ulises amaya human eyes ray tracing and modeling approach

8/12/2019 Ulises Amaya Human Eyes Ray Tracing and Modeling Approach

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UNIVERSITY OF CALIFORNIARIVERSIDE

Human Eyes Ray Tracing and Mde!ing a""rac#

A "r$ec% su&mi%%ed in "ar%ia! sa%is'ac%in' %#e re(uiremen%s 'r %#e degree '

Mas%er ' Science

In

Cm"u%er Science

)y

U!ises Amaya

Augus% *++,

-r$ec% Cmmi%%ee.Dr/ Vic%r 0rdan1 C#air"ersnDr/ Eamnn 2eg#


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C"yrig#% &yU!ises Amaya

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T#e "r$ec% ' U!ises Amaya is a""r3ed.

Cmmi%%ee C#air"ersn

Uni3ersi%y ' Ca!i'rnia1 Ri3erside


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Human Eyes Ray Tracing and Modeling Approach

U!ises Amaya Mas%er4s "r$ec%Ad3isr. Dr/ Vic%r 0rdan

Uni3ersi%y ' Ca!i'rnia1 Ri3ersideCm"u%er Science and Engineering De"ar%men%

uamaya5a%6cs/ucr/edu

ABSTRACT

In this project a ray tracer is constructed with the flexibility to specify multilayered

objects with properties such as transparency, absorption, shininess, reflectivity and

refractivity among others that create an approximate model of a human eye. The iris is

modeled using a number of probability and randomness functions to specify the colour

and intensity at every point.

1. Introduction

Ray %racing is a cm"u%er gra"#ics g!&a! i!!umina%in rendering me%#d/ I% %races %#e

rays ' !ig#% &ac78ards/ A ray is s#% 'rm a se!ec%ed 3ie8"in% %#rug# a *D grid r

image "!ane and in% a 3ir%ua! 8r!d and 'ina!!y &ac7 % %#e !ig#% surce/ In%ersec%ins

8i%# %#e &$ec%s are cm"u%ed and %#e "i9e! is c!ured accrding % a num&er ' 'ac%rs

s"eci'ied &y %#e &$ec%s1 %#e !ig#%s and %#e "%ica! "#ysics !a8s/

T#rug# 3arius ma%#ema%ica! mde!s 8#ic# are s#8n in %#is dcumen% 8e are

a&!e % cns%ruc% %#e iris &y s"eci'ying %#e R:) 3a!ue a% e3ery "in% in %#e crres"nding"i9e!/ T#e ray %racing gi3es us %#e in%ersec%in1 %#en 8e ge% %#e i!!umina%in "r"er%ies '

%#e ma%eria! and %#e ma%#ema%ica! mde! gi3es us %#e R:) 3a!ue/ ;e a!s use cn%r!!ed

randmness % mde! an a""r9ima%in ' 8#a% #a""ens in %#e &i!gica! mde! ' %#e

eye/


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. Bac!ground

Ray %racing #as &een arund 'r a 8#i!e n8/ T#ere #as &een muc# researc# in %#is C:

%ec#ni(ue/ T#is %ec#ni(ue is an a""rac# n #8 8e see in %#e rea! 8r!d/ Lig#% is

genera%ed 'rm many surces1 and %ra3e!s %#rug# many mediums/ I% may &unce arund

mu!%i"!e &$ec%s as i% ge%s a&sr&ed and sca%%ered/ )y a&sr&ed 8e mean %#a% %#e !ig#% as a

'rm ' energy is "ar%ia!!y %rans'rmed % an%#er 'rm/ )u% in ray %racing 8#a% 8e care

a&u% is %#e ac%ua! !ig#% %#a% ge%s % ur eyes/ S in %#is case 8e say %#a% i% is a&sr&ed and

%#us 8e !se sme !ig#%/

In ray %racing a ray is s#% 'rm a se!ec%ed 3ie8"in% r camera %#rug# a *D

image "!ane and in% a 3ir%ua! 8r!d/ T#e ray is %raced as i% %ra3e!s and in%ersec%s %#e

