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Кореляційні методи обчислення геометричних і топологічних ознак зображень: Автореф. дис… канд. фіз.-мат. наук / К.М. Чекотун, НАН України. Ін-т кібе

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

?inoeooo e?aa?iaoeee ?iai? A.I. Aeooeiaa

OAeE 681.3.21

*AEIOOI Einoyioei Ieoaeeiae/

EI?AEssOe?EI? IAOIAeE IA*ENEAIIss AAIIAO?E*IEO

? OIIIEIA?*IEO ICIAE CIA?AAEAIUe

01.05.02 – iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee

Aaoi?aoa?ao aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a ?inoeooo? e?aa?iaoeee ?iai? A.I. Aeooeiaa IAI Oe?a?ie.

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

EE?E*AIEI Ieeiea
Oaaei?iae/,

?inoeooo e?aa?iaoeee

?i. A.I. Aeooeiaa IAI
Oe?a?ie,

i?ia?aeiee iaoeiaee
ni?a?ia?oiee

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

EIIIIA Iaaei Nieiiiiiae/,

?inoeooo e?aa?iaoeee

?i. A.I. Aeooeiaa IAI
Oe?a?ie,

caa?aeoaa/ a?aeae?eo,

eaiaeeaeao
o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

AeII*AIEI Aieiaeeie?
Noaiaiiae/,

Ee?anueeee oi?aa?neoao ?i.
Oa?ana Oaa/aiea,

caa?aeoaa/ eaoaae?e.

I?ia?aeia onoaiiaa : ?inoeooo eini?/ieo aeine?aeaeaiue IAI
Oe?a?ie oa

IEA Oe?a?ie, a?aeae?e
eini?/ieo ?ioi?iaoe?eieo

oaoiieia?e oa nenoai.

Caoeno a?aeaoaeaoueny “___” ___________ 199__ ?. i ____ aiae. ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.194.02 i?e ?inoeooo?
e?aa?iaoeee

?i. A.I. Aeooeiaa IAI Oe?a?ie

ca aae?anith: 252650, INI, Ee?a 22, i?iniaeo Aeaaeai?ea Aeooeiaa, 40.

C aeena?oaoe??th iiaeia iciaeiieoeny a iaoeiai-oaoi?/iiio a?o?a?
?inoeoooo.

Aaoi?aoa?ao ?ic?neaiee “___”_________199__ ?.

O/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee
NEIssANUeEEE A.O.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. No??iea c?inoaiiy aeooaeueiino? ?ici?ciaaaiiy
cia?aaeaiue o ia?oo /a?ao iia’ycaia c oei, ui aenieii?iaeoeoeai?
eiii’thoa?e ? caniae aaaaeaiiy cia?aaeaiue noaee aeinooiieie ianiaiio
niiaeeaa/aa?. O oe?e aaeoc? aaea ?niothoue /eneaii? i?iaeoeoe: a?ae
aaoiiaoe/iiai aaaaeaiiy oaeno?a (OCR), eeaneo?eaoe?? ee?oei o iaaee/ieo
aeine?aeaeaiiyo ? aei ci?o ?iaio?a ia neeaaeaeueiiio ae?iaieoeoa?.

Ia?iaoe? ? ?ici?ciaaaiith cia?aaeaiue aoei i?enay/aii ?iaioe ?. Aeoaee,
I. Oa?oa, O. I?aooa, A.E.I. Oi?ia, E. Oo, E. Ooeoiaae, A.A. ?aaoiaiea,
A.?. Aaneeue?aa, I.O. Ee?e/aiea, I.?. Oeac?iaa?a, O.E. A?ioethea, A.E.
Caaee?aee, A.I. ?oneia, A.A. A?eoeeea, N.A. Aoiaea, A.I. Eeeea, O.
A?aiaiaea?a, A.I. Aaiieea, A.ss. *a?aiiaie?na, A.A. Iao?eea oa ?i. O
oeeo i?aoeyo oa ?ioeie aaoi?aie noai?aii oi?iaeuei? oai??? eeaneo?eaoe??
ia?ac?a ca ia/eneaieie iciaeaie. ?acii c oei, aoai aeai?o iciae, ye? a
aeinoaoiuei iienoaaee caaeaiee eean cia?aaeaiue, aein? caeeoa?oueny ia
oi?iae?ciaaiei.

