On Syn he ic AER Gene a ion
Alejand o Lina es-Ba anco1, Gab iel Jimenez-Mo eno1, An ón Ci i -Ballcels1, and
Be nabé Lina es-Ba anco2
1A qui ec u a y Tecnología de Compu ado es. ETSI In o má ica, A . Reina Me cedes s/n,
41012 Se illa, SPAIN. Phone: 95-455-6145, Fax: 95-455-6449, E-mail: [email p o ec ed]
2Ins i u o de Mic oelec ónica de Se illa, Se illa, SPAIN.
Abs ac
In his pape se e al so wa e me hods o
gene a ing syn he ic AER s eams om images s o ed
in a compu e 's memo y a e p oposed and e alua ed.
E alua ion c i e ia co e execu ion ime, dis ibu ion
e o and how hey pe o m wi h wo ecei e cell
models. A ha dwa e PCI o AER in e ace is p esen ed.
1. In oduc ion
Add ess-E en -Rep esen a ion (AER) was p oposed in
1991 by Si ilo i [1] o ans e he s a e o an a ay o
neu ons om one chip o ano he . I uses mixed analog
and digi al p inciples and exploi s pulse densi y
modula ion o code in o ma ion. The s a e o he neu ons
is a con inuous ime a ying analog signal.
Fig. 1 explains he p inciple behind he AER basics.
The Emi e chip con ains an a ay o cells (like, o
example, a came a o a ificial e ina chip) whe e each
pixel shows a con inuously a ying ime dependen s a e
ha changes wi h a slow ime cons an (in he o de o
milliseconds). Each cell o pixel includes a local oscilla o
ha gene a es digi al pulses o minimum wid h (a ew
nanoseconds). The densi y o pulses is p opo ional o he
s a e o in ensi y o he pixel. Each ime a pixel gene a es a
pulse (which is called "e en "), i communica es wi h he
a ay pe iphe y and a digi al wo d ep esen ing i s code o
add ess is placed on he ex e nal in e -chip digi al bus ( he
AER bus). Addi ional handshaking lines (Acknowledge
and Reques ) a e also used o comple e he asynch onous
communica ion.
In he ecei e chip, he pulses a e di ec ed o he pixels
o cells whose code o add ess was on he bus. This way,
pixels wi h he same code o add ess in he emi e and
ecei e chips will "see" he same pulse s eam. The
ecei e cell in eg a es he pulses and econs uc s he
o iginal low equency con inuous- ime wa e o m. Pixels
ha a e mo e ac i e a e accessing he bus mo e equen ly
han hose less ac i e.
T ansmi ing he pixel add esses allows pe o ming
ex a ope a ions on he images while hey a el om one
chip o ano he . Fo example, inse ing p ope ly coded
memo ies (ie. EEPROM) allows ans o ma ion (ie.
shi ing and o a ion) o images. Also, he image
ansmi ed by one chip can be ecei ed by many e- cei e
chips in pa allel, by p ope ly handling he asyn- ch onous
communica ion p o ocol. The peculia na u e o he AER
p o ocol also allows o e y e ficien con olu ion
ope a ions wi hin a ecei e chip [2].
The e is a g owing communi y o AER p o ocol use s
o bio-inspi ed applica ions in ision and audi ion
sys ems, as demons a ed by he success in he las yea s
o he AER g oup a he Neu omo phic Enginee ing
Wo kshop se ies [3]. The goal o his communi y is o
build la ge mul i-chip and mul i-laye hie a chically
s uc u ed sys ems capable o pe o ming complica ed
a ay da a p ocessing in eal ime. The success o such
sys ems will s ongly depend on he a ailabili y o obus
and e ficien de elopmen and debugging AER- ools
[4][5]. One such ool is a compu e in e ace ha allows
no only eading an AER s eam in o a compu e and
displaying i on sc een in eal- ime, bu also he opposi e:
om images a ailable in he compu e 's memo y, gene a e
a syn he ic AER s eam in a simila manne as would do a
dedica ed VLSI AER emi e chip [1][6][7].
In Sec ion 2 we e iew some syn he ic AER gene a ion
me hods and p esen some imp o emen s o e ea lie
p esen ed ones [4][5]. In Sec ion 3 di e en me hods a e
e alua ed a ending o h ee c i e ia: execu ion ime, e o
o dis ibu ion and dis ance be ween ideal dis ibu ion in
wo kind o ecep o s, he Boahen in eg a o [8] and he
Mo a a in eg a o [9]. Finally, sec ion 4 p esen s a
ha dwa e in e ace.