&$ec%s in %#is 8r!d/ T#e c!ses% in%ersec%in is s%red and secndary rays are s"a8ned

'rm %#e in%ersec%in "in%/ T#ese secndary rays may &e re'!ec%ed rays r re'rac%ed rays

in %#e case %#a% %#e sur'ace is %rans"aren% r %rans!ucen%/ An%#er %y"e ' rays named

s#ad8 rays is a!s used/ T#ese rays %es% 8ea%#er %#e !ig#% surces


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;#ere Ix is %#e resu!%ing c!ur1 A, D, S, are %#e crres"nding cn%ri&u%ins 'rm

am&ien%1 di''use and s"ecu!ar !ig#%s/ R1 L and V are %#e re'!ec%in1 !ig#% and 3ie8 3ec%rs

crres"nding!y and N is %#e nrma! % %#e in%ersec%ed "in%/ N%ice %#a% %#e mde! #as

&een e9%ended % incr"ra%e a%%enua%in as 8e!!/ ;e 8i!! %a!7 mre a&u% %#is during %#e

descri"%in ' %#e mde!/

". E#tended Algorithm

T#e &asic a!gri%#m %#a% 8e use is ray %racing/ T#e rays are %raced u" % a rd!e3e!

' de"%#/ T#is !e3e! 8as c#sen ar&i%rari!y1 a de"%# ' , 8as a!s %es%ed 8i%# n 3isi&!e

resu!%s/ I% is % n%ice %#a% in ray %racing1 in%ersec%ins and de"%# !e3e! cn%ri&u%e

cnsidera&!y % %#e %ime cm"!e9i%y/ T#is a!gri%#m 8as e9%ended &y inc!uding

a%%enua%in and a&sr"%in/ A%%enua%in simu!a%es %#e sca%%ering ' !ig#% as i% %ra3e!s

%#rug# %#e en3irnmen%/ A&sr"%in is %#e amun% ' !ig#% &eing

a medium inside an &$ec%/

T#e !a%%er is %#e ne %#a% cn%ri&u%es mre % %#e !7 ' %#e eye/ T#e 'irs% is

inc!uded s %#a% %#e sys%em is mre cm"!e%e in case %#a% %#e anima%r 8an%s % inc!ude

&$ec%s a% 3ery di''eren% de"%# dis%ances/ A%%enua%in is &asica!!y dis%ance*/ A&sr"%in

is mde!ed using )eer4s La8.

Lig#% u% = !ig#% in G e@e G c G dB

8#ere einside %#e "aren%#esis is %#e amun% %#a% %#e medium a&sr&s1 cis %#e densi%y '

%#e medium and dis %#e dis%ance %#a% %#e !ig#% #as %ra3e!ed/

Cns%ruc%i3e S!id :eme%ry @CS:B is a!s incr"ra%ed in %#e sys%em/ Using

CS: 8e are a&!e % cns%ruc% eac# "ar% ' %#e eye se"ara%e!y/ T#is is dne s %#a% 8e can

s"eci'y 'r eac# "ar% a di''eren% inde9 ' re'rac%in @IORB1 as 8e!! as ce''icien%s 'r %#e

amun% ' re'rac%in1 re'!ec%in1 a%%enua%in1 a&sr"%in1 c!ur and s#ininess/ T#is a!!8s


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us % crea%e a 3ir%ua! eye 8#ic# is simi!ar % %#e &i!gica! eye/ Figure i!!us%ra%es a crss

sec%in ' %#e eye s %#a% %#e reader &ecmes 'ami!iar 8i%# i%/

Fig/ A crss sec%in ' %#e #uman eye

$. Construction o% the Eye

;e &egin &y using CS: % cns%ruc% %#e sc!era 8i%# %8 !ayers/ T#e %" !ayer

a!!8s !ig#% % g %#rug# a &i% mre %#an %#e !8er ne/ )%# #a3e %#e same IOR and

same 8#i%e c!ur/ T#en 8e cn%inue % cns%ruc% %#e crnea/ Again i% #as %8 !ayers and

