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Адаптивні алгоритми усунення імпульсних шумів зі зображень з використанням порядкових статистик: Автореф. дис… канд. техн. наук / Ю.Б. Рицар, НАН Ук

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Iaoe?iiaeueia aeaaeai?y iaoe Oe?a?ie

I?i?noa?noai ?ioi?iaoe?? Oe?a?ie

Aea?aeaaiee iaoeiai-aeine?aeiee ?inoeooo

?ioi?iaoe?eii? ?io?ano?oeoo?e

OAeE 621.391

?EOeA?

TH??e Aiaaeaiiae/

aaeaioeai? aeai?eoie onoiaiiss ?iioeuenieo ooi?a c? cia?aaeaiue c
aeei?enoaiissi ii?ssaeeiaeo noaoenoee

Niaoe?aeuei?noue: 05.13.06 – Aaoiiaoeciaai? nenoaie oi?aae?iiy oa

i?ia?aneai? ?ioi?iaoe?ei? oaoiieia??

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

Euea?a – 1998

Caaaeueia oa?aeoa?enoeea ?iaioe

Aeooaeuei?noue oaie. Nenoaie oeeo?iai? ia?iaee cia?aaeaiue iathoue
oe?iea aeei?enoaiiy o ??ciiiai?oieo iaeanoyo ethaenueei? ae?yeueiino?,
cie?aia a i?ioean? aiae?co ?aioaai?anueeeo, oaieiaeo, ?aae?ia?ao?/ieo
cia?aaeaiue i?iieneiai? aeaoaeoineii?? oa iaaee/ii? ae?aaiinoeee,
aa?ioioia?ao?e ?ica?aeoaaeueiiai oa?aeoa?o aeey ciiaeoaaiiy caiieo
?ano?n?a, ae?aa?ai naeni?/ieo aeaieo, aeaeo?iiii-i?e?ineii?/ieo
oioia?ao?e, oiui. Aeiiae, ye? noaaeyoueny i?e ?ic?iaoe? oaeeo nenoai,
ia?aaeaa/athoue iie?auaiiy yeino? ioeeo?iaaieo cia?aaeaiue, ui o?nii
iia’ycaii c aiae?cii oa ?ioa?i?aoaoe??th io?eiaii? ?ioi?iaoe??. Oiio
iie?auaiiy yeino? cia?aaeaiue, iaoiiaeaia iiyaith ia ieo ooi?a ??ciiai
iioiaeaeaiiy, iaaeae? caeeoa?oueny aeooaeueiith i?iaeaiith. Cie?aia,
iayai?noue ?iioeuenieo aeeeae?a, ye iaea?eueo iioe?aiiai ??ciiaeaeo
caaaae ia cia?aaeaiiyo, ni?e/eith?oueny iiieeeaie
eiaeoaaiiy/aeaeiaeoaaiiy oa ao?aoaie ?ioi?iaoe?eieo iaeao?a i?ae/an
ia?aaea/? a?coaeueii? ?ioi?iaoe?? eaiaeaie ca’yceo, aiane?aeie
iaiieaaeie o naini?ieo i?eno?iyo ? a?aeaiaeaaa/ao cia?aaeaiue, cai?a
neaioaaeueii? aia?aoo?e a i?ioean? ia?aaaaeaii? oioi- oa a?ao?/ieo
iaoa??ae?a o oeeo?iao oi?io, oiui. ?iioeueni? ooie nooo?ai
niioai?ththoue cia?aaeaiiy ia eeoa c oi/ee ci?o a?coaeueiiai ni?eeiyooy,
aea e c iaeyaeo ia ?o ianooiio ia?iaeo, oneeaaeithth/e iiaeeeaino?
aeyaeaiiy eiioo??a oa ae??aieo aeaoaeae. Ia?aaaaeii ?ica’ycaiiy caaea/?
o?eueo?aoe?? ?iioeueniiai ooio caiaeeoueny aei aeeiiaiiy iine?aeiaiino?
iia?aoe?e, oeyoii aeaoaeooaaiiy oa ia?iaee i?enae?a, niioai?aieo
?iioeuenaie, ? ia?aoai?aiiy cia?aaeaiiy o oi?io, c?o/i?oo aeey
iiaeaeueoiai a?coaeueiiai oa//e iaoeiiiai aiae?co.

