Image Segmen a ion Inspi ed by Cellula Models using
ha dwa e p og amming
Ja ie Ca ne o, Daniel D´ıaz-Pe nil, Helena Molina-Ab il, Ped o Real
Uni e si y o Se illa, Depa men o Applied Ma hema ics, Se illa, Spain.
ja[email p o ec ed], sb[email p o ec ed], [email p o ec ed], [email p o ec ed]
Abs ac Se e al ea u es o image segmen a ion make i sui able o bio–inspi ed ech-
niques. I can be pa allelized, locally sol ed and he inpu da a can be easily encoded using
ep esen a ions inspi ed by na u e. In his pape , we p esen a new ha dwa e sys em ha
ollows he Memb ane Compu ing app oach, and pe o ms edge–based segmen a ion, noise
emo al and h esholding o digi al images.
Keywo ks: Image Segmen a ion, Compu a ional Algeb aic Topology, Memb ane Compu -
ing, Tissue-like P Sys ems, FPGA.
1 In oduc ion
Na u al Compu ing s udies compu a ional pa adigms inspi ed om a ious wellknown na u al
phenomena in physics, chemis y and biology [10]. All hese compu a ional pa adigms ha e in
common an al e na i e way o encoding he in o ma ion, adap ed o he bio–inspi ed subs a e,
and he use o in insic pa allelism o na u al p ocesses.
Wi hin his wide ield o bio–inspi ed models, Memb ane Compu ing [13, 14] a e heo e ical
models o compu a ion based on he s uc u e and unc ioning o cells as li ing o ganisms ha a e
able o p ocess and gene a e in o ma ion. The compu a ional de ices in Memb ane Compu ing
a e called P sys ems. Roughly speaking, a P sys em consis s o a memb ane s uc u e, in he
compa men s o which mul i se s o objec s a e placed. These mul i se s e ol e acco ding o
gi en ules. In he mos ex ended model, he ules a e applied in a synch onous non-de e minis ic
maximally pa allel manne , bu some o he seman ics a e being explo ed.
Se e al a emp s o b idging p oblems om Algeb aic Topology wi h Na u al Compu ing can
be ound in he li e a u e ([3, 2, 9]). Ne e heless, he ad an ages o Memb ane Compu ing ha e
no been ye exploi ed wi hin he digi al opology ield. Only sequen ial ools ha e been de eloped
(see [5]) in he bes case.
In his pape , we design a pa allel ha dwa e sys em based on a memb ane compu ing model
o implemen ing a segmen a ion algo i hm. Segmen a ion in compu e ision (see [16]), e e s o
he p ocess o pa i ioning a digi al image in o mul iple egions (se s o pixels). This p oblem has
se e al ea u es ha make i sui able o echniques inspi ed by na u e. One o hem is ha i can
be pa allelized and locally sol ed. Rega dless how la ge is he pic u e, he segmen a ion p ocess
can be pe o med in pa allel in di e en local a eas o i . Ano he in e es ing ea u e is ha he
basic necessa y in o ma ion can be easily encoded by bio–inspi ed ep esen a ions.
P e ious e sions o he issue–like P sys em segmen a ion model ha e been published in [4].
The sys em p esen ed he e is mo e e ol ed ha he ones in oduced in hose p elimina y wo ks,
whe e he noise emo al was no included, and he implemen a ion was done using a sequen ial
so wa e ha could no ake ad an age o he pa allel na u e o he heo e ical model.
The ha dwa e ool we p opose he e consis s o a Field-P og ammable Ga e A ay uni (FPGA).
FPGAs a e p e ab ica ed silicon de ices ha can be elec ically p og ammed o become almos any
kind o digi al ci cui o sys em. They ha e many ad an ages o e Applica ion Speci ic In eg a ed
143
Ci cui s (ASIC ). De eloping an ASIC akes e y much ime and is expensi e. Fu he mo e, i is
no possible o co ec e o s a e ab ica ion. In con as o ASICs, FPGAs a e con igu ed a e
ab ica ion and hey also can be econ igu ed. This is done wi h a ha dwa e desc ip ion language
(HDL) which is compiled o a bi s eam and downloaded o he FPGA ([1]). FPGAs con ain
p og amable logic componen s called logic blocks, and a hie a chy o econ igu able in e connec s
ha allow he blocks o be wi ed oge he . Logic blocks can be con igu ed o pe o m complex
combina ional unc ions, o me ely simple logic ga es like AND and XOR. The FPGA used he e
also includes memo y elemen s in he logic blocks.
