Mul i- esolu ion low-powe Gaussian il e ing by
econ igu able ocal-plane binning
J. Fe n´andez-Be ni a, R. Ca mona-Gal´ana, F. Pozas-Flo es a,´
A. Za ´andyband
´
A. Rod ´ıguez-V´azquezb
aIns i u e o Mic oelec onics o Se ille (IMSE-CNM)
CSIC-Uni e sidad de Se illa, Spain.
bCompu e and Au oma ion Resea ch Ins i u e (MTA-SZTAKI)
Hunga ian Academy o Sciencies, Budapes , Hunga y.
ABSTRACT
Gaussian fil e ing is a basic ool o image p ocessing. Noise educ ion, scale-space gene a ion o edge de ec ion
a e examples o asks whe e diffe en Gaussian fil e s can be success ully u ilized. Howe e , hei implemen a ion
in a con en ional digi al p ocesso by applying a con olu ion ke nel h oughou he image is qui e inefficien .
No only he alue o e e y single pixel is aken in o conside a ion sucessi ely, bu also con ibu ions om hei
neighbo s need o be aken in o accoun . P ocessing o he ame is se ialized and memo y access is in ensi e
and ecu en . The esul is a low ope a ion speed o , al e na i ely, a high powe consump ion. This inefficiency
is specially ema kable o fil e s wi h la ge a iance, as he ke nel size inc eases significan ly. In his pape , a
diffe en app oach o achie e Gaussian fil e ing is p oposed. I is o ien ed o applica ions wi h e y low powe
budge s. The key poin is a econfigu able ocal-plane binning. Pixels a e g ouped acco ding o he a ge ed
esolu ion by means o a di ision g id. Then, wo consecu i e shi s o his g id in opposi e di ec ions ca y
ou he sp ead o in o ma ion o he neighbo hood o each pixel in pa allel. The ou come is equi alen o he
applica ion o a 3×3 binomial fil e ke nel, which in u ns is a good app oxima ion o a Gaussian fil e , on he
o iginal image. The a iance o he closes Gaussian fil e is a ound 0.5. By epea ing he ope a ion, Gaussian
fil e s wi h la ge a iances can be achie ed. A ough es ima ion o he necessa y ene gy o each epe i ion un il
eaching he desi ed fil e is below 20nJ o a QCIF-size a ay. Finally, expe imen al esul s o a QCIF p oo -
o -concep ocal-plane a ay manu ac u ed in 0.35μm CMOS echnology a e p esen ed. A maximum RMSE o
only 1.2% is ob ained by he on-chip Gaussian fil e ing wi h espec o he co esponding equi alen ideal fil e
implemen ed off-chip.
Keywo ds: Focal-plane p ocessing, Gaussian ke nels, binomial fil e mask, low-powe sma image senso s
1. INTRODUCTION
Gaussian ke nels a e a undamen al componen o a compu a ional app oach o isual pe cep ion mo i a ed
by physics and biological ision.1Con olu ion wi h Gaussian ke nels and Gaussian de i a i es cons i u e a
canonical class o image ope a o s o ea ly ision. As a amily, Gaussian ke nels o m a semi-g oup. One
impo an p ope y is ha any coa se scale ep esen a ion can be ob ained om any ep esen a ion a a fine
le el. Addi ionaly, Gaussian ke nels ha e he p ope y o p ese ing local ex ema in he image, i. e. no minima
no maxima a e acciden ally in oduced when a Gaussian blu is applied in o de o sup ess fine scale de ails o
he image.2Because o hese p ope ies, Gaussian fil e s a e able o gene a e a scale space3and, consequen ly, a
mul i-scale image ep esen a ion.4I is wo h men ioning ha scale-space ope a o s ha e a simila o m o he
ecep i e fields obse ed in neu ophysiological s udies.5This ype o image ep esen a ion is ce ainly use ul o
image in e p e a ion. As he e is no a p io i knowledge abou he scale o he ele an elemen s in he scene, a
mul i-scale ep esen a ion co e s all he possible anges. Image ea u es can hen be ex ac ed a diffe en scales