Iioae?eiaai? o e?oa?aoo?? aaeaioeai? aeai?eoie a?o/eciyieo
(ss?ineaanueeee E.I., E?a?ae?a Ae.N., E?i A., E?ii?iae I.A., *i/?a I.A.)
oa caei?aeiiieo o/aieo (I?oan ?., Aaiaoeaiiioein A., Aa?iooaei ?.,
Eoiaeo A., I?o?a N., E? Aeae., A?aaa?i A.) ia aeathoue caaeia?eueieo
?acoeueoao?a aeey ?ica’yceo caaaeaiiy onoiaiiy ?iioeuenieo ooi?a.
Iaaeie?eaie oeeo aeai?eoi?a ? iaiao?aei?noue aaaaeaiiy ao?aeieo
ia?aiao??a ia?iaee, ?o iaiaaeai?noue aei e?eueeino? ooiiaeo eiiiiiaio oa
??aiy caooieaiiino? cia?aaeaiue, oaiaeaioe?y aei ?icieooy e?a?a ?
eiioo??a, iecueea oaeaeeiae?y ia?iaee.

O ?aieao aeaii? ?iaioe caaea/a aeine?aeaeaiue noi?ioeueiaaia ye
?ic?iaea aoaeoeaieo iaoiae?a onoiaiiy ?iioeuenieo ooi?a c? cia?aaeaiue.
Iinoaaeaia caaaeaiiy a?oioo?oueny ia i?eioeei? «aeaoaeooaaiiy-ia?iaea» ?
iieyaa? o aeyaeaii? oi/ie cia?aaeaiiy, iioeiaeaeaieo ?iioeuenieie
aeeeaeaie, oa aaeaioeai?e ?ioa?iieyoe?? cia/aiue ooieoe?? yne?aaino? o
caeaoaeoiaaieo oi/eao cia/aiiyie ii?yaeeiaeo noaoenoee, ia/eneaieie a
ieie? oeeo i?enae?a.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?eia
?iaioa aeeiiaia a ?aieao aea?aeathaeaeaoii? oaie «Iaoiaee oa oaeaee?
aeai?eoie aaoiiaoe/iiai a?coaeueiiai aiae?co o??ueiiiiae?aieo aeaoaeo?a
o eiino?oeoe?eieo iaoa??aeao ? i?iieneiaeo ae?iaao» o O?ceei-iaoai?/iiio
?inoeooo? ?i. A.A. Ea?iaiea IAI Oe?a?ie, iiia? aea?aeaaii? ?a?no?aoe?? –
0196U007180, oeo? oaie – IAe 32/159.

Iaoa ?iaioe iieyaa? o ?ic?iaoe? oa aeine?aeaeaii? aaeaioeaieo
aeai?eoi?a onoiaiiy ?iioeuenieo ooi?a c? cia?aaeaiue c aeei?enoaiiyi
ii?yaeeiaeo noaoenoee. Aeey aeinyaiaiiy iinoaaeaii? iaoe o ?iaio?
?ica’ycothoueny ianooii? caaea/?:

aiae?c a?aeiieo aeai?eoi?a iae?i?eii? o?eueo?aoe?? ?iioeuenieo ooi?a;

?ic?iaea aeaoaeoi?a i?enae?a cia?aaeaiiy, iioeiaeaeaieo ?iioeuenieie
ooiaie, aeey ?o ianooiii? ia?iaee;

?ic?iaea iaoiaeeee aoaeoeaii? ?ioa?iieyoe?? cia/aiue ooieoe?? yne?aaino?
o i?enaeao cia?aaeaiiy, caeaoaeoiaaieo, ye iioeiaeaeaieo ?iioeuenieie
ooiaie;

aea?? e?eoa???a yeino? aeey ii??aiyeueiiai aiae?co ??cieo iaoiae?a
o?eueo?aoe?? ia cia?aaeaiiyo, niioai?aieo ?iioeuenieie ooiaie;