&%# are ms%!y %rans"aren%/ T#e u%er !ayer #as %#e IOR ' %#e crnea 'und in %#e

!i%era%ure1 8#ic# is ' // T#e secnd !ayer ac%s as %#e in%er'ace &e%8een %#e crnea and

%#e iris/ In %#e rea! eye %#ere is a sma!! amun% ' a(uus #umr 8#ic# #as a di''eren%

IOR and s %#e secnd !ayer #as %#e IOR ' %#e a(uus #umr 8#ic# is ' //

F!!8ing is %#e cns%ruc%in ' %#e re%ina 8#ic# is mde!ed 3ery simi!ar % %#e sc!era/

T#e main di''erence is %#a% %#e a&sr"%in is #ig#er and %#e c!ur is red since is i%

%#e ne main!y made u% ' &!d 3esse!s/ ;e n8 arri3e a% %#e !ens/ T#e !ens is %#e %#er


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main "ar% ' %#e eye %#a% is res"nsi&!e 'r re'rac%ing %#e !ig#% a'%er %#e crnea/ I% 8as

mde!ed as c!se % %#e rea! ne as "ssi&!e/ T#e !i%era%ure s#8s #uman !ens as s!ig#%!y

nn symme%ric/ T#e crea%ed !ens #as IOR ' / and is a!ms% 'u!!y %rans"aren%/ T#e !ens

again #as %8 !ayers 8#ic# ma7e i% "ssi&!e % c#ange %#e IOR 'rm %#e !ens % %#e

a(uus #umr/ Here 8e s#8 a 'e8 images i!!us%ra%ing %#e di''eren% "ar%s ' %#e 3ir%ua!

eye using CS:/

Fig */ Sc!era1 Iris and !ens crea%ed using CS:/ T#e sc!era is %#e 8#i%e "ar% ' %#e eye 8#ic# is #!!8 and

8i!! #s% %#e iris and !ens/ T#e iris &ase is a %runca%ed cne 8i%# a #!e in %#e midd!e and %#e !ens is s!ig#%!y

nnJsymme%ric #a3ing ne side &igger %#an %#e %#er/


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$.1 Iris

T#e iris is %#e ms% in%eres%ing and cm"!ica%ed "ar% ' %#e eye/ ;i%# i%s

cm"!ica%ed "a%%erns 8#ic# are uni(ue % e3ery indi3idua! and %#e c!urs %#a% em&e!!is#

%#ese "a%%erns1 8e #a3e #ad a %ug# %ime 'inding %#e rig#% ma%#ema%ica! 'unc%ins %#a%

8u!d a!!8 us % mde! %#e iris/ T#e iris &ase is a cneJs#a"ed disc s#8n in 'igure /

T#e c!urs are gi3en % i% de"ending n %#e "si%in ' %#e "i9e!/ )asica!!y 'r e3ery

"i9e! 8e cm"u%e1 %#rug# a series ' 'unc%ins %#a% 8e 8i!! descri&e n81 i%s

crres"nding c!ur/ Firs% %#ere are a 'e8 %#ings % n%ice/ )y !7ing a% 3arius rea!

e9am"!es 8e can &ser3e %#a% c!se % %#e cen%er ' %#e eye %#ere is a ring ' s#ar"er r

s!ig#%!y di''eren% c!ur %#an %#e res% ' %#e iris/ A!s1 %#a% %#e "a%%erns %end % &e radia!

ra%#er %#an %angen%ia! and 'ina!!y %#a% %#ere is a dar7er ring in %#e cn%ur ' %#e iris as i%

merges in% %#e sc!era/

Fig/ A "ic%ure ' a rea! iris1 n%ice %#a% c!se % %#e "u"i!