E??i oiai, iaiao?aei?noue ?ica’ycoaaoe neeaaei? caaea/? a ?aaeueiiio
/an? aena?oeth? iaiaaeai?noue o?aaeeoe?eii? ia/enethaaeueii?
a?o?oaeoo?e. Ia?aeaeueiei ia/eneaiiyi ? iae?iiiae?aiei ia?aaeai
i?enay/aii ?iaioe, cie?aia, ?.I. Iie/aiiaa, A.A. Ii?iciaa, A.I.
Eeeiaiea, I.I. ??cieea, A.A. ssuaiea, A.I. Eonnoey.

Oaeei /eiii, aeooaeueiith ? ?ic?iaea iiaeo iaoiae?a ia/eneaiiy iciae
cia?aaeaiue, i???ioiaaieo ia ?aae?caoe?th ia?aeaeueieie caniaaie.

Iaoa ?iaioe ? iniiai? caaaeaiiy. Iaoith aeena?oaoe?eii? ?iaioe ?
?icaeoie iaoaiaoe/ieo cania?a aeyaeaiiy iciae cia?aaeaiue, ?iaa??aioieo
aei oe?ieiai eeano ia?aoai?aiue ? i?eaeaoieo aeey ia?aeaeueii?
?aae?caoe??, aeene?aoia ?ioa?i?aoaoe?y a?aeiia?aeieo oi?ioe ?
?icia?aeaethaaiiy iaea?aeaieo aeai?eoi?a.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie. ?iaioa aeeiioaaeanue a
iaoeiai-aeine?aeiiio i?iaeo? I?i?noa?noaa Oe?a?ie o ni?aaao iaoee ?
oaoiieia?e ? 06.02/01717 “I?ia?aiii-aeai?eoi?/ia oa iaoaiaoe/ia
caaacia/aiiy aeine?aeaeaiiy aeieia?/iiai noaio nooo?ai iaiaeii??aeieo
a?oioiaeo na?aaeiaeu”.

Iaoeiaa iiaecia. Aeanoeaino?, ye? oa?aeoa?ecothoue cia?aaeaiiy a
iai?yieo, nenoaiaoeciaaii c oi/ee ci?o aeei?enoaiiy ?o ye iciae. Aia?oa
iiaoaeiaaii aeene?aoi? aea?aaeaioe oi?ioe aeey ia/eneaiiy oa?aeoa?enoee
ia iniia? aeanoeainoae ooieoe?iiaea oeio aaoiei?aeyoe?eieo ia?aoai?aiue
a?ae ooieoe?? ina?oeaiino?. Cae?eniaii ?icia?aeaethaaiiy iaea?aeaieo
aeai?eoi?a. Ocaaaeueiaii iiiyooy caoiee iaeano? ? aia?oa iaea?aeaii
no?oeoo?iee iien iaiioeeeo iaeanoae /a?ac caoiee aeueo ii?yaee?a. Aia?oa
iiaoaeiaaii ia?aeaeueiee aeai?eoi aeae?eaiiy caoie iaeano?.

I?aeoe/ia oe?ii?noue ?iaioe. Oai?aoe/i? ?acoeueoaoe ?iaioe iiaeooue
aeei?enoiaoaaoeny i?e aeine?aeaeaii? aeanoeainoae ooieoe?iiae?a a?ae
aaoiei?aeyoe?eieo ia?aoai?aiue, i?e ?ic?iaoe? iiaeo iciae cia?aaeaiue oa
aeai?eoi?a ?o ia/eneaiiy, iniaeeai ia?aeaeueieo.