?ic?iaea aaeaioeaieo aeai?eoi?a iiia?aaeiuei? o?eueo?aoe?? ooi?a c?
ci?oaiei caeiiii ?iciiae?eo;

?ic?iaea oaeaeeeo aeai?eoi?a ia/eneaiiy ii?yaeeiaeo noaoenoee aeey
caaacia/aiiy ?aae?caoe?? iiia?aaeiuei? o?eueo?aoe?? ooi?a a oiiaao
aei?noeeo /aniaeo iaiaaeaiue;

i?iaaaeaiiy aenia?eiaioaeueieo aeine?aeaeaiue aeey ii??aiyeueii? ioe?iee
aoaeoeaiino? i?iiiiiaaieo aaeaioeaieo ?aeaioeo?eaoe?eieo aeai?eoi?a
onoiaiiy ?iioeuenieo ooi?a c? cia?aaeaiue ia oanoiaeo oa ?aaeueieo
i?eeeaaeao ca aeiiiiiaith eiii’thoa?iiai iiaeaethaaiiy.

Iaoeiaa iiaecia ?iaioe iieyaa? o ianooiiiio :

cai?iiiiiaaii i?aeo?ae aei eeaneo?eaoe?? iae?i?eieo iaoiae?a
o?eueo?aoe?? ?iioeuenieo ooi?a ia cia?aaeaiiyo ca oeiaie o?eueo??a;

aia?oa aeey aeyaeaiiy i?enae?a cia?aaeaiiy, iioeiaeaeaieo ?iioeuenieie
ooiaie, ?ic?iaeaii oa aenia?eiaioaeueii ia?aa??aii iaoiae aeaoaeooaaiiy,
ui a?oioo?oueny ia aiae?c? a?noia?ai;

cai?iiiiiaaii oa aeine?aeaeaii aoaeoeaio iaoiaeeeo ?ioa?iieyoe??
cia/aiue ooieoe?? yne?aaino? o caeaoaeoiaaieo iioeiaeaeaieo oi/eao
cia?aaeaiiy aaeaioeaii aea?aieie cia/aiiyie ii?yaeeiaeo noaoenoee;

cai?iiiiiaaii oa aeine?aeaeaii no?oeoo?ii-aaeaioeaiee aeai?eoi
iiia?aaeiuei? o?eueo?aoe?? ooi?a c? ci?oaiei caeiiii ?iciiae?eo;

?ic?iaeaii oaeaeeee ?aeo?neaiee aeai?eoi ia/eneaiiy cia/aiue ii?yaeeiaeo
noaoenoee.

I?aeoe/ia cia/aiiy ?acoeueoao?a. ?ic?iaeai? o aeena?oaoe?ei?e ?iaio?
aaeaioeai? aeai?eoie aeathoue iiaeeea?noue aoaeoeaii onoaaoe ?iioeueni?
ooie i?ae/an iiia?aaeiuei? ia?iaee ioeeo?iaaieo cia?aaeaiue a iioe/i?e
ano?iiii??, iaaee/i?e ae?aaiinoeoe?, i?iieneia?e aeaoaeoineii??, a
oaeiae a ?ioeo ae?eyieao ethaenueei? ae?yeueiino?, iia’ycaieo c
caaea/aie iie?auaiiy yeino? cia?aaeaiue, niioai?aieo ?iioeuenieie
ooiaie. Cai?iiiiiaai? iaoiaee iiaeooue aeei?enoiaoaaoeny i?ae/an
?ic?iaee oa canoinoaaiiy nenoai i?eeiio/ia?aaea/? a?coaeueii?
?ioi?iaoe?? eaiaeaie ca’yceo, aeey iiia?aaeiuei? ia?iaee ?aae?ia?ao?/ieo
iaaee/ieo ? i?iieneiaeo cia?aaeaiue a oiiaao aei?noeeo /aniaeo
iaiaaeaiue, aeey onoiaiiy iiieeie neaioaaeueii? aia?aoo?e a i?ioean?
ia?aaaaeaii? oioi- oa a?ao?/ieo iaoa??ae?a o oeeo?iao oi?io aeey
iiaeaeueoiai aiae?co.