%#ere is an area 8#ic# #as a di''eren% c!ur/

T#e a""rac# 8e %a7e is % ge% %#e "i9e!s in a %angen%ia! 8ay1 %#is means %#a% 8e

ge% a!! %#e "i9e!s %#a% !ie in cer%ain ang!e and cm"u%e %#eir c!ur/ T#e c!ur is

cm"u%ed accrding % a cm&ina%in ' 'unc%ins/ T#e 'irs% %#a% 8e 8i!! descri&e is an

e9"nen%ia! "r&a&i!is%ic 'unc%in/ T#is 'unc%in gr8s ra"id!y and a!!8s us % dar7en


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%#e u%er edge ' %#e iris 8#ic# crres"nds % %#e !as% *+K ' i%/ Using :aussian 8#i%e

nise 8e are a&!e % ma7e %#is dar7er ring !7 mre &i!gica! as ""sed % n!y a ring

&y i%se!'/ T#e c!urs used are &!ue and green1 red is main%ained a% + &u% &y 3arying %#e

red 8e can &%ain c!urs suc# as 'r &r8n eyes/ T#is 'unc%in is descri&ed &y %#e

'!!8ing e(ua%in/

- = @J-B G @J e@I G @ J G 7BBB > -

;#ere - is %#e "r&a&i!i%y1 I and 7 are ini%ia! "arame%ers/ T#e ne9% %8 'unc%ins are %#e

nes %#a% gi3e c!ur % %#e res% ' %#e iris/

C!ur = J A@C G % C G 9B A@JC > C G 9B

A@C G 9B A@JC > C G 9B

;#ere A is %#e arctangent1 C is a cns%an% se% &y %#e user1 % is %#e radius 'rm %#e cen%er

' %#e "u"i! and 9 is a randm num&er &e%8een + and / )y 3arying %#e cns%an% C1 %#e

user can ma7e %#e 'unc%in decrease a% a di''eren% ra%e/ Fig s#8s di''eren% 8ays %#a%

%#e 'unc%in can decrease/ T#is num&er is c#sen randm!y and %#is is #8 8e c!ur

%angen%ia!!y %#e !ines in %#e iris/ S %#a% %#e !ines are n% n!y discree% %#e resu!% '


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Fig / di''eren% 8ays in 8#ic# C!ur can g 'rm green in% &!ue

;i%# a!! ' %#e a&3e 8e ac#ie3e an iris 8#ic# ges sm%#!y 'rm green in%

&!ue1 %#a% c#anges in%ensi%y de"ending n %#e radius dis%ance and %#a% near %#e u%er ring

i% dar7ens (uic7!y/ T#e %angen%ia! !ines are &%ained %#e same 8ay &y 8r7ing 8i%# %#e

arc%angen% &u% %#is %ime 8i%# mre "recisin/ Fig , s#8s e9am"!es ' #ig# (ua!i%y

renderings/ T#e &!ue re'!ec%in n %" is a s"#ere in %#e 8r!d n% s#8n in %#e image/

Fig ,/ Fina! rendering ' %#e 3ir%ua! #uman eye


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&. 'iscussion and Results

;e #a3e "resen%ed an a""rac# % crea%e 3ir%ua! #uman eyes 8i%# a cm&ina%in

' a ray %racer and a ma%#ema%ica! mde! 'r %#e iris/ T#is a!!8s %#e '!e9i&i!i%y % crea%e

di''eren% c!urs 'r %#e iris1 eyes 8i%# a cn%rac%ed r di!a%ed "u"i!1 di''eren% !7s

de"ending n %#e a&sr"%in ' %#e iris r %#er "ar%s ' %#e eye1 red eyes !i7e %#e nes in

%#e "ic%ures 8i%# '!as#1 and eyes 8i%# c!urs %#a% are nnJ#uman/ T#e cde is

im"!emen%ed in C>> and a!!8s 'r easy c#ange ' 'unc%ins %#a% mde! %#e eye and

s%raig#% 'r8ard mdi'ica%in ' %#e c#arac%eris%ics ' %#e "ar%s ' %#e eye !ayer &y !ayer

suc# as s#ininess1 a&sr"%in1 am&ien%1 di''use and s"ecu!ar cm"nen%s1 amun% '

re'rac%in and re'!ec%in1 inde9 ' re'rac%in and densi%y ' %#e ma%eria!/ I% is a!s

im"r%an% % men%in %#a% su"er sam"!ing is incr"ra%ed in %#e cde 8#ic# a!!8s %#e

user % s"eci'y %#e num&er ' rays s#% %#rug# eac# "i9e! in %#e image "!ane/ T#e #ig#