2. Syn he ic AER Gene a ion
One can hink o many so wa e algo i hms o
ans o m a bi map image (s o ed in a compu e ’s
memo y) in o an AER s eam o pixel add esses [4][5]. In
all o hem he equency o appea ance o he add ess o a
gi en pixel mus be p opo ional o he in ensi y o ha
pixel. I pixel signal ime cons an is much slowe han
in e -e en iming, he p ecise loca ion o he add ess
pulses is no c i ical. The pulses can be sligh ly shi ed
om hei nominal posi ions; he AER ecei e s will
in eg a e hem o eco e he o iginal pixel wa e o m.
Wha e e algo i hm is used, i will gene a e a ec o o
add esses ha will be sen o an AER ecei e chip ia an
AER bus. Le us call his ec o he “ ame ec o ”. The
ame ec o has a fixed numbe o ime slo s o be filled
wi h e en add esses. The numbe o ime slo s depends on
he ime assigned o a ame ( o example
) and he ime equi ed o ansmi a
single e en ( o example ). I we ha e an
image o NxM pixels and each pixel can ha e a g ey le el
alue om 0 o K, one possibili y is o place each pixel
add ess in he ame ec o as many imes as he alue o
i s in ensi y, and dis ibu e i wi h equidis an posi ions. In
he wo s case (all pixels wi h maximum alue K), he
Fig. 1: AER in e -chip communica ion scheme
D1
D2
D3
CHIP1
ARBITER+ENCODER
DIGITAL
BUS
DECODER
D1
D2
D3
CHIP2
FAST T ame 40ms=
Tpulse 10ns=
ame ec o would be filled wi h NxMxK add esses. No e
ha his numbe should be less han he o al numbe o
ime slo s in he ame ec o . Depending
on he o al in ensi y o he image he e will be mo e o
less emp y slo s in he ame ec o . Each algo i hm would
implemen a pa icula way o dis ibu ing hese add ess
e en s, and will equi e a ce ain ime.
A. The Scan me hod
In his me hod a ame is scanned many imes. Fo each
scan, e e y ime a non-ze o pixel is eached i s add ess is
pu on he ame ec o in he fi s a ailable slo , and he
pixel alue is dec emen ed by one. I a pixel alue is ze o,
a blank slo is le in he ame ec o . This me hod is e y
as . Howe e , he esul ing e en dis ibu ion is e y
di e en om he one an AER e ina, o example, would
p oduce. Pa icula ly, he e en s o pixels wi h low
in ensi y will appea only a he beginning o he ame
ec o .
B. The Uni o m me hod
In his me hod, he objec i e is o dis ibu e
equidis an ly he e en s o one pixel along he ame
ec o . The image is scanned pixel by pixel only once. Fo
each pixel, he gene a ed pulses mus be dis ibu ed a
equal dis ances. As he ame ec o is ge ing filled, he
algo i hm may wan o place add esses in slo s ha a e
al eady occupied. This si ua ion is called a 'collision'.In
his case, we p opose h ee solu ions:
The Back-Fo wa d (Uni o m-BF me hod) solu ion will
pu he e en in he nea es emp y slo o he ame ec o .
The Fo wa d (Uni o m-F me hod) solu ion will pu he
e en in he ollowing emp y slo in he ame ec o .
And he Winne -Takes-All (Uni o m-WTA me hod)
solu ion will pu in he collision posi ion o he ec o he
e en ha p oduces a lowe e o and will igno e he
o he s. The winning e en is he one o he pixel wi h he
lowes in ensi y.
Uni o m-BF, Uni o m-F and Uni o m-WTA me hods,
appa en ly, will make mo e mis akes a he end o he
p ocess han a he beginning. The execu ion ime g ows
conside ably because he collisions consume an impo an
amoun o ime o be esol ed.
C. The Random me hod
This me hod places he add ess e en s in he slo s
ob ained by a pseudo- andom numbe gene a o based on
Linea Feedback Shi Regis e s (LFSR) [10]. Due o he
p ope ies o he LFSR used, each slo posi ion is
gene a ed only once, excep posi ion ze o, and no
collisions appea . I a pixel in he image has in ensi y p,
hen he me hod will ake p alues om he
pseudo- andom numbe gene a o and places he pixel
add ess in he co esponding pslo s o he ame ec o .
They will no be equidis an bu will appea along he
comple e add ess sequence andomly. This me hod is
as e han any o he Uni o m me hods.