?aae?caoe?y iaoeiai-oaoi?/ieo ?acoeueoao?a. Oai?aoe/i? oa i?aeoe/i?
?acoeueoaoe, io?eiai? o aeena?oaoe?ei?e ?iaio?, aeei?enoaii o
iaoeiai-aeine?aeieo ?iaioao eaai?aoi??? «Aaoiiaoecaoe?? iaoeiaeo
aeine?aeaeaiue» oa a?aeae?eo «O?ce/ieo iniia ?oeioaaiiy oa i?oeiino?
eiino?oeoe?eieo iaoa??ae?a» O?ceei-iaoai?/iiai ?inoeoooo ?i. A.A.
Ea?iaiea IAI Oe?a?ie. Ia ?o iniia? noai?aii i?ia?aiia caaacia/aiiy
aeey nenoaie a?coaeueiiai eiio?ieth oa oaoi?/ii?
ae?aaiinoeee, ui a?oioo?oueny ia eiii’thoa?iiio aiae?c? ioeeo?iaaieo
cia?aaeaiue. ?ic?iaeai? aaeaioeai? aeai?eoie ai?iaaaeaeaii i?e ?ic?iaoe?
i?aenenoaie aaiaeo oa ia?iaee cia?aaeaiue i?iieneiai? aeaoaeoineii??
aeey aaoiiaoe/ii? onoaiiaee aecia/aiiy oa?aeoa?enoee
ei?ic?eii-iaoai?/ieo ?oeioaaiue iaoa??ae?a AOE?-01, ui cana?ae/aii aeoii
ai?iaaaeaeaiiy.

Ai?iaaoe?y ?acoeueoao?a ?iaioe. ?acoeueoaoe aeine?aeaeaiue oa iniiai?
iieiaeaiiy aeenaoaoe?eii? ?iaioe aeiiia?aeaeenue oa iaaiai?thaaeenue ia
:

Ae?oa?e Anaoe?a?inuee?e i?aeia?iaei?e eiioa?aioe?? «Oe?IA?AC’94»
(Ee?a, 1994);

O?ao?e i?aeia?iaei?e eiioa?aioe?? «?ici?ciaaaiiy ia?ac?a oa aiae?c
cia?aaeaiue «PRIA’95» (I?inuee, A?ei?onue, 1995);

I?aeia?iaei?e iaoeiai-oaoi?/i?e eiioa?aioe?? «No/ani? i?iaeaie
aaoiiaoeciaaii? ?ic?iaee ? ae?iaieoeoaa ?aae?iaeaeo?iiieo cania?a ?
i?aeaioiaee ?iaeaia?ieo eaae??a» (Euea?a, 1996);

O?ao?e i?aeia?iaei?e eiioa?aioe?? «Oaeaeiioi?eaoe?? o no/anieo
noiooieeao, eaaaeueieo ? ?aae?iiiaieo na?a?nao «TELSIKS’97» (I?o,
THaineaa?y, 1997);

*aoaa?o?e i?aeia?iaei?e eiioa?aioe?? «?ici?ciaaaiiy ia?ac?a oa ia?iaea
?ioi?iaoe?? «PRIP’97» (I?inuee, A?ei?onue, 1997);

iaoeiaiio nai?ia?? «Ia?iaea neaiae?a ? cia?aaeaiue : oai??y, aeai?eoie
oa canoinoaaiiy» O?ceei-iaoai?/iiai ?inoeoooo ?i. A.A. Ea?iaiea IAI
Oe?a?ie.

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
iioae?eiaaii o 14 iaoeiaeo i?aoeyo, c ieo 4 noaoo? o oaoiaeo
iaoeiaeo aeaeaiiyo oa iaeei iaoaio.