?ic?iaeaiee i?ia?aiiee eiiieaen iiaea aeei?enoiaoaaoeny aaciina?aaeiuei
aeey ?ici?ciaaaiiy cia?aaeaiue (iai?eeeaae, ?oeiienieo aoea), a oaeiae
aeey iiaoaeiae c ?nioth/eo iciae iioeiaeueii? nenoaie iciae aeey
eiie?aoii? caaea/?.

Ai?iaaoe?y ?acoeueoao?a ?iaioe. ?acoeueoaoe aeine?aeaeaiue, ui aeeth/ai?
aei aeena?oaoe??, aeiiia?aeaeenue ia O?ao?e anaoe?a?inuee?e
i?aeia?iaei?e eiioa?aioe?? “Ia?iaeaiiy neaiae?a ? cia?aaeaiue oa
?ici?ciaaaiiy ia?ac?a” (Oe?Ia?ac 96), iaoeiaeo nai?ia?ao ?inoeoooo
e?aa?iaoeee ?i. A.I. Aeooeiaa IAI Oe?a?ie (1999 ?.).

Ioae?eaoe??. Ca iaoa??aeaie aeena?oaoe?? iioae?eiaaii /ioe?e iaoeia?
i?aoe?, o oiio /ene? o?e noaoo? o oaoiaeo aeaeaiiyo.

Iniaenoee aianie aeena?oaioa a ?iaioao, aeeiiaieo o ni?aaaoi?noa?. A
?iaio? [1] aaoi? aeena?oaoe?? iaea?aeaa aeene?aoiee aea?aaeaio aeyaeaiiy
aaiiao?i-oiiieia?/ieo iciae cia?aaeaiue c ioe?ieith iioeaie, ui
aeieeathoue ca ?aooiie aeene?aoecaoe??.

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?eia ?iaioa neeaaea?oueny ?c
anooio, o?ueio ?icae?e?a, aeniiae?a oa nieneo e?oa?aoo?e. Caaaeueiee
ianya ?iaioe neeaaea? 136 noi??iie. Oaeno aeena?oaoe?? i?noeoue 111
?enoie?a oa 26 oaaeeoeue. A?ae?ia?ao?y i?noeoue 157 iaeiaioaaiue.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiao?oueny aeooaeuei?noue oaie aeine?aeaeaiue,
oi?ioeth?oueny iaoa ?iaioe, iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a ?
?o i?aeoe/ia oe?ii?noue. Iaaiaeeoueny noeneee ci?no ?icae?e?a
aeena?oaoe??.

O ia?oiio ?icae?e? aeine?aeaeothoueny aeanoeaino? cia?aaeaiiy a
iai?yieo.

.

, ui

,
(1)

,
(2)

, (3)

,
(4)

.
(5)

(?en. 1).

?en. 1

i?i?ethno?iaaii ia ?en. 2.

?en. 2.

ia/eneth?oueny ia iniia? oai?aie 1, aeiaaaeaii? I.O. Ee?e/aieii.

, a yeeo aiia cacia? ?ic?ea?a ia?oiai ?iaeo (?en. 3), oi

,

,

,

.

?en. 3.

?niothoue iaiaaeai? /anoeii? iio?aei?.

caaea?oueny iai?yiie ? aea?oueny icia/aiiy ??cieo aeae?a ii?ooaiue
iioeeino? “a iai?yieo”. Oe? icia/aiiy aeaui iiaeeo?eiaai? ii??aiyii c
i?aoeyie Ee?e/aiea I.O., Eaiaoe I.I., Eooeaiea A.A.

– aioo??oi?.

.

, ui

.

o aeaeyae? ia’?aeiaiiy

,

iathoue oae? aeanoeaino?:

, (6)

. (7)

iaceaa?oueny

,

.

.

caoo?eoiaai?.

?en. 4.

, oaeeo, ui

Ia ?en. 5 ioa?? caoo?eoiaaiee.

?en. 5.

Aiaeia?/ii aei caoiee iaeano? a iai?yieo aaiaeeoueny iiiyooy caoiee
ioai?o a iai?yieo. Ia ?en. 6 caoiea ioai?o caoo?eoiaaia.