Al hough we ocus he e in a p oblem ha can be conside ed a he simple om he image
analysis poin o iew, his wo k p o ides a i s p omising s ep owa ds he use ulness o memb ane
compu ing wi hin he image p ocessing ield.
Wi h he ad–hoc sys em we p opose, he execu ion o he segmen a ion p ocess consumes
always he same ime, independen ly o he image size. The ha dwa e design is unique and alid
o dealing wi h highe dimensional images.
The pape is o ganized as ollows: Fi s ly, he bio–inspi ed o mal amewo k o he wo k is
de ined. Nex , we in oduce he amily o issue–like P sys ems ha has been de eloped o ob ain
image segmen a ion. In Sec ion 4 he ha dwa e sys em ha implemen s he memb ane s uc u e
is shown. The pape inished wi h some conclusions and u u e wo k.
2 Fo mal F amewo k
In he ini ial de ini ion o he cell-like model o P sys ems [13], memb anes a e hie a chically
a anged in a ee–like s uc u e. I s biological inspi a ion comes om he mo phology o cells,
whe e small esicles a e su ounded by la ge ones. This biological s uc u e can be abs ac ed
in o a ee–like g aph, whe e he oo ep esen s he skin o he cell (i.e., he ou e mos memb ane)
and he lea es ep esen memb anes ha do no con ain any o he memb ane.
In issue P sys ems, he ee-like memb ane s uc u e is eplaced by a gene al g aph. This
model has wo biological inspi a ions (see [12, 11]): in e cellula communica ion and coope a ion
be ween neu ons. The common ma hema ical model o hese wo mechanisms is a ne o p ocesso s
dealing wi h symbols and communica ing hese symbols along channels speci ied in ad ance. The
communica ion among cells is based on sympo /an ipo ules. In sympo ules, objec s coope -
a e o a e se a memb ane oge he in he same di ec ion, whe eas in he case o an ipo ules,
objec s esiding a bo h sides o he memb ane c oss i simul aneously bu in opposi e di ec ions.
Fo mally, a issue-like P sys em o deg ee q≥1 wi h inpu is a uple o he o m
Π=(Γ,Σ,E,w
1, . . . , wq,R,i
Π,o
Π)
whe e
1. Γis a ini e alphabe , whose symbols will be called objec s,
2. Σ(⊂Γ) is he inpu alphabe ,
3. E⊆Γ( he objec s in he en i onmen ),
4. w1, . . . , wqa e s ings o e Γ ep esen ing he mul ise s o objec s associa ed wi h he cells
a he ini ial con igu a ion,
5. Ris a ini e se o communica ion ules o he ollowing o m: (i, u/ , j), o i, j ∈{0,1,2,...,
q},i%=j,u, ∈Γ∗,
6. iΠ,o
Π∈{0,1,2, . . . , q},
A issue-like P sys em o deg ee q≥1 can be seen as a se o qcells labeled by 1,2, . . . , q. We will
use 0 o e e o he label o he en i onmen , iΠand oΠdeno e he inpu egion and he ou pu
egion (which can be he egion inside a cell o he en i onmen ) espec i ely.
144
The s ings w1, . . . , wqdesc ibe he mul ise s o objec s placed in he qcells o he sys em. We
in e p e ha E⊆Γis he se o objec s placed in he en i onmen , each one o hem a ailable in
an a bi a y la ge amoun o copies.
The communica ion ule (i, u/ , j) can be applied o e wo cells labeled by iand jsuch ha
uis con ained in cell iand is con ained in cell j. The applica ion o his ule means ha he
objec s o he mul ise s ep esen ed by uand a e in e changed be ween he wo cells. No e ha
i ei he i= 0 o j= 0 hen he objec s a e in e changed be ween a cell and he en i onmen .
Rules a e used as usual in he amewo k o memb ane compu ing, ha is, in a maximally
pa allel way (a uni e sal clock is conside ed). In one s ep, each objec in a memb ane can only
be used o one ule (non-de e minis ically chosen when he e a e se e al possibili ies), bu any
objec han can pa icipa e in a ule o any o m mus do i , i.e., a each s ep a maximal se o
ules is applied.
3 Segmen ing Digi al Images
In his sec ion, a amily o P sys ems is de ined o ob ain an edge–segmen a ion o a 2D digi al
image. Fi s o all, he sys em applies a basic noise il e in o de o elimina e some pickle noise
ha could a ec he segmen a ion p ocess. Nex , he sys em pe o ms a h esholding o he image
o sol e he p oblem o deg ada ion o colou s o pixels in he bounda y o adjacen egions wi h
di e en colou s. Once his p ocess is inished, he sys em applies he ules de ined in [4] ob aining
he image segmen a ion.