and scale-in a ian ea u es can be highligh ed as cha ac e is ic o wha e e akes place in he isual field.6I is
no s ange ha isual a en ion models based on saliency make ex ensi e use o hese ope a o s.7
Fu he au ho in o ma ion:
Jo ge Fe n´andez-Be ni: E-mail: be [email protected], Telephone: +34 954466666
Bioelec onics, Biomedical, and Bioinspi ed Sys ems V; and Nano echnology V, edi ed by Ángel B. Rod íguez-Vázquez,
Rica do A. Ca mona-Galán, Gus a o Liñán-Cemb ano, Raine Adelung, Ca s en Ronning, P oc. o SPIE Vol. 8068,
806806 · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.886555
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The iso opic Gaussian ke nel, cen e ed a he o igin, employed o gene a e a scale-space ep esen a ion o a
wo-dimensional image, is defined as a pa ame ized unc ion g:R2×R+→Rwhe e:
G(x;ξ)= 1
2πξe−|x|2/2ξ⇔ˆ
G(k;ξ)=e−2π2|k|2ξ(1)
in which ξis e e ed as he scale pa ame e and co esponds o he a iance o he Gaussian ke nel (ξ=σ2),
and ˆ
G(·) is he Fou ie ans o m o G(·). One ad an age om he poin o iew o he implemen a ion is ha
he Gaussian ke nel is sepa able in o wo o hogonal unc ions G1(·)andG2(·):
G(x;ξ)=G1(x1;ξ)∗G2(x2;ξ)= 1
2πξ e−x2
1/2ξ∗e−x2
2/2ξ(2)
Gi en ha he image plane is disc e ized, he unc ion G(·) is only e alua ed a alid poin s o he g id.
Fo a ela i ely la ge σ, i. e. highe scales, he numbe o elemen s o he ke nel ha canno be neglec ed is
p ohibi i ely la ge, as can be seen below:
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.04 0.00 0.00
0.00 0.04 1.00 0.04 0.00
0.00 0.00 0.04 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.03 0.11 0.03 0.00
0.00 0.11 0.44 0.11 0.00
0.00 0.03 0.11 0.03 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.01 0.02 0.01 0.00
0.01 0.06 0.10 0.06 0.01
0.02 0.10 0.16 0.10 0.02
0.01 0.06 0.10 0.06 0.01
0.00 0.01 0.02 0.01 0.00
σ=0.4σ=0.6σ=1.0
In ac , a minimum size o 6σhas been es ima ed in o de o a oid excessi e ipple in he s op band in oduced by
unca ion.8In e ms o he equi ed compu ing powe and esou ces, he dynamic adap a ion o he ke nel size
ep esen s a significan d awback. An al e na i e app oach will be ime-mul iplexing he smoo hing ope a o s.
In o he wo ds, epea edly applying smalle ke nels in o de o ob ain a highe scale pa ame e , wha di ec ly
de i es om he semi-g oup cha ac e is ic o he Gaussian ke nels:
G(x;ξ1+ξ2)=G(x;ξ1)∗G(x;ξ2)(3)
ha can easily be unde s ood in he Fou ie domain:
ˆ
G(k;ξ1+ξ2)=e−2π2|k|2(ξ1+ξ2)=e−2π2|k|2ξ1·e−2π2|k|2ξ2=ˆ
G(k;ξ1)ˆ
G(k;ξ2)(4)
The e o e, we need o selec an elemen a y Gaussian fil e , o an app oxima ion, ha can be easily implemen ed,
bo h in e ms o he numbe o non-ze o elemen s o he ke nel and in e ms o he ela ions be ween hem. The
2-D binomial fil e 4is a good candida e:
B2=B2∗B2T=1
4121
∗1
4⎡
⎣
1
2
1
⎤
⎦=1
16 ⎡
⎣
121
242
121
⎤
⎦(5)
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1
1
0
1
101 1
Figu e 1: Focal-plane capaci o g id o cha ge edis ibu ion
which is he esul o con ol ing a ho izon al, B2, and a e ical, B2T, 1-D binomial masks. Each o hese 1-D
fil e s a e, in u n, he esul o con ol ing wice he elemen a y a e aging mask, B1:
B2=B1∗B1=1
211
∗1
211
=1
4121
(6)
Because o he cen al limi heo em, he ans e unc ion and he mask o he binomial fil e app oxima e
he Gaussian fil e wi h an equi alen a iance. In he case o he ke nel exp essed in Eq. (5) he a iance is 0.5,
and he e o commi ed in he app oxima ion o he equi alen Gaussian fil e is a ound 0.8%, depending on
he inpu image.