?en. 6.

? oi?ioee aeey ?o ia/eneaiiy.

:

, (8)

i?iaeoe?y

– e?euee?noue ioai??a;

– ai ioai?o. Ia ?en. 7 iieacaii aeaiaioe, c yeeo neeaaea?oueny
ocaaaeueiaia oe?eia.

?en. 7.

Ocaaaeueiaia oe?eia ia/eneth?oueny ca oi?ioeith (I.O. Ee?e/aiea)

,
(9)

. (10)

.

Ia/eneth?oueny aaniethoia oe?eia ca oi?ioeith (I.O. Ee?e/aiea):

, (11)

,

.

Ni?aaaaeeeaa ianooiia oai?aia.

Oai?aia 2. sseui ciai?oi?e ? aioo??oi? eiioo?e iaeano? iioee?, oi
e?euee?noue aioo??oi?o eiioo??a

,

, (12)

.

iaceaa?ii

,

-ai ioai?o.

, ui

,

oa a i?ioeeaaeieo aei ieo iai?yieao.

?en. 8.

E?euee?noue e?aei?o caoie a iai?yieo ia/eneth?oueny ca oi?ioeith (I.O.
Ee?e/aiea):

. (13)

Oaeei /eiii, aaaaeai? oa?aeoa?enoeee ia/eneththoueny /a?ac oi?ioee (9),
(11), (13). A?aeiia?aei? ooieoe?? iia’ycai? i?ae niaith
ni?aa?aeiioaiiyie:

,

,

,

).

iiaeia aaaaeaoe

,

yeui caaeai? cia/aiiy a oi/eao n?oee:

– e?ie n?oee.

ia? aeaeyae

,

.

.

sse a?aeiii, aieiaiei iieacieeii aoaeoeaiino? ?icia?aeaethaaiiy
aeai?eoio ? eiao?oe??io i?enei?aiiy:

,

– /an aeeiiaiiy ia?aeaeueiiai aeai?eoio ia iaoei?, aeey yei? a?i
i?ecia/aiee.

Iieacaii, ui aeey aeai?eoio ia/eneaiiy ocaaaeueiaii? oe?eie

,

– /an aeeiiaiiy aeaiaioa?ii? iia?aoe?? ia?aeaeueiiai aeai?eoio, a aeey
ia/eneaiiy e?eueeino? iioeeinoae ? aaniethoii? oe?eie:

.

Ae?oaee ?icae?e i?enay/aiee caoieai (ia “a iai?yieo”) aeaiaei??ieo
iaeanoae. Ianooii? icia/aiiy ocaaaeueiththoue iiiyooy caoiee, yea ?,
iai?eeeaae, o a?aeii?e iiiia?ao?? Aeoaee ?., Oa?oa I. ? aaiaeyoue
iiiyooy caoie aeueo ii?yaee?a.

,

, iathoue oae? aeanoeaino?:

;

;

ca’ycia.

iaceaa?oueny caoieith iaeano? D.

, iaceaa?oueny caoiea caoiee (n-1)-ai ii?yaeeo. Ia ?en. 9 caoiee
ia?oiai ii?yaeeo caoo?eoiaai? iaeeia?iith, a ae?oaiai – iiaea?eiith
oo?eoiaeith.

?en. 9.

Iienii iaeano? iaceaa?ii eiaeai c ianooiieo ae?ac?a, ye? ? eiiiiceoe??th
iioeeeo iaeanoae:

,
(14)

,
(15)

, …, (16)

,…,
(17)

Oiaoi aeey iaeano? ia ?en. 9 iiene aoaeooue aeaeyaeaoe oae:

?en. 10.

Aeiaiaeeoueny, ui c? c?inoaiiyi ii?yaeeo caeo/aieo a iien caoie c?inoa?
oi/i?noue iieno, oiaoi ciaioo?oueny a?aenoaiue i?ae iaeanoth oa ??
iienii.

A?aenoaiith i?ae iaeanoyie iaceaa?ii ieiuo ??cieoe?:

, (18)

– ieiua iaeano?.

