adap he empla es ei he globally, o example, using a gene ic algo i hm [16], o locally. Thus, no only associa i e memo ies can be cons uc ed, e.g., [17], bu he plas ici y o he b ain migh be di ec ly modeled [13]. Fig. 4. The ex ended cell o he CNN-UM. B. The CNN-Uni e sal Machine (CNN-UM) [7] I we u nish each CNN cell p ocesso wi h local memo- ies [local analog memo y (LAM) and local logic memo y (LLM)] and a local communica ion and con ol uni (LCCU) o send/ ecei e in o ma ion o/ om he global analogic p o- g amminguni (GAPU), wege he ex endedCNNcell o he CNN-UM a chi ec u e. Fo p ac ical easons, in each cell we add a local logic uni (LLU) and a local analog ou pu uni (LAOU) which ake inpu s and send ou pu s om/ o hei local memo ies, LLM and LAM, espec i ely. Fig. 4 shows he ex ended cell schema ically. The GAPU is he conduc o o he ex ended cell a ay, communica ing wi h each cell ia he LCCUs o each cell. The GAPU con ains h ee egis e s and a global analogic con ol uni (GACU), he la e o which is he hos o he s o ed p og am and con ols he whole a ay compu e . The h ee egis e s s o e he cloning empla es [analog p og am- ming-ins uc ion egis e (APR)], he local logic ins uc ions [logic p og am-ins uc ion egis e (LPR)], and he swi ch con igu a ion codes [swi ch con igu a ion egis e (SCR)], espec i ely. The CNN-UM can be iewed as an a ay compu e de- ined on lows [18]. Algo i hms can be cons uc ed whe e he elemen a y ins uc ion is he solu ion o a pa ial di e - en ial equa ion (PDE). This co espondence was highligh ed al eady in he seminal pape [5] o he hea equa ion; also, in [19], a mechanical sys em was modeled by a CNN. La e , sys ema ic me hods ha e been de ised o con e PDEs de- ined in con inuous space in o CNN dynamics [20]. Recen ad ances in compleximage p ocessing show ha PDE-based echniques seem o be supe io in many espec s (e.g., [21]). The d awback is hei high compu a ional complexi y when implemen ed in digi al p ocesso s. He e, using a CNN, solu- ion o a nonlinea PDE is he basic ask. The nex example shows a complex analogic spa ial/ em- po al algo i hm used o he calcula ion o he inne bound- a ies o he le en icle in an echo-ca diog am [22]. Ac i e wa es [23] a e used as algo i hmic s eps. Fo e e ence, we 1246 PROCEEDINGS OF THE IEEE, VOL. 90, NO. 7, JULY 2002 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 15,2020 a 14:17:43 UTC om IEEE Xplo e. Res ic ions apply. Fig. 5. The bold a ows ep esen di e en cloning empla es. Some o hem a e pe o ming he solu ion o complex nonlinea PDEs as elemen a y ins uc ions; hese a e w i en on he le -hand side o he igu e wi h hei execu ion imes on he igh -hand side. In addi ion, se e al simple ins uc ions and empla es a e used, o ins ance, local logic ope a ions. also show he execu ion imes o he algo i hmic s eps on he so-called ACE4k chip [10]. C. Example 1 A low diag am is depic ed in Fig. 5 o he analogic CNN algo i hm wi h some ypical in e media e esul s. Obse e ha i can be in e p e ed as a combina ion o h ee image lows me ging and b anching du ing he p ocessing s age o a single ame. He e he hi d low s ands o he in o ma ion calcula ed om he cu en ame, he second one o he in- e media e esul s ob ained om he p e ious ame, while he i s one ep esen s he bina y masks gene a ed om he p e ious esul . The co e o he h ee main p ocessing s ages o he algo i hm can also be desc ibed by PDEs (le ): 1) image il e ing and econs uc ion de i ed om nonlinea di usion PDEs; 2) mo ion es ima ion de i ed om op ical low PDEs; and 3) igge wa e- ype ac i e con ou -based bounda y acking de i ed om eac ion-di usion nonlinea PDEs. These PDE app oxima ions, execu ed on he ACE4K chip, can be comple ed wi hin a millisecond, allowing he p ocessing sys em o each