The es o he pape is dedica ed o an efficien implemen a ion o he binomial fil e based on he use o ocal-
plane mul i- esolu ion capabili ies. I is o ganized as ollows. Fi s we will show how econfigu able esolu ion is
implemen ed by adding he possibili y o binning pixels oge he and allowing o cha ge edis ibu ion among
hem. Then we will demons a e ha he effec o epea edly a e aging he pixels in shi ed di isions o he ocal-
plane g id is ha o applying a binomial fil e . Finally, some expe imen al esul s, ob ained wi h a p o o ype
chip ab ica ed in a 0.35μm CMOS echnology, a e displayed, confi ming he alidi y o he app oach.
2. CHARGE REDISTRIBUTION AND PIXEL BINNING
A he ocal plane o a CMOS image , he pho ogene a ed cu en is di ec ly sensed and (o ) in eg a ed.9In he
la e case, he pixel alue is a ol age a he sensing capaci o . This ol age is s o ed, a leas empo a ily, so i
can be ead ou . I an elec onic shu e is p o ided,10 he pixel ol age is main ained un il he nex ese , wi hin
he accu acy pe mi ed by leakages. Fully-pa allel ope a ions can be pe o med on o hese ol ages a he ocal
plane wi hou using an ex e nal memo y as hese capaci o s ac as a dis ibu ed analog memo y. I swi ches a e
p o ided be ween he capaci o s, as can be seen in Fig. 1, he s o ed cha ge edis ibu es ending in he a e aging
o he ini ial ol ages. Le us conside ha , by se ing he app op ia e con ol pa e n, a sub-image o size m×n
is isola ed. This is ealized by u ning on he m−1 signals ha con ol he connec ions be ween he m ows
o pixels, and he n−1 signals ha con ol he connec ions be ween he ncolumns in Fig. 1. By enabling he
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elec ical pa hs be ween he m×ncapaci o s, he pixels whose o iginal alues a e p0
ij,...,p
0
i+m−1,j+n−1end in:
pi+k,j+l∀k∈{0,...,m−1},∀l∈{0,...,n−1}
=1
mn
m−1

k=0
n−1

l=0
p0
i+k,j+l(7)
I is wo h o men ion ha he esul is exac ly he same i he swi ches con o ming he m×n egion a e se
om he s a , as cha ge edis ibu es in pa allel wi h pho ocu en in eg a ion. This is called pixel binning.11
Conside now a egula subdi ision o he ocal-plane g id. Fo ins ance, an al e na e sequence o 1’s and 0’s
is loaded in o he ow and column connec ion con ol egis e s o Fig. 1. I means ha he ull- esolu ion image
o M×Npixels is di ided in o 2 ×2-pixel blocks. As he ou pixels wi hin each block a e connec ed oge he ,
hey will end up ha ing he same pixel alue:
pi,j i∈{1,3,5,...,M−1},j∈{1,3,5,...,N−1}
=1
4p0
ij +p0
i,j+1 +p0
i+1,j +p0
i+1,j+1(8)
ha is he a e age o he o iginal alues o he ou pixels con ained in he block. We ha e assumed ha Mand
Na e e en. The esul ing image con ains M/2×N/2 pixels, wi h he connec ion scheme depic ed in Fig. 2(a). I
will be he s a ing poin o he p ocessing we will explain la e . Ano he ele an assump ion is ha any ea u e
ha we a e in e es ed in mus be no iceable a his esolu ion. The ollowing analysis applies o images di ided
in blocks o any size as long as hei dimensions a e e en and he esul s o be expec ed a e M/2×N/2-pixel o
smalle images.