In o de o emo e noise, he sys em will apply he la gely used a e age il e because o i s
simplici y and good esul s. Fo each pixel, he p ocess consis s o calcula ing he colou a e age
o i s adjacen pixels. I he dis ance be ween he pixel and i s a e age is bigge han a h eshold
, he pixel will be conside ed as noise and i will be eplaced by i s colou a e age.
Th esholding is a me hod o image segmen a ion whose basic aim is o ob ain a bina y image
om a colou one. The idea is o spli he se o pixels in o wo se s (black and whi e) depending on
i s b igh and a ixed alued, he h eshold. I he b igh o he pixel is g ea e han he h eshold,
hen he pixel is labelled as objec . O he wise, i is labelled as backg ound. A e labelling, a new
bina y image is c ea ed by colou ing each pixel whi e o black, depending on he label.
The basic h esholding me hod can be gene alized in a na u al way. Ins ead o ge ing a
bina y image by labelling he o iginal se o pixels by {0,1}, we can conside a la ge se o labels,
{1, . . . , k}so we ob ain a inal image wi h kle els. Ano he na u al gene aliza ion is o eplace
he colou in o ma ion by ano he scale on he ea u es o he pixel (b igh , in ensi y, g ay scale,
e c.).
The digi al image is subdi ided in mul iple pixels o ming a ne wo k o poin s o N2. Le
C⊆Nbe he se o all colou s in he gi en image in a ce ain o de . |C| is de ined as he numbe
o colou s in C. We will assume ha each pixel is associa ed o a colou o he image. Then, we
encode he pixel (i, j) wi h associa ed colou a∈Cwi h he objec aij o he sys em.
Conce ning he adjacency be ween pixels, he 4–neighbo hood ela ion be ween hem is con-
side ed [15]. F om a memb ane compu ing poin o iew i is easie o wo k wi h 8-adjacency.
Gi en a 2Ddigi al image, o each n∈N, we conside he issue-like P sys em
Π=(Γ,Σ,E,w
1,w
2,R,i
Π,o
Π),
de ined as ollows:
(a) Γ=Σ∪{a"
ij,a
""
ij,¯aij,A
ij :1≤i, j ≤n, a ∈C},
(b) Σ={aij :1≤i, j ≤n, a ∈C},
(c) E=Γ−Σ,
(d) w1= n2
1,w2=∅,
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(e) Ris he ollowing se o communica ion ules:
1. (1,
i/ i+1,0) wi h i=1,...,18.
These ules a e used as coun e o know when sys em can begin he h esholding phase.
2. (1,a
ij,b
ij−1,c
i−1j−1,d
i−1j,e
i−1j+1,
ij+1,g
i+1j+1,h
i+1j,i
i+1j−1/
a (a)ij ,b
ij−1,c
i−1j−1,d
i−1j,e
i−1j+1,
ij+1,g
i+1j+1,h
i+1j,i
i+1j−1,0)
wi h
∗1≤i, j ≤n,
∗a, b, c, d, e, , g, h, i ∈C,
∗a (a)=(b+c+d+e+ +g+h+i)/8 and
∗|a−a (a)|> .
These se o ules a e used o de ec he noise and co ec i wi h he colou a e age o
i s adjacen pixels.
3. (1,
19 aij/a"
ij,0)
wi h
∗a∈Cand
∗1≤i, j, k, l ≤n.
These ules a e used o ade objec s aij om cell 1 agains objec s a"
ij om he en i-
onmen . So, we can do he h esholding in he nex s ep.
4. (1,b
"
ij/a""
ij,0)
wi h
∗1≤i, j ≤n,
∗m=(|C|/k),
∗a, b ∈C,a<b≤a+(m−1), a=m·land
∗l=0,1,2,...,k.
These ules a e used o disc e ize he colo s di iding he se o colo s in kin e als o
leng h m.
5. (1,a
""
ijb""
kl/¯aijAijb""
kl,0),
wi h
∗a, b ∈C, a < b,
∗1≤i, j, k, l ≤n.
These ules a e used when image has wo adjacen pixels wi h di e en associa ed colo s
(bo de pixels). Then, he pixel wi h less associa ed colo is ma ked and he sys em
b ings om he en i onmen an objec ep esen ing his ma ked pixel (edge pixel).