Oai?aia 3. sseui a?aenoaiue i?ae iaeanoyie caaeaia oi?ioeith (18), oi
aeey iaeano? D oa iine?aeiaiino? ?? iien?a (14) – (17) aeeiio?oueny:

, (19)

(20)

Iienaii aeai?eoi, yeee ia cia?aaeaii?, caaeaiiio eiioo?ii, aeae?ey?
caoiee ia?oiai ii?yaeeo. Oeae aeai?eoi aeeiio?oueny ?aeo?neaii aeey
eiaeii? caoiee, aeae?eyth/e oaeei /eiii caoiee aeueo ii?yaee?a.

, aea oi/eai iaeano? a?aeiia?aea? 1, a oi/eai oiio – 0. ?acoeueoao eiai
?iaioe – aeae?eueea ianea?a o??? ae ?ici??iino?, o eiaeiiio c yeeo
caienaia ie?aia caoiea, oiaoi oi/eai caoiee a?aeiia?aea? 1, a ?io?
aeaiaioe aei??aiththoue ioeth (?en. 11).

?en. 11.

Aeai?eoi neeaaea?oueny c oaeeo iniiaieo aeie?a.

(?en. 12)).

?en. 12.

Ooo aeei?enoiao?oueny aeai?eoi aeae?eaiiy e?aei?o caoie a iai?yieo c
ia?oiai ?icae?eo. ?iaioo oeueiai aeieo iieacaii ia ?en. 13. I?e/iio
??cieie /eneaie iicia/ai? e?eoa/ee ??cieo caoie.

?en. 13.

2. Ia?oee e?ie caeeaaiiy caoie. Ia ?en.14 caoo?eoiaai? /anoeie caoie,
ye? aeyaeythoueny ia oeueiio aoai?. Oi/ea A iaeaaeeoue caoioe?, yeui
ai?eciioaeueiee aai aa?oeeaeueiee a?ae??cie, i?iaaaeaiee ?c oe??? oi/ee,
ia?aoeia? e?eoa/eo ? ia ia?aoeia? iaeanoue. Oi/oe? A i?enaith?oueny
/enei, yeei iicia/aia e?eoa/ea. Ia ?en. 14 iieacaii ia?oee e?ie
caeeaaiiy caoie.

?en. 14.

3. Aeuee e?ie caeeaaiiy caoie. Oi/oe? i?enaith?oueny /enei, ia yea
“iaooiaoiaoueny” a?ae??cie, i?iaaaeaiee ?c oe??? oi/ee a iaeio ?c
/ioe?ueio noi??i, i?e oiia?, ui ua ?ai?oa a?i ia ia?aoiaoueny c
iaeanoth.

E?ie (3) iiaoi?th?oueny yeonue iaia?aae aecia/aio e?euee?noue ?ac?a. Oey
e?euee?noue caeaaeeoue a?ae neeaaeiino? iaeanoae, ye? ieaio?oueny
ia?iaeyoe. Iai?eeeaae, aeey iaeano? ia ?en. 14 aeinoaoiuei o?ueio
e?ie?a.

4. ?icae?eaiiy caoie ii ie?aieo ianeaao.

O aeena?oaoe?ei?e ?iaio? aeai?eoi ?icienaii aeaoaeueii a oa?i?iao
aeaiaioa?ieo iia?aoe?e.

Iieacaii, ui aoaeoeai?noue ?icia?aeaethaaiiy

,

– /an aeeiiaiiy aeaiaioa?ii? iia?aoe?? ia?aeaeueiiai aeai?eoio.

O o?aoueiio ?icae?e?, uia ioe?ieoe, iane?eueee aaaaeai? oa?aeoa?enoeee
iiaeooue ?icae?eyoe caaeai? eeane cia?aaeaiue, ?icaeyaea?oueny i?inoee
i?eeeaae: iaienai? a?ae ?oee oeeo?e “0” . . . “9”.