3. GAUSSIAN FILTERING BY GRID SHIFTING
Le us s a wi h an image, o size M×N-pixels, s o ed in a capaci o g id like ha o Fig. 1. The g id has been
di ided in o 2 ×2-pixel blocks, wi hin which cha ge has been allowed o edis ibu e. I means ha ou ini ial
image is o size M/2×N/2-pixels and has ou capaci o s s o ing he same ol age, i. e. he same pixel alue
(Fig. 2(a)). Le us concen a e on he ans o ma ion ha is going o be suffe ed by he alue pij s o ed a he
posi ion indica ed by he a ow in Fig. 2(a). A a ce ain poin in ime, he al e na e sequences o 1’s and 0’s a
he ow and column connec ion con ol egis e s a e shi ed one space down and o he igh , espec i ely. The
(a) (b)
Figu e 2: (a) Focal-plane di ision in 2 ×2-pixel blocks and (b) shi ed g id.
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pixel g ouping scheme changes om ha o Fig. 2(a) o he one depic ed in Fig. 2(b). Consequen ly, because o
a new edis ibu ion o he cha ge in he newly o med blocks, he alue o he ma ked node becomes:
p
ij =1
4(pi−1,j−1+pi−1,j +pi,j−1+pij )(9)
The alues a he neighbo ing nodes, ha we e o iginally pij as well, a e now a e aged in hei new 2 ×2-pixel
blocks, so hey ha e been ans o med in o:
p
i,j+1 =1
4(pi−1,j +pi−1,j+1 +pij +pi,j+1) (10)
p
i+1,j =1
4(pi,j−1+pij +pi+1,j−1+pi+1,j) (11)
p
i+1,j+1 =1
4(pij +pi,j+1 +pi+1,j +pi+1,j+1) (12)
I he con ol sequences a e shi ed back o he o iginal posi ion, one space up and o he le , hen he new
alues exp essed by Eqs. (9)-(12) and a e aged once mo e, esul ing in:
p
ij =1
16 (pi−1,j−1+2pi−1,j +pi−1,j+1 +2pi,j−1+4pij +2pi,j+1 +pi+1,j−1+2pi+1,j +pi+1,j+1) (13)
No ice ha he M×N-pixel image has unde gone wo shi s o he connec ion scheme ollowed by he
a e aging o he pixel alues wi hin he esul ing 2 ×2-pixel blocks. Each combina ion o g id shi ing and
a e aging has he same effec as applying he a e aging mask:
B1=B1∗B1T=1
211
∗1
21
1=1
411
11
(14)
o e a M/2×N/2-pixel image. By doing i wice, we a e applying he 3 ×3 binomial fil e mask o Eq. (5):
B1∗B1=1
411
11
∗1
411
11
=1
16 ⎡
⎣
121
242
121
⎤
⎦=B2(15)
ha is p ecisely wha is exp essed in Eq. (13). This heo e ical esul has been checked by nume ical simula ion∗,
yielding 0.16% RMSE o a 256 ×256-pixel image o Lena. This small e o is associa ed o diffe ences in he
ounding e o commi ed on ollowing he diffe en me hods.
4. CHIP MEASUREMENTS
Al hough he abo e desc ibed p ocedu e may heo e ically ende he same esul s as he di ec con olu ion wi h
he binomial fil e mask, i s physical implemen a ion in ol es a numbe o swi ches o econfigu e and shi he
connec ion g id. Swi ching e o becomes mo e appa en when he s o age capaci o s a e small. In his sec ion
we a e showing he esul s ob ained by implemen ing binomial fil e ing by shi ed a e age g ids in a p o o ype
chip wi h ocal-plane econfigu abili y and mul i- esolu ional capabili ies. The p o o ype chip (Fig. 3)12 has
been ab ica ed in a 0.35μm CMOS p ocess wi h an i- eflec i e coa ing and educed pho odiode da k esponse.
A summa y o he chip cha ac e is ics and ea u es is gi en a Table 1. This chip was no o iginally hough o
ope a e ollowing he al eady explained scheme, bu i has a econfigu able ocal-plane connec ion g id, like ha
in Fig. 1, ha p o ides mul i- esolu ion capabili ies.