4. (1,¯aija""
ij+1¯ai+1j+1b""
i+1j/¯aij ¯aij+1Aij+1¯ai+1j+1b""
i+1j,0)
wi h
∗a, b ∈C, a < b and
∗1≤i, j ≤n−1.
(1,¯aija""
i−1j¯ai−1j+1b""
ij+1 /¯aij ¯ai−1jAi−1j¯ai−1j+1b""
ij+1,0)
wi h
∗a, b ∈C, a < b and
∗2≤i≤n, 1≤j≤n−1.
(1,¯aija""
ij+1¯ai−1j+1b""
i−1j/¯aij ¯aij+1Aij+1¯ai−1j+1b""
i−1j,0)
wi h
146
∗a, b ∈C, a < b and
∗2≤i≤n, 1≤j≤n−1.
(1,¯aija""
i+1j¯ai+1j+1b""
ij+1 /¯aij ¯ai+1jAi+1j¯ai+1j+1b""
ij+1,0)
wi h
∗a, b ∈C, a < b and
∗1≤i, j ≤n−1.
These ules ma k wi h a ba he pixels ha a e adjacen o wo pixels wi h he same
colo ha we e ma ked be o e, bu wi h he condi ion ha he ma ked objec s a e
adjacen o an o he pixel wi h a di e en colo . An edge objec ep esen ing he las
ma ked pixel is b ough om he en i onmen .
5. (1,A
ij/λ,2), wi h 1 ≤i, j ≤n.
This ule is used o send he edge pixels o he ou pu cell.
( ) iΠ= 1, oΠ= 2.
The inpu da a o he sys em is gi en by he se {aij :a"∈C,1≤i, j ≤n}, codi ying he
pixels o he image.
4 A Ha dwa e Tool
A ha dwa e sys em implemen ing he issue-like P sys em desc ibed abo e is shown in Figu e 1.
The sys em consis s o p ocessing uni s capable o deal wi h 4 ×4 images. These uni s can be
combined like a puzzle in o de o p ocess n×mimages.
A4×4 sec ion o he ini ial image is passed ough he I/O po o each p ocessing uni . The
esul ing image is also ead om his po . The Bo de Pixels and Adjacen Pixels po s a e used
o in e connec p ocessing uni s in o de o deal wi h bigge size images.
The and kpo s speci y he maximum dis ance be ween he pixel and i s a e age (noise
il e ), and he numbe o di e en le els o he h esholding espec i ely.
Looking inside he p ocessing uni , a i s sigh wo image uni s can be dis inguished. The
pu pose o hese uni s is o s o e he o iginal elemen s o he image and he esul ing ones a e
applying he sys em ules ( hey ep esen he mul i–se o he cell). Al hough he p ocess could
be pe o med using only one image uni , one o hem will be used o ead/w i e he image, while
he o he one is p ocessing. The e o e, he sys em does no was e any ime in w i ing he new
image and is able o p ocess and ead he esul ing one ( he sys em is always wo king).
The in e connec ion ci cui is esponsible o connec ing each pixel and i s adjacen ones o i s
pixel p ocessing uni , and connec he esul ing objec wi h he image uni s. The pixel p ocessing
uni sends his in o ma ion o he ou ule uni s (NoiseFil e ing, Th esholding and Segmen a ion
one and wo), collec s he ecei ed in o ma ion and sends he esul ing objec o he in e connec ion
ci cui . The e o e, ou ule uni s a e needed o each pixel.
Each ule uni ep esen s a se o heo e ical ules ha can no be execu ed a he same ime
o he same pixel. Fo example, o a pixel in he noise il e ing p oblem, a mos only one ule
will be applied o his pixel in o de o change he pixel by i s a e age, so o ha pixel, all he
ules acco ding wi h he noise il e ing can be g ouped in one concu en compu a ion uni , he
noise il e ing uni .
The implemen a ion o his ha dwa e ool allows he sys em o apply he maximum numbe o
ules a each momen , using only ou ule uni s o pixel o sol e he whole p oblem. The e o e,
he sys em wo ks exac ly like he heo e ical model in e ms o complexi y, ime, concu ency and
esul s.
The p ocessing uni con olle con ols all he sys em, in o de o make he di e en pa s wo k
p ope ly.
147

Figu e 1: Ha dwa e sys em
4.1 Implemen a ion
As men ioned abo e, a FPGA has been used o implemen he desc ibed sys em. Mo e p ecisely,
he design is based on he XC6SLX45T-FGG484-3CES FPGA chip o Xilinx. This chip has been
chosen due o i s quali y–cos ela ion.
