Àëãîðèòì ïîèñêà èìïóëüñíîãî øóìà íà èçîáðàæåíèè
Ñ.Â. Áåëèì
belimsv@omsu.ru Ñ.Á. Ëàðèîíîâ me@stas-larionov.ru
Îìñêèé ãîñóäàðñòâåííûé óíèâåðñèòåò èì. Ô.Ì. Äîñòîåâñêîãî, Îìñê, Ðîññèÿ
Àííîòàöèÿ
 ñòàòüå ïðåäëîæåí àëãîðèòì âûÿâëåíèÿ èìïóëüñíîãî øóìà. Èçîá- ðàæåíèå ïðåäñòàâëÿåòñÿ â âèäå ãðàôà. Íà ãðàôå èùóòñÿ ñîîáùå- ñòâà. Ñîîáùåñòâà, ñîñòîÿùèå èç îäíîãî ïèêñåëÿ ñ÷èòàþòñÿ ïîâðå- æäåííûìè. Ïðîâåäåí êîìïüþòåðíûé ýêñïåðèìåíò. Àëãîðèòì ïîêà- çàë âûñîêóþ ýôôåêòèâíîñòü.
Ââåäåíèå
Ïîèñê íà èçîáðàæåíèèè ïèêñåëåé, ïîâðåæäåííûõ èìïóëüñíûì øóìîì, ìîæíî îòíåñòè ê çàäà÷àì îáó÷åíèÿ áåç ó÷èòåëÿ. Îñíîâíîé ïîäõîä, èñïîëüçóåìûé â ïîäàâëÿþùåì êîëè÷åñòâå àëãîðèòìîâ, ñîñòîèò â àíàëèçå ñêîëüçÿùåãî îêíà [1, 2]. Ïîä ñêîëüçÿùèì îêíîì ïîíèìàåòñÿ íåêîòîðàÿ ëîêàëüíàÿ îáëàñòü èçîáðàæåíèÿ ïî- ñëåäîâàòåëüíî ïðîõîäÿùàÿ âñå ïèêñåëè. Èç ñðàâíåíèÿ õàðàêòåðèñòèê öåíòðàëüíîãî ïèêñåëÿ îêíà ñ îñòàëü- íûìè ïèêñåëÿìè îêíà äåëàåòñÿ âûâîä î åãî ïîâðåæäåíèè. Îòëè÷èå ìåòîäîâ äåòåêòèðîâàíèÿ ïîâðåæäåííûõ ïèêñåëåé äðóã îò äðóãà ñîñòîèò â âûáîðå ðàçìåðîâ ñêîëüçÿùåãî îêíà è àëãîðèòìà ïðèíÿòèÿ ðåøåíèÿ î ïîâðåæäåíèè ïèêñåëÿ [3, 4, 5]. Òàêèå àëãîðèòìû ðàáîòàþò äîñòàòî÷íî áûñòðî, òàê êàê èìåþò ëèíåéíóþ òðóäîåìêîñòü ïî êîëè÷åñòâó ïèêñåëåé èçîáðàæåíèÿ. Îäíàêî ýôôåêòèâíîñòü ïîèñêà ïîâðåæäåííûõ ïèê- ñåëåé ñóùåñòâåííî çàâèñèò îò ïîëüçîâàòåëüñêèõ íàñòðîåê. Íàïðèìåð, àëãîðèòì SD-ROM [1], ëåæàùèé â îñíîâå áîëüøîãî êîëè÷åñòâà äðóãèõ àëãîðèòìîâ, ñîäåðæèò ÷åòûðå ïàðàìåòðà, âûáèðàåìûõ ïîëüçîâàòåëåì.
Âàðüèðîâàíèå äàííûõ ïàðàìåòðîâ ìîæåò ìåíÿòü ýôôåêòèâíîñòü ïîèñêà ïîâðåæäåííûõ ïèêñåëåé îò 62%
äî 96%. Ïðè ýòîì îñòàåòñÿ âûñîêèì ïðîöåíò ëîæíûõ ñðàáàòûâàíèé.
Óëó÷øåíèå ðåçóëüòàòîâ óäàåòñÿ äîáèòñÿ íà îñíîâå àëãîðèòìîâ, àíàëèçèðóþùèõ íå òîëüêî íåáîëüøóþ ëîêàëüíóþ îáëàñòü, íî è âñå èçîáðàæåíèå â öåëîì.  êà÷åñòâå òàêèõ ìîæíî îòìåòèòü àëãîðèòìû íà îñíîâå àññîöèàòèâíûõ ïðàâèë [6, 7], ìåòîäàõ ïîääåðæêè ïðèíÿòèÿ ðåøåíèé [8], à