Iniaenoee aianie aaoi?a. On? ?acoeueoaoe, ui neeaaeathoue iniiaiee ci?no
?iaioe, io?eiai? aaoi?ii naiino?eii. I?e oeueiio, o i?aoeyo, iaienaieo o
ni?aaaoi?noa?, caeiaoaa/aa? iaeaaeaoue : iaa?oiooaaiiy oa ?ic?iaea
iaoiaeeee aeaoaeooaaiiy i?enae?a cia?aaeaiiy, iioeiaeaeaieo a?ia?iei
?iioeueniei ooiii [3]; iinoaiiaea caaea/? ? ?ic?iaea aeai?eoi?a
aeaoaeooaaiiy oa aoaeoeaii? ?ioa?iieyoe?? ooieoe?? yne?aaino? o i?enaeao
cia?aaeaiiy, ?aeaioeo?eiaaieo, ye iioeiaeaeaieo ?iioeuenieie ooiaie [3,
6]; aeine?aeaeaiiy aoaeoeaiino? oa eiii’thoa?ia iiaeaethaaiiy
no?oeoo?ii-aaeaioeaiiai aeai?eoio iiia?aaeii? o?eueo?aoe?? ooi?a c?
ci?oaiei caeiiii ?iciiae?eo [2, 8, 11]; ?aae?caoe?y oa aeine?aeaeaiiy
aoaeoeaiino? aeai?eoia ia?aaea/? a?coaeueii? ?ioi?iaoe?? [5]; ?ic?iaea
oa aaeineiiaeaiiy aoaeoeaiino? oaeaeeiai ?aeo?neaiiai aeai?eoio
ia/eneaiiy ii?yaeeiaeo noaoenoee aeey iiia?aaeiuei? o?eueo?aoe??
caooieaieo cia?aaeaiue [7, 11, 13]; aeine?aeaeaiiy oa aiae?c
aeanoeainoae iae?i?eieo o?eueo??a ia iniia? ii?yaeeiaeo noaoenoee [9,
10, 12].

No?oeoo?a ? ia’?i aeena?oaoe??. Aeena?oaoe?y neeaaea?oueny c? anooio,
/ioe?ueio ?icae?e?a, aeniiae?a, ia?ae?eo aeei?enoaieo aeaea?ae ?
aeiaeaoe?a. ?iaioa aeeeaaeaia ia 181 noi??ioe? ae?oeiaaiiai oaenoo,
i?noeoue 60 ?enoie?a, 15 oaaeeoeue. Ia?ae?e aeei?enoaieo aeaea?ae
i?noeoue 133 a?ae?ia?ao?/i? iineeaiiy.

Iniiaiee ci?no ?iaioe

O anooi? iaa?oioiaaii aeooaeuei?noue i?iaeai, ui aeine?aeaeothoueny o
?iaio?, iinoaaeaii iaoo oa caaea/? aeine?aeaeaiue, noenei aeeeaaeaii
?acoeueoaoe, io?eiai? a aeena?oaoe??, oa noi?ioeueiaaii iniiai?
iieiaeaiiy, ye? aeiinyoueny ia caoeno.

oa eiia??i?noth iiyae eiaeii? eiiiiiaioe ia cia?aaeaii? qi :

.

Ia i?aenoaa? i?iaaaeaiiai iaeyaeo a?aeiieo aeai?eoi?a c?iaeaii aiae?c
oa cai?iiiiiaaii eeaneo?eaoe?th iae?i?eieo iaoiae?a o?eueo?aoe??
?iioeuenieo ooi?a ca oeiaie o?eueo??a. A?aoiaoth/e i?e?iaeo ?iioeuenieo
ooi?a ia cia?aaeaiiyo, ca?aeii ?ic?iaeaii? eeaneo?eaoe?? noi?ioeueiaaii
aeniiaie i?i aeioe?euei?noue aeei?enoaiiy aaeaioeaieo ?aeaioeo?eaoe?eieo
aeai?eoi?a, ye iaea?eueo aoaeoeaieo cania?a onoiaiiy ?iioeuenieo ooi?a
i?e iaeii/aniiio caa?aaeaii? no?oeoo?e oa ae??aieo aeaoaeae cia?aaeaiiy.

Aeey ii??aiyeueii? ioe?iee yeino? cia?aaeaiue, ia?iaeaieo ??cieie
o?eueo?aie, i?iaaaeaii aiae?c oa aea?aii ianooii? e?eoa??? yeino? –
e?eoa??e iaeneioio a?aeiioaiiy neaiae/ooi, oaeoi? iie?auaiiy oa
ei?aeyoe?eiee eiao?oe?aio. Iieacaii, ui aeai? e?eoa??? a?aeiia?aeathoue
anoaiiaeaiei aeiiaai a??ia?aeiino? a?aeoai?aiiy cia?aaeaiue.