No e ha by using an LFSR i would be possible o
ob ain wo e y close add esses in a ew calls. This can be
a oided using a b-bi coun e o he mos significan bi s
o he add ess. Fo each alue o he LFSR, ou add esses
a e gene a ed by inc emen ing he coun e . This ensu es
absence o collisions. Fig. 2 shows he LFSR s uc u e
wi h a 2-bi coun e o a 128x128 ame wi h 256 g ey
le els.
D. The Random-Squa e me hod
Fo he Random me hod wi h a fixed size coun e om
1 o he maximum g ey le el, he e en dis ibu ion o
high ac i i y pixels is accep able, bu poo o low le el
alues. Subs i u ing he coun e by ano he LFSR, he
dis ibu ion could be imp o ed.
Fo a 128x128 ame wi h maximum g ey le el o 255,
an 8-bi LFSR (LFSR-8) is used o selec ing 255 slices o
128x128 posi ions, and ano he 14-bi LFSR (LFSR-14)
selec s he posi ion inside he slice. The image is scanned
only once. Fo each pixel a 14-bi numbe is gene a ed by
he LFSR-14, and he LFSR-8 is called as many imes as
he in ensi y le el o he pixel would indica e. Fig. 3 shows
he LFSRs used by his Random-Squa e me hod.
E. The Exhaus i e me hod
This algo i hm also di ides he add ess e en sequence
in o Kslices o NxM posi ions o a ame o NxM pixels
wi h a maximum g ey le el o K. Fo slice k, an e en o
pixel (i,j) is sen on ime i he ollowing condi ion is
asse ed:
(1)
and
(2)
whe e Pi,j is he in ensi y alue o he pixel (i,j) [4][5].
The Exhaus i e me hod ies o imp o e he
Random-Squa e one by dis ibu ing he e en s o each
pixel in o he Kslices a equal dis ances. The algo i hm
scans he ame K imes. In i e a ion k, i he p e ious
condi ion is ue, hen he co esponding e en is sen ,
o he wise he algo i hm will wai o he ollowing e en
(no e en is sen a ime ).
3. E alua ion Resul s
In his Sec ion we compa e he me hods p oposed
abo e and es ima e how he pe o mance o he me hods is
a ec ed by he a fic o load o e en s in he AER bus. To
ca y ou his analysis a se o andom images ha e been
gene a ed, which ep esen a popula ion o images.
This se o images has been ob ained conside ing wo
aspec s: (a) i s his og am mus be close o a Gaussian
dis ibu ion and (b) he numbe o e en s equi ed o
ansmi hem. This way, a 100% e en load co esponds o
an image wi h all pixels a maximum alue. Consequen ly,
an image wi h 10% o e en load, ep esen s an image ha
uses 10% o he possible e en s. Le us gene a e a ‘Tes
Image Se ’ (TIS) composed o nine images wi h e en load
o 10%, 20%, 30%, ... and 90%. This se will be used o
T ame/Tpulse
Fig. 2: Random me hod s uc u e: LFSR wi h a 2-bi coun e .
Fig. 3: Random-Squa e s uc u e: LFSR-8 and LFSR-14 .
kP
ij,
×()modK Pij,
+K≥
NM×k1–()×i1–()M×j++ =
compa e he algo i hms acco ding o he ollowing
c i e ia:
A. Execu ion Time
Fig. 4 shows he execu ion ime e sus he e en load o
he images. The Scan and Exhaus i e me hods ollow an
almos cons an ela ion because he e en load does no
a ec much he execu ion ime o hese algo i hms.
B. Dis ibu ion E o
In an ideal AER dis ibu ion all e en s o one pixel a e
equidis an in ime: cons an equency o e en s. In his
sec ion, he dis ibu ion o e en s ob ained wi h each
me hod is e alua ed. Le us call ‘Dis ibu ion E o ’how
much he e en dis ibu ion gene a ed by a me hod
de ia es om he ideal dis ibu ion.
Le us suppose Dij is he ideal dis ance be ween e en s
o pixel (i,j)o aNxM image wi h Kg ey le el alues.
Then
(3)
whe e Pi,j is he in ensi y alue o pixel (i,j).
Le us suppose is he dis ance be ween he k- h
e en and he (k+1)- h one.
(4)
whe e is he posi ion o e en kin he ame
ec o .Then we can measu e he mean e o o a pixel as
he a e age o he di e ences be ween he ideal and eal
dis ance. The e o exp ession is:
(5)
I is easy o see ha he wo s case o his e o
measu emen is when all he e en s a e oge he in he
add ess sequence. The e o e, in o de o compa e he e o
ob ained o di e en me hods and images, he e o o
each pixel mus be no malized wi h espec o he
maximum e o associa ed o he pixel. The ollowing
exp ession is he maximum e o o pixel (i,j):
wi h (6)
Fo , he dis ibu ion e o is ze o, because only
one e en has o be sen .