?icaeyaea?oueny o?e aa??aioe aeei?enoaiiy ocaaaeueiaii? oe?eie ?
aaniethoii? oe?eie ye aaeoi??a iciae:

;

;

) oa aea? a?aenoai? a oeeo i?inoi?ao. Iaoae

,

? ioe?ith?oueny ye?noue eeaneo?eaoe?? ca iaoiaeii iaeaeeae/iai non?aea.

Eiino?oththoueny ooieoe?? ianoiaeino? aeey no?oeoo?, ui aeeth/athoue
caoiee o?eueee ia?oiai ii?yaeeo, oa aeey no?oeoo?, ui aeeth/athoue
caoiee aeueo ii?yaee?a, ? aeine?aeaeothoueny a?aeiia?aei? i?inoi?e
iciae.

Aenia?eiaioe iieacaee, ui i?e eeaneo?eaoe?? aaaaoueio ia?ac?a o
i?inoi?ao aaeeei? ?ici??iino? ia aaea?oueny aeinyaoe i?eeiyoii? yeino?
?ici?ciaaaiiy. Oiio i?iiiio?oueny aeaiaoaiiee aeai?eoi ?ici?ciaaaiiy.
Nii/aoeo aeo?aei? eeane ae?eyoueny ia a?oie ca caoieiaith no?oeoo?ith, a
ia’?eoe eiaeii? a?oie eeaneo?eothoueny ca iciaeaie a iai?yieo. I?e
oaeiio i?aeoiae? oeeo?e, iaienai? a?ae ?oee c aeinoaoiueith
oiiieia?/iith i?aaeeuei?noth, ai?ciathoueny iaeaea aac iiieeie.

INIIAI? ?ACOEUeOAOE OA AENIIAEE

Iniiai? ?acoeueoaoe aeena?oaoe??:

1. ?icaeiooi iaoaiaoe/i? caniae aeyaeaiiy iciae cia?aaeaiue ia iniia?
aeanoeainoae ooieoe?iiaea oeio aaoiei?aeyoe?eieo ia?aoai?aiue a?ae
ooieoe?? ina?oeaiino?.

2. Iiaoaeiaaii aeene?aoi? aea?aaeaioe oi?ioe aeey ia/eneaiiy
oa?aeoa?enoee cia?aaeaiiy a iai?yieo.

3. Cae?eniaii ?icia?aeaethaaiiy iaea?aeaieo aeai?eoi?a aeey a?o?oaeoo?e
oeio aaaaoioa?iaeo iae?iia?aae.

4. Aaaaeaii iiiyooy caoiee k-ai ii?yaeeo iaiioeei? iaeano?.
Cai?iiiiiaaii no?oeoo?iee iien iaeano? /a?ac eiiiiceoe?th caoie.

5. Iiaoaeiaaii ia?aeaeueiee aeai?eoi aeae?eaiiy caoie.

6. Ia iniia? caoieiai? no?oeoo?e ? iciae o iai?yieo ?ic?iaeaii aeai?eoi
?ici?ciaaaiiy iaienaieo a?ae ?oee oeeo?.

Iniiai? iieiaeaiiy aeena?oaoe?? iioae?eiaai? a oaeeo i?aoeyo:

1. Ee?e/aiei I.O., Eooeaiei A.A., *aeiooi E.I. Auaeaeaiea aaiiao?i –
oiiieiae/aneeo i?eciaeia ecia?aaeaiee iaoiaeii aaoiei??aeyoeeiiiuo
i?aia?aciaaiee // I?iaeaiu oi?aaeaiey e eioi?iaoeee. – 1997. – ?1. – N.
138-152.

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*AEIOOI E.I. Ei?aeyoe?ei? iaoiaee ia/eneaiiy aaiiao?e/ieo ? oiiieia?/ieo
iciae cia?aaeaiue.- ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.05.02 – iaoaiaoe/ia
iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee. – ?inoeooo e?aa?iaoeee ?iai?
A.I. Aeooeiaa IAI Oe?a?ie, Ee?a, 1999.