O ae?oaiio ?icae?e? ?icaeyiooi caaea/o ?aeaioeo?eoaaiiy oi/ie
cia?aaeaiiy, iioeiaeaeaieo ?iioeuenieie ooiaie, ? cai?iiiiiaaii
aoaeoeai? i?aeoe/i? ?aae?caoe?? ?iioeuenieo aeaoaeoi??a. I?iaaaeaii
aiae?c a?aeiieo aaeaioeaieo ?aeaioeo?eaoe?eieo aeai?eoi?a o?eueo?aoe??
?iioeuenieo ooi?a, ui a?oioothoueny ia no?aoaa?? “aeaoaeooaaiiy-ia?iaea”
i?enae?a cia?aaeaiiy, niioai?aieo ?iioeuenaie, aeacaii ?o ia?aaaae oa
iaaeie?ee. Cai?iiiiiaaii ianooiia ??aiyiiy aaeaioeaii? o?eueo?aoe??
?iioeuenieo ooi?a

aea f(x,y) – ?acoeueoao ia?iaee o oi/oe? c eii?aeeiaoaie (x,y); g(x,y)
– cia/aiiy cia?aaeaiiy, niioai?aiiai m-eiiiiiaioiei ?iioeueniei ooiii;
b(x,y) – ?aeaioeo?eaoe?eiee ia?aiao?, ui i?eeia? cia/aiiy 0 aai 1 a
caeaaeiino? a?ae ?acoeueoaoo aeaoaeooaaiiy o aeai?e oi/oe? (x,y);
E[g(x,y)] – cia/aiiy ?acoeueoaoo iae?i?eii? o?eueo?aoe?? a ieie? oi/ee
(x,y). Ia ?en. 1 iiaeaii no?oeoo?io noaio ?ic?iaeaiiai aaeaioeaiiai
?aeaioeo?eaoe?eiiai aeai?eoio onoiaiiy ?iioeuenieo ooi?a.

?en. 1. No?oeoo?ia noaia aaeaioeaiiai ?aeaioeo?eaoe?eiiai aeai?eoio
onoiaiiy ?iioeuenieo ooi?a c? cia?aaeaiue

O a?aeiia?aeiino? c aea?aiith no?aoaa??th ia?iaee iieacaii, ui
aoaeoeai?noue onoiaiiy ?iioeueniiai ooio ia?aaeon?i caeaaeaoeia a?ae
i?aaeeueiiai ?aeaioeo?eoaaiiy iioeiaeaeaieo ooiii oi/ie, ine?eueee
iai?aaeeueiee a?aea?? i?enae?a aeey ianooiii? o?eueo?aoe?? i?eaaaea aei
caeeoeo ooi?a oa iaaaaeaiiai ?icieooy e?a?a ? ae??aieo aeaoaeae
cia?aaeaiiy. Aeey ?aeaioeo?eoaaiiy i?enae?a cia?aaeaiiy, iioeiaeaeaieo
a?ia?iei ?iioeueniei ooiii, cai?iiiiiaaii oa aeine?aeaeaii ?iioeueniee
aeaoaeoi?, yeee a?oioo?oueny ia ciaoiaeaeaii? oa iii?/aii? on?o oi/ie
cia?aaeaiiy, cia/aiiy yeeo ??ai? a?aie/iei cia/aiiyi a?aaeaoe?e
yne?aaino? Smin ? Smax.