Finally, we define a ma ix (NE) wi h he same size o
he es image, and whe e each elemen (i,j) ep esen s he
e o no malized o pixel (i,j).
(7)
Fig. 5 shows he measu e o he NE ma ix calcula ed o
he nine es images using he me hods p oposed. The
x-axis ep esen s he image e en load and he y-axis is he
mean no malized e o .
C. In eg a o Cells
Conside he ecep o cells p oposed by Boahen [8]
(diode-capaci o in eg a o ) and by Mo a a [9] ( wo
capaci o s wo king in wo phases). We ha e modelled he
ideal beha io o hese cells in MATLAB. Then o each
syn he ic AER gene a ion me hod, di e en ame ec o s
we e ob ained. These ame ec o s we e hen used o eed
an a ay o in eg a o s o ei he he Boahen ype o he
Mo a a ype. Fig. 6 and Fig. 7 show he dis ance be ween
he ideal dis ibu ion o e en s and he eal dis ibu ion due
o each me hod using ou “Tes Image Se ” (TIS) and o
each ecep o model.
4. Ha dwa e In e ace
All simula ions p esen ed ha e been pe o med in
so wa e. Howe e , he final goal is o build a dedica ed
10 % 20 % 30 % 40 % 50 % 60 % 70 % 80 % 90 %
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Compa ision o execu ion ime
Cha ge o e en s in AER bus (%)
no milized execu ion ime
Scan
Uni o m−BF
Uni o m−F
Uni o m−WTA
Random
Random−Squa e
Exhaus i e
Fig. 4: Execu ion ime compa ision o so wa e implemen a ion
Dij,NMK××()Pij,
⁄=
dkij,
dkij,pk1+ij,pkij,
–=
pk
eij,
Dij,dkij,
–
k1=
Pij,
∑
Pij,
------------------------------------------
=
meij,2Dij,1–()11Pij,
⁄–()⋅⋅=Pij,1≠
Pij,1=
NEij,eij,meij,
()⁄=
10 20 30 40 50 60 70 80 90
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Dis ibu ion e o s e en cha ge
Cha ge o e en s in AER bus (%)
No malized mean e o
Scan
Uni o m−BF
Uni o m−F
Uni o m−WTA
Random
Random−Squa e
Exhaus i e
Fig. 5: Mean o NE ma ix o me hods along inc emen al cha ge
o e en s in AER bus.
10 20 30 40 50 60 70 80 90
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Beha io o syn he ic me hods o Boahen in eg a o model
Cha ge o e en s in AER bus (%)
no malized mean dis ance o ideal dis ibu ion
Scan
Uni o m−BF
Uni o m−F
Uni o m−WTA
Random
Random−Squa e
Random−Ha dwa e
Exhaus i e
Fig. 6: No malized mean dis ance be ween me hods and ideal
dis ibu ion o Boahen in eg a o .
ha dwa e ha ans o ms a ideo ame sequence in o an
AER s eam in eal ime. Such ha dwa e is p esen ly unde
de elopmen . A his momen a PC based sys em is
a ailable whe e he ame-AER ans o ma ions a e
pe o med in so wa e bu he esul ing ame ec o is
dumped h ough he compu e PCI bus on o an AER bus.
Fig. 8 shows he a chi ec u e o he p esen ha dwa e
in e ace. This is a PCI in e ace based on he LogiCORE
PCI o Xilinx ha uses I/O space o configu a ion and
memo y space o AER o ma eading and w i ing. I has
wo AER buses, one o incoming AER da a and ano he
o ou going one. The e a e wo FIFOs o bo h di ec ions.
I has a p og ammable imes amp assignmen o incoming
AER and p og ammable wai s a es o ou going AER.
The e is an in e up gene a ion o a oiding o e flows a
he incoming FIFO.
The sys em has been implemen ed using VHDL and
syn hesized in o a Vi exE 600 FPGA. I has been es ed
on a Nalla ech Ballyinx p o o yping boa d unde Linux
ope a ing sys em. I can ead o w i e an AER e en e e y
. I , hen his implies
.