The fil e ing p ocedu e explained abo e has been p og ammed in o he chip es en i onmen . The esul s
ob ained on-chip ende a 1.12% RMSE o he fi s applica ion o he fil e . This o e all e o is a ibu able
o he accumula ed swi ching e o s and also o he noisy eadou . Fig. 4 depic s he o iginal 176 ×144-pixel
∗Ma lab R
 iles o compa ing he esul s o ealizing binomial il e ing ei he di ec ly o by g id shi ing and a e aging
can be ound a h p://www.imse-cnm.csic.es/wi isne /spie iles/
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Figu e 3: Gene al iew and mic opho og aphs o he CMOS p o o ype chip
Technology 0.35μm CMOS 2P4M 3.3V
Vendo (P ocess) Aus ia Mic osys ems (C35OPTO)
Diesize(wi hpads) 7280.8μm×5780.8μm
Cell size 34.07μm×29.13μm
Fill ac o 6.45%
Resolu ion QCIF: 176×144 px
Pho odiode ype n-well/p-subs a e
FPN 0.72%
PRNU (50% signal ange) 2.42%
Sensi i i y 0.15V/(lux·s)
Measu ed powe consump ion 5.6mW@12kSa/s
Maximum h oughpu 110kSa/s (9μs/Sa)
Table 1: Summa y o he p o o ype chip ea u es.
image cap u ed by he chip, oge he wi h he downsampled, a e pixel binning, 88 ×77-pixel e sion, ha
is he ini ial image o bo h he on-chip and he off-chip (ideal) fil e ing. S a ing om his image, sucessi e
s eps has been ealized in o de o gene a e a space scale. Each s ep implies he con olu ion wi h he binomial
fil e mask (B2), ei he by a e aging and shi ing he connec ion g id on-chip o di ec ly applying he mask
off-chip wi h Ma lab R
. This can be seen in Fig. 5. The fi s column ep esen s he image fil e ed on-chip. The
second he off-chip, ideal, e sion s a ing om he same inpu (Fig. 4(b)). The hi d column is he diffe ence
no malized o he alue o he maximum indi idual pixel e o de ec ed a each s ep. This maximum de ia ion
is 3.17%, 3.83%, 3.69%, 3.82%, 5.07%, 4.74%, 4.79%, 4.96% and 5.66%, espec i ely. Fo he comple e image,
he measu ed RMSE is 1.12%, 1.39%, 1.55%, 1.69%, 1.82%, 1.92%, 2.02%, 2.12% and 2.23%, espec i ely o
each s ep. No ice ha he ideal fil e ing has he effec o a e aging he ze o-mean noise in oduced by eadou a
e e y s ep o he on-chip fil e ing. This noise is e-sampled each ime a new image is deli e ed om he on-chip
p ocessing. The consequence is ha he e o ends o inc ease as we go up he scale space.
An impo an ea u e o his al e na i e me hod o compu e he scale space is ha he incidence on he
powe budge is a below he milliwa . Fo each epe i ion, shi ing he g id and a e aging wice is es ima ed
o equi e 20nJ. This es ima ion is ob ained by simula ion and ep esen s swi ching he comple e connec ion g id
wice. Image cap u e and eadou a e excluded om his sum. A 30 ps, i ep esen s 0.6μW, wha is ce ainly
negligible and below he p ecision o ou measu emen se up.
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5. CONCLUSIONS
Theo e ical backg ound o he implemen a ion o an app oxima ed Gaussian fil e by using mul i- esolu ion
capabili ies a he ocal-plane is gi en. Ideally, he only diffe ence wi h he di ec applica ion o he binomial
fil e con olu ion mask is ende ed by he ounding e o o he compu ing ha dwa e. We ha e implemen ed his
p ocedu e in a p o o ype chip wi h all he necessa y means o econfigu e he ocal-plane connec ion scheme.
The esul s e idence he alidi y o ou assump ion. The on-chip fil e ing app oxima es he ideal wi hin a 1.2%
e o . The incidence o his p ocessing in he o al powe budge o he sma image ope a ion is negligible.
ACKNOWLEDGMENTS
This wo k is pa ially unded by he Andalusian Regional Go e nmen h ough p ojec 2006-TIC-2352, by
he Spanish Minis y o Science and Inno a ion h ough p ojec TEC 2009-11812, co- unded by he Eu o-
pean Regional De elopmen Fund, and also suppo ed by he Office o Na al Resea ch (USA), h ough g an
N000141110312.
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Figu e 5: On-chip fil e ing, ideal and amplified diffe ence.
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Figu e 5: (Con .) On-chip fil e ing, ideal and amplified diffe ence(c)
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