(ua!i%y renderings 8#ere made 8i%# rays "er "i9e! and %#e cm"u%a%in %ime is ' %#e

rder ' , minu%es n a - IV mac#ine 8i%# :& ' RAM/ T#e cde is n% "%imied and

can &e dne s &y using a 2DJTree da%a s%ruc%ure/ T#e cde n!y incr"ra%es as

"rimi%i3es %#e cne1 s"#ere and "!ane1 a cu&e cu!d a!s &e desira&!e % ma7e mre and

di''eren% mde!s/ T#e cde can &e 'ur%#er &ene'i%ed i' a &e%%er i!!umina%in mde! is

incr"ra%ed as 8e!! as mre 'unc%ins % mde! di''eren% %y"es ' irises suc# as %#e ne

' a ca%/ Figures and s#8 di''eren% %y"es ' resu!%s and #8 %#e eyes 8u!d !7 8i%#

%#e surrunding en3irnmen% ' '!es# and eye!as#es/ T#e surrunding en3irnmen%s

8#ere n% crea%ed &y us and are used n!y 'r i!!us%ra%i3e "ur"ses/


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Fig / Fina! renderings ' a di!a%ed eye1 di''eren% c!urs1 a redJeye !i7e %#e nes %#a% a""ear in a

'!as# '%gra"#1 and an eye 8i%# e9aggera%ed densi%y/

Fig / T#e iris is incr"ra%ed in 3ir%ua! en3irnmen%s n% crea%ed &y me % s#8 %#a% i% rea!!y

gi3es a 'ee!ing ' a na%ura! eye/

Ac!no(ledgements

I 8u!d !i7e % %#an7 Dr/ Vic%r 0rdan 'r #is guidance during %#e curse ' %#is "r$ec%/

T#e s'%8are discussed in %#is re"r% 8as &ui!% n %" ' %#e CS+ undergradua%e

cm"u%er gra"#ics "r$ec% &y Mi7i7 Ma%sunaga/ I 8u!d a!s !i7e % %#an7 a!! %#a%

"ar%ici"a%ed in %#e scien%i'ic discussins 'r %#eir 3a!ua&!e in"u%/


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Re%erences

/ T#e #uman eye. s%ruc%ure and 'unc%in C!yde ;/ Oys%er1 /

*/ Ha!!iday Resnic71 Fundamen%a!s ' -#ysics1 E1 ;i!ey PP

/ Cm"u%er :ra"#ics. "rinci"!es and "rac%ice/ Q/ D/ F!ey/ ,

/ Ray Tracing in'rma%in.

888/siggra"#/rgeduca%inma%eria!sHy"er:ra"#ray%racer%race+/#%m

,/ Qenni'er )eers1 The T ay Tracing !roject, Uni3ersi%y ' ;as#ing%n1 )%#e!!/

/ )eer4s La8 888/s#u/ac/u7sc#!sscic#em%u%ria!sm!s"ec&eers/#%m

/ Eye s%ruc%ure images and in'rma%in.

#%%".888/mydr/cm/aude'au!%/as"Ar%ic!e=*

#%%".888/%edmn%gmery/cm%#eeye3er3ie8/#%m!

#%%".#y"er"#ysics/"#yJas%r/gsu/edu#&ase3isineyesca!/#%m!

P/ Eye surrundings in 'ig/ .

A7i 'rm %#e m3ie "#inal #antasy$ The Spirits %ithin&

#%%".888/des7%"e9c#ange/cmga!!erya!&umsDJ8a!!"a"ersDeyes&ig/$"g

ulises amaya human eyes ray tracing and modeling approach

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