Aeena?oaoe?y i?enay/aia ?icaeoeo iaoaiaoe/ieo cania?a aeyaeaiiy iciae
cia?aaeaiue ia iniia? aeanoeainoae ooieoe?iiaea oeio aaoiei?aeyoe?eieo
ia?aoai?aiue a?ae ooieoe?? ina?oeaiino?. Iiaoaeiaaii aeene?aoi?
aea?aaeaioe oi?ioe aeey ia/eneaiiy oa?aeoa?enoee cia?aaeaiiy a iai?yieo.
Cae?eniaii ?icia?aeaethaaiiy iaea?aeaieo aeai?eoi?a. Ocaaaeueiaii
iiiyooy caoiee iaeano? ? iaea?aeaii no?oeoo?iee iien iaiioeeeo iaeanoae
/a?ac caoiee aeueo ii?yaee?a. Iiaoaeiaaii ia?aeaeueiee aeai?eoi
aeae?eaiiy caoie iaeano?.

Eeth/ia? neiaa: aaoiei?aeyoe?y, iaiioeea iaeanoue, ia?aeaeueiee
aeai?eoi, caoiea iaeano?, iciaee cia?aaeaiiy.

*AEIOOI E.I. Ei??aeyoeeiiiua iaoiaeu au/eneaiey aaiiao?e/aneeo e
oiiieiae/aneeo i?eciaeia ecia?aaeaiee.- ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
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Aeenna?oaoeey iinayuaia ?acaeoeth iaoaiaoe/aneeo n?aaenoa auyaeaiey
i?eciaeia ecia?aaeaiee ia iniiaa naienoa ooieoeeiiaea oeia
aaoiei??aeyoeeiiiuo i?aia?aciaaiee io ooieoeee inaauaiiinoe. Iino?iaiu
aeene?aoiua yeaeaaeaiou oi?ioe aeey au/eneaiey oa?aeoa?enoee
ecia?aaeaiey a iai?aaeaiee. Inouanoaeaii ?ania?aeeaeeaaiea iieo/aiiuo
aeai?eoiia. Iaiauaii iiiyoea caeeaa iaeanoe e iieo/aii no?oeoo?iia
iienaiea iaauioeeuo iaeanoae /a?ac caeeau aunoeo ii?yaeeia. Iino?iai
ia?aeeaeueiue aeai?eoi auaeaeaiey caeeaia iaeanoe.

Eeth/aaua neiaa: aaoiei??aeyoeey, iaauioeeay iaeanoue, ia?aeeaeueiue
aeai?eoi, caeea iaeanoe, i?eciaee ecia?aaeaiey.

CHEKOTUN K.M. Correlation methods for calculating geometrical and
topological features of image.- Manuscript.

The dissertation for degree of Candidate of physical-mathematical
Science by speciality 01.05.02 – mathematical simulation and calculus
methods. – NAS of Ukraine V.M. Glushkov Institute of Cybernetics, Kyiv,
1998.

Mathematical methods for image feature extraction based on properties of
autocorrelation of illumination function are developed in the thesis.

. The definitions of different types of convexity distortion “in
direction” are given: gulfs of region, holes and gulfs of hole:

, that is a sum of region projection and the projections of the
elements mentioned above, can be calculated by formula

,

.

,

are fixed.

can be

– grid step. The error of such a discretization have been found.

The parallel algorithms for calculating image characteristics in
direction are built for multilayer neural-like architecture. Speed-up
coefficients are estimated.

Concept of gulf is developed in Chapter 2. Higher order gulfs are
defined. On the picture the gulfs of order 1 are single-hatched and the
gulfs of order 2 are double-hatched.

The following expression are regarded as a region descriptions. They are
compositions of convex envelops of respective gulfs.

.

It is proved, that the higher order gulfs is included in description,
the more precise is description. The parallel algorithm for gulf
extraction have been built.

Recognition of handprinted characters is proposed as a test problem.

Keywords: autocorrelation, non-convex region, parallel algorithm, gulf
of region, image feature.

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