i s peak pe o mance a ound ou housand ame/sec ( igh ). D. Mul ilaye and Complex Cell CNN-UM The mul ilaye CNN s uc u e was al eady in oduced in [5]. I is used when se e al 2-D CNN laye s a e necessa y Fig. 6. Fig. 3 shows he ini ial s a e and he ou pu image (a T =2 elapsed ime). The e exis s a e y wide ca alog o empla es co e ing a my iad o applica ions. Also, because hese empla es a e p og ammable by de ini ion, lea ning can be inco po a ed o adap he empla es. Ei he globally, o example, using a gene ic algo i hm [16], o locally. Thus, no only associa i e memo ies can be cons uc ed, e.g., [17], bu he plas ici y o he b ain migh be di ec ly modeled [13]. o desc ibe he spa ial- empo al dynamics. In many cases, he laye s a e jus cascaded, and he consecu i e ins uc- ions o he CNN-UM a e adequa e o model he same p ocess. Howe e , in hose cases whe e in e laye eedback does exis , we need he mul ilaye CNN s uc u e. Such a mul ilaye CNN is use ul o modeling he e eb a e e ina [12]. Fig. 6 shows he concep ual a chi ec u e o a second-o de dynamics, h ee-laye cell which has been p o o yped in he ROSKA AND RODRÍGUEZ-VÁZQUEZ: TOWARDS VISUAL MICROPROCESSORS 1247 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 15,2020 a 14:17:43 UTC om IEEE Xplo e. Res ic ions apply. Fig. 7. Using he CACE1K chip, p og amming he laye ime cons an s and he A - empla es on he wo dynamic laye s, a double wa e p opaga ion can be p og ammed. The esul ing sequence o snapho s shows he di e en speed and he di e en ypes o wa es on he wo laye s. chip called CACE1K [11]. The dynamic ope a ion is gi en acco ding o he ollowing exp essions: (4) whe e ep esen s he buil -in di e ence a i hme ic. The ope a ion o his p o o ype is hence con olled by he 23 pa ame e s in ol ed in (4), gi en as (5) plus he ela i e alues o he ime cons an s o Laye s 1 and 2, o aling 25 di e en pa ame e s. Many ypes o nonlinea wa es ( igge -, a eling-, au o-, and spi al-wa es) can be ob ained by p ope ly con olling hese pa ame e s [23]. E. Example 2 This example illus a es he gene a ion o double-wa e p opaga ion using he CACE1K chip [11]. The empla e ele- men alues o his ope a ion a e (6) and he a io be ween he ime cons an s o he wo laye s is . Using he same chip, e y ecen ly we ha e been able o implemen some o he key inne e inal e ec s, impossible o ealize on i s -o de laye s. Mo e de ailed e- sul s a e epo ed elsewhe e [24]. Ou ques o make a p og ammable p o o ype spa ial- em- po al compu e which could also se e as a isual mic op o- cesso could be jus i ied in wo ways. On he one hand, we ha ep o enea lie ha heCNN-UMis uni e sal.Ina sense, i is equi alen o he Tu ing machine. The p oo was eal- ized by implemen ing he game o li e. On he o he hand, in each cell, wi h no mo e han ou laye s, we can imple- men any nonlinea mul i-inpu single-ou pu ope a o wi h ading memo y. This is only one side o he s o y. On he o he side, which is simila o he digi al compu e s o Tu ing machines in which he - ecu si e unc ions a e he o mal desc ip ions o he algo i hms wi h p o en capabili ies, we ha e also de e mined he equi alen o mal no ion o algo- i hms as he - ecu si e unc ions wi h simila p ope ies [18]. Hence, we ha e all he heo e ical backg ound o es- ablish ou new ype o compu e o opog aphic ope a ions, in pa icula o ision. Mo eo e , i has u ned ou ha he neu omo phic cons uc s o mos o he opog aphic senses wi h accompanying p ocessing a e qui e simila o hose o CNN models [9]. III. ANALOGIC VISUAL MICROPROCESSOR IN SILICON CNN-based analogic isual mic op ocesso s ha e simi- la i ies wi h he so-called single ins uc ion mul iple da a (SIMD) sys ems [25], al hough hey wo k di ec ly on analog signal ep esen a ions ob ained h ough embedded op ical senso s and hence do need nei he a on -end senso y plane no analog- o-digi al con e e s. The a chi ec u e o hese isual mic op ocesso s is illus a ed in Fig. 8 h ough wo p o o ype chips, namely, ACE4K [10] and ACE16K [26]. In bo h cases, as in o he ela ed chips [11], [27]–[29], he a chi ec u e includes a co e a ay o in e connec ed elemen- a y p ocessing uni s, su ounded by a global ci cui y. This la e ci cui y is in ended o : • con ol and iming; • ad essing and bu e ing o he co e cells; • inpu /ou pu ; • s o age o use -selec able ins uc ions (p og ams) o con ol he sequence o ope a ions o he p ocessing co e; • s o age o use -selec able analogic p og amming pa- ame e con igu a ions ( empla es). 1248 PROCEEDINGS OF THE IEEE, VOL. 90, NO. 7, JULY 2002 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 15,2020 a 14:17:43 UTC om IEEE Xplo e. Res ic ions apply. Fig. 8. A chi ec u es o analogic isual mic op ocesso chips: (a) ACE4K [10] and (b) ACE16K [26]. On he o he hand, he co e o in e connec ed p ocessing uni s embeds di e en unc ions on a common silicon sub- s a e (see Fig. 9 o illus a ion pu poses), namely: • 2-D sensing; • 2-Danalog/digi ala ayp ocessingconcu en wi h he signal sensing; • 2-D spa io- empo al p ocessing de e mined by local, ecep i e- ield-like p og ammable in e connec ions; • 2-D memo y banks o concu en online uploading and downloading o sho - e m analog and digi al da a. Se e al analogic isual mic op ocesso chips in di e en CMOS echnologies ha e been epo ed du ing he las ew yea s. Pa icula ly, [10], [11], and [26]–[29] epo hose im- plemen a ions wi h a leas 20 20 pixels. Table 1 p esen s a summa y o some o hei mos ele an da a. Some columns ROSKA AND RODRÍGUEZ-VÁZQUEZ: TOWARDS VISUAL MICROPROCESSORS 1249 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 15,2020 a 14:17:43 UTC om IEEE Xplo e. Res ic ions apply. Fig. 9. llus a ing he embedding o di e en unc ional ea u es a he co e p ocessing a ay o isual mic op ocesso s. (a) Mic opho og aph o he ACE4K chip (le ) and concep ual ep esen a ion o he dis ibu ed unc ions embedded in he co e a ay ( igh ). (b) Layou o a p ocessing uni o he ACE16K showing he a eas occupied by he di e en unc ions ealized concu en ly by he co e a ay. co espond o chips in ended o black and whi e inpu im- ages,while o he sa e o chips whichaccep g ay-scaleinpu images. As wi h any o he analog p ocessing ci cui , igu es o me i abou pe o mance mus con empla e accu acy and a ea occupa ion in addi ion o speed and powe consump- ion. The speed measu e he e is p opo ional o he numbe o cells, he in e se o he ime cons an , and a weigh ed numbe o mul iplie s pe cell. Any compa ison mus e e o he numbe o ope a ions pe second and o he accu acy. The da a in he able highligh s he ollowing. • The e is a adeo be ween a ea occupa ion (cell den- si y)andaccu acy,on heonehand,andspeedo ope a- ionandpowe consump ion,on he o he . This adeo is ypical o analog in eg a ed ci cui s [33]. • Thee olu ion owa dscaled-down echnologies epo s ad an ages in e ms o speed and cell densi y. Ac u- ally, he ACE16K chip has 128 128 esolu ion and is capable o ealizing sequences o 64 ins uc ions; using up o 32 di e en empla es (each empla e con- sis ing o 24 8-bi -coded analog p og amming alues) du ing a sequence; loading and downloading ull-size g ay-scale images o and om he cache memo y, and ha ingalwayseigh ull-sizeimagesa ailable o usage du ing he low; wi h an in e nal p ocessing ime o 160 ns, and p o iding digi ally coded ou pu images (ob ained wi h a ba e y o in e nal con e e s) wi h a downloading ime o 0.128 ms. The capabili y o design cells wi h maximum densi y, speed and accu acy, and minimum a ea and powe consump- ion elies basically on he exploi a ion o all unc ional ea u es o e ed by he MOS ansis o . This is e y di e en om digi al design, in which only he swi ching capabili y o he MOS ansis o is exploi ed. The design o he en i ies which in e connec he cells (synapses) de ines one o he 1250 PROCEEDINGS OF THE IEEE, VOL. 90, NO. 7, JULY 2002 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 15,2020 a 14:17:43 UTC om IEEE Xplo e. Res ic ions apply. Table 1 Summa y and Compa ison o Chip Implemen a ions majo issues. In o de o do his, di e en possibili ies may be chosen a p io i, as illus a ed in Fig. 10. In all cases, elec ical con ollabili y is p o ided by de aul . Howe e , he di e en s a egies exhibi qui e a di e en pe o mance in he p esence o sys ema ic and andom e o sou ces, as well as a di e en incidence o he global signal ansmission e o s. Hence, ca e ul analysis and op imiza ion is needed o selec he bes app oach. Such analysis and op imiza ion a e needed o achie e he cell densi y and accu acy le els ea u ed by las gene a ion chips. The backg ound o such p ocedu es can be ound in [3], [10], [11], [26], and [28]. IV. ABOUT SCALING DOWN I is expec ed ha he pe o mance igu es ea u ed o hese chips can be u he enhanced as echnology scales ROSKA AND RODRÍGUEZ-VÁZQUEZ: TOWARDS VISUAL MICROPROCESSORS 1251 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 15,2020 a 14:17:43 UTC om IEEE Xplo e. Res ic ions apply. Fig. 10. Using a single NMOST o ol age- o-cu en ans o ma ion. Only i s -o de e ms a e included in he displayed beha io al equa ions. down. Howe e , one p oblem a ises due o he necessi y o main aining analog accu acy, and hence he quali y o he analog design, as ansis o sizes dec ease. Below we i s iden i y misma ch as he main limi o he analog accu- acy and hen explo e di e en adeo s associa ed wi h he analog design in he p esence o misma ch. A. Misma ch Ve sus Noise as a Limi ing Fac o Misma ch makes wo nominally iden ical de ices beha e di e en ly when hey a e used in a eal in eg a ed ci cui . Basedon he o mula iono misma chas a unc iono de ice geome ies in [30], he a iance o he la ge-signal anscon- duc ance pa ame e , he h eshold ol age , and he slope ac o 4as unc ion o he de ice a ea and aspec a io can be ep esen ed as (7) whe e is he ansis o channel a ea and is he ansis o aspec a io. Ano he accu acy limi ing ac o is noise. The equi alen noise cu en o an MOS ansis o can be exp essed as [31] (8) whe e and a y be ween 1 and 2, wi hin he ohmic egion and o his quan- i y in sa u a ion, and is he small-signal ansconduc ance pa ame e . 4In he o iginal model, he a iance was o mula ed o he body e ec ac o  1  ( n ) can be ob ained as a unc ion o  ( V ) and  (  ) . Le us conside ha he only signi ican misma ch e o is ha o he la ge-signal ansconduc ance pa ame e —as i ac ually happens in many p ac ical ci cui s used o es- ablishing in e connec ions in analog a ay p ocesso s [32], [33]. In e ms o he ansis o a ea and aspec , his e o is exp essed as (9) Unde simila assump ions, he noise con ibu ion can be ap- p oxima ed by (10) Using ypical pa ame e s o CMOS 0.5- m echnologies (V, V, V, cm V s , m , V F) and conside ing a bandwid h o 1–5 MHz, we conclude ha , o de ices wi h channel a eas o abou 50 m , he ma ching le el se s an accu acy sligh ly abo e 8 b while o his same a ea and a channel aspec a io o 0.1 he noise poses a limi in he esolu ion o 10.48 bi , a beyond om ha posed by misma ching phenomena. B. The E ec o he Scaling P ocess Le us assume ha la e al dimensions scale as (11) Thus, he ga e oxide hickness, which app oxima ely e ol es in cu en echnologies as , scales as (12) 1252 PROCEEDINGS OF THE IEEE, VOL. 90, NO. 7, JULY 2002 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 15,2020 a 14:17:43 UTC om IEEE Xplo e. Res ic ions apply.