5. Conclusions
Algo i hms o ans o ming synch onous ame based
ideo s eams in asynch onous add ess e en s eams a e
p esen ed and e alua ed. Th ee c i e ia (execu ion ime,
e o dis ibu ion and dis ance o ideal beha io wi h wo
in eg a o models) ha e been e alua ed o he se en
so wa e me hods. A ha dwa e in e ace be ween a
compu e (PCI) and a bioinspi ed sys em (AER) has also
been p esen ed.
The esul s p esen ed in Sec ion 3 show ha : (a)
So wa e based Uni om me hods a e no alid o
eal- ime due o he o e head in oduced by collision
esolu ion. A ha dwa e e sion is cu en ly unde
de elopmen o sol e hese p oblems. (b) Uni o m
me hods ha e lowe dis ibu ion e o han o he s o he
es se (TIS). (c) Recons uc ion o images, using wo
models o spike based in eg a o s, show ha any me hod
could be alid wi h small di e ences among hem. The
Uni o m-WTA has he wo s esul s in his aspec due o
he educ ion o e en s by collisions.
6. Acknowledgemen s
This wo k was pa ially suppo ed by spanish g an s
TIC1999-0446-C02-02, TIC2000-0406-P4-05 (Vic o ),
FIT-07000/2002/921 (A quimedes), TIC2002-10878-E,
TIC-2003-08164-C03-01 (Saman a), and EU g an
IST-2001-34124 (Ca ia ).
7. Re e ences
[1] M. Si ilo i, Wi ing Conside a ions in analog VLSI
Sys ems wi h Applica ion o Field-P og ammable
Ne wo ks, Ph.D. Disse a ion, Cal ech, Pasadena CA,
1991.
[2] T. Se ano-Go a edona, A. G. And eou, B.
Lina es-Ba anco, “AER Image Fil e ing A chi ec u e o
Vision-P ocessing Sys ems,” IEEE T ans. Ci c. and Sys .
Pa -I, ol. 46, No. 9, Sep embe 1999.
[3] A. Cohen, R. E ienne-Cummings, T. Ho iuchi, G.
Indi e i, S. Shamma, R. Douglas, C.Koch and T.
Sejnowski, Repo on he 2003 Wo kshop on
Neu omo phic Enginee ing, Tellu ide, CO, June 29 o
July 19, 2003. {www.ini.unizh.ch/ ellu ide}
[4] A. Lina es-Ba anco, S udy and E alua ion o AER
In e aces o Neu omo phic Sys ems, Ph.D. Disse a ion,
Uni e si y o Se ille, Spain, 2003. (In spanish)
[5] A. Lina es-Ba anco, R. Senhadji-Na a o, I.
Ga cía-Va gas, F. Gómez-Rod íguez, G. Jimenez and A.
Ci i , “Syn he ic Gene a ion o Add ess-E en o
Real-Time Image P ocessing,” P oc. ETFA 2003, Lisbon,
Sep embe , ol. 2, pp. 462-467.
[6] K. Boahen, “Communica ing Neu onal Ensembles
be ween Neu omo phic Chips,” Neu omo phic Sys ems,
Kluwe Academic Publishe s, Bos on 1998.
[7] M. Mahowald, VLSI Analogs o Neu onal Visual
P ocessing: A Syn hesis o Fo m and Func ion. Ph.D.
Disse a ion. Cal ech, Pasadena, Cali o nia 1992.
[8] K. Boahen, “Re inomo phic ision sys ems II:
Communica ion channel design,” P oc. o he IEEE
ISCAS, ol. supplemen , pp. 14-17. May 1996.
[9] A. Mo a a, E ic A. Vi oz, Philippe Venie , “A
communica ion Scheme o Analog VLSI Pe cep i e
Sys ems,” IEEE Jou nal o Solid-S a e Ci cui s, ol. 30,
No. 6, pp. 660-669, June 1995.
[10] S.W. Golomb, Shi Regis e Sequences. Laguna Hills,
CA: Aegean Pa k P ess, 1982.
10 20 30 40 50 60 70 80 90
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Beha io o syn he ic me hods o Mo a a in eg a o model
Cha ge o e en s in AER bus (%)
no malized mean dis ance o ideal dis ibu ion
Scan
Uni o m−BF
Uni o m−F
Uni o m−WTA
Random
Random−Squa e
Random−Ha dwa e
Exhaus i e
Fig. 7: No malized mean dis ance be ween me hods and ideal
dis ibu ion o Mo a a in eg a o .
Fig. 8: Ha dwa e In e ace A chi ec u e.
Tpulse 40ns=T ame 40ms=
NMK×× T ame/Tpulse
≤106
=