The implemen a ion o he sys em in o a FPGA equi es ou s eps: Desc ip ion, syn hesis,
implemen a ion and p og amming.
Fi s ly, he sys em is desc ibed by a ha dwa e desc ip ion language. Fo his pu pose, we
ha e used VHD (VHSIC ha dwa e desc ip ion language). VHD is a well known language ha has
been widely used in elec onic design au oma ion o desc ibe digi al (ou case) and mixed-signal
sys ems. Due o he ac ha we wo k wi h a pa allel code, he usual p og amming pa adigms
a e no sui able he e. Wo king wi h elec ical elemen s o ces us o deal wi h signal luc ua ions,
i-s a e bu e s, e c.
Once he sys em has been desc ibed, we a e able o pe o m unc ional simula ions (Figu e 2).
The second and hi d s eps a e needed in o de o ansla e he desc ibed sys em in o a logic
sys em (in e ms o logic doo s, NAND, XOR, e c..) and o glue hem oge he con o ming a
unique ile espec i ely.
Once he syn hesis and implemen a ion a e comple e, di e en empo al simula ions (mo e
accu a e han he unc ional one) can be pe o med.
Finally, he ile is compiled o be p og ammed in he FPGA chip. Because o he inexac ness
o he simula ions, some inal adjus men s need o be done in o de o make he eal sys em wo k.
148
Figu e 2: Simula ion
Se e al so wa e ools (called IDEs (In eg a ed De elopmen En i onmen )) a e a ailable o
con ol he implemen a ion p ocess. We ha e used he Xilinx ISE Webpack ool and he Xilinx
ISim simula ion ool o simula e he beha io o he sys em.
Wi h his implemen a ion, he sys em is able o p ocess any image o size n×musing a mos
ou clock cycles.
In Figu e 2 a simple simula ion example is shown. In his example wo images a e segmen ed
wi hin eigh clock cycles. The i s image consis s o a whi e iangle a he op– igh co ne
o he image. The second one has whi e pixels a he le side, and black pixels a he igh
side (img o ig(0:3) signal). The signal change is used o in o m he sys em ha he esul has
been ob ained ( esul singal). Al hough he esul is eady a e he ou h clock cycle (40 h
picoseconds in he simula ion), i is no ecei ed un il he 44 h picosecond. The eason is ha he
simula ion, signal change changes a ha poin . Tha does no change he ac ha he sys em
s a s p ocessing he new image a he 45 h picosecond. The e o e, he second image is esol ed
a he 80 h picosecond (again 4 clock cycles) and hen, he esul is ob ained (when he change
signalis ac i a ed) a he 88 h picosecond.
5 Final Rema ks
In his pape , we p esen a new ool o ob ain a segmen a ion o digi al images. The sys em
ollows a memb ane compu ing app oach, and ha dwa e p og amming (VHDL) is used o de elop
an ad–hoc p ocesso o sol e he p oblem.
This is a i s s ep in a new esea ch line whe e e y di e en a eas like Compu a ional Algeb aic
Topology, Image P ocessing, Memb ane Compu ing and Ha dwa e P og amming a e being mixed
o gene a e new use ul ools.
In he nex u u e, we plan o ollow wo pa hs. Fi s ly, he de elopmen o he sys em in o de
o deal wi h mo e complica ed image p ocessing p oblems. Mo eo e , i is a compulso y ask o
compa e ou sys em wi h some o he exis ing ha dwa e segmen a ion me hods ([8, 6, 7]).
On he o he hand, we plan o de elop new ools o compu e homological in o ma ion on digi al
images (homology g oups, spanning ees, homology g adien ec o ield, e c.). Un il now, his
homological in o ma ion has been ypically ob ained using sequen ial algo i hms o , in he bes
case, pa ially pa allel algo i hms. We belie e ha he use o FPGA and P sys ems can help in
he pa alleliza ion o some o he exis ing me hods.
Acknowledgemen s
DDP acknowledge he suppo o he p ojec s TIN2008-04487-E and TIN-2009-13192 o he Min-
is e io de Ciencia e Inno aci´on o Spain and he suppo o he P ojec o Excellence wi h In es-
igado de Reconocida Val´ıa o he Jun a de Andaluc´ıa, g an P08-TIC-04200. JC, HMA and PR
acknowledge he suppo o he p ojec MTM2009-12716 o he Minis e io espa˜nol de Educaci´on y
Ciencia, he p ojec PO6-TIC-02268 o Excellence o Jun a de Andaluc´ıa, and he Compu a ional
Topology and Applied Ma hema ics PAICYT esea ch g oup FQM-296.
149
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