Aeey aeyaeaiiy oi/ie cia?aaeaiiy, iioeiaeaeaieo m-eiiiiiaioiei
?iioeueniei ooiii, ?ic?iaeaii ? aeine?aeaeaii ?iioeueniee aeaoaeoi?. A?i
a?oioo?oueny ia aiae?c? aeiaaeueii? a?noia?aie cia?aaeaiiy ?
neeaaea?oueny c aiae?caoi?a aaee/ei a?noia?aiieo cia/aiue oa aiae?caoi?a
oe?eie a?noia?aiieo ??ai?a. Ia i?eeeaaeao oanoiaeo cia?aaeaiue,
niioai?aieo ?iioeuenieie ooiaie c ??ciei a?aenioeii caooieaiiino?,
i?iaaaeaii ii??aiyeueiee aiae?c aeaoaeoi??a a?aeiieo aaeaioeaieo
?aeaioeo?eaoe?eieo aeai?eoi?a c ?ic?iaeaiei ?iioeueniei aeaoaeoi?ii
(eii?aeeiaoe eiaeiiai ?iioeuena ai??i?ii a?aeii?). Aeey ia’?eoeaii?
ioe?iee i?aaeeueiiai aeaoaeooaaiiy ooiiaeo cia/aiue aeei?enoaii nooi?iue
oni?oiiai ?aeaioeo?eoaaiiy ISR, yeee aecia/a?oueny ca oi?ioeith

,

) – e?euee?noue iioeiaeaeaieo i?enae?a, ui caeaoaeoiaai? ye
iioeiaeaeai?.

Aenia?eiaioaeuei? aeine?aeaeaiiy iieacaee, ui c? ca?eueoaiiyi a?aenioeo
caooieaiiino? ia cia?aaeaii?, nooi?iue oni?oiiai ?aeaioeo?eoaaiiy
?iioeuenieo aeeeae?a aeey ?o ianooiii? o?eueo?aoe?? i?aeoe/ii ia
ci?ith?oueny ? noaiiaeoue ia iaioa 96%. Oea i?aee?aneth? ?iaanoi?noue
cai?iiiiiaaieo ?iioeuenieo aeaoaeoi??a oa ?oi? ia?aaaae iaae a?aeiieie
?aeaioeo?eaoe?eieie i?aeoiaeaie, aeey yeeo aeacaia aaee/eia noaiiaeoue
40-65 %.

O o?aoueiio ?icae?e? iinoaaeaii ? ?ica’ycaii caaea/o aaeaioeaii?
?ioa?iieyoe?? cia/aiue ooieoe?? yne?aaino? o aeyaeaieo ca aeiiiiiaith
?ic?iaeaieo ?iioeuenieo aeaoaeoi??a oi/eao cia?aaeaiiy, niioai?aieo
?iioeueniei ooiii. ?icaeyae oe??? caaea/? ? iniaeeai aaaeeeaei,
ine?eueee iaa?oue i?e i?aaeeueiiio ?aeaioeo?eoaaii? ooiiaeo i?enae?a
ianooiia ia?iaea caeaoaeoiaaieo cia/aiue iiaea i?eaanoe aei iaaaaeaiiai
?icieooy eiioo??a ? ae??aieo ia’?eo?a, a oaeiae aei iiaeeeaiai caeeoeo
?iioeuenieo caonoe?a ia cia?aaeaii?. I?iiiio?oueny i?iaiaeeoe aaeaioeaio
cai?io caeaoaeoiaaieo iioeiaeaeaieo oi/ie cia?aaeaiiy cia/aiiyie
iiaeeo?eiaaiiai iae?i?eiiai o?eueo?a. Inoaii?e a?oioo?oueny ia
ia/eneaii? ii?yaeeiaeo noaoenoee aeayeiai ieieo oeeo oi/ie aac
a?aooaaiiy ?ioeo niioai?aieo i?eae?a oeueiai ieieo :

,

; {g’i (x,y)} – oii?yaeeiaai? a ii?yaeeo c?inoaiiy cia/aiiy ieieo
oeaio?aeueiiai i?enaea g(x,y), ui i?eeiathoue o/anoue a ia/eneaii?
?acoeueoaoo ia?iaee a oi/oe? (x,y). Cia/aiiy g’i aecia/athoueny
ianooiieie /eiii :

,

aea ordering {.} – ooieoe?y aii?yaeeoaaiiy aaee/ei o ii?yaeeo
c?inoaiiy; N – e?euee?noue aeaiaio?a aa??aoe?eiiai ?yaeo gi o a?ei?
ia?iaee W(x,y), ui ia? ?ici?? L(L, i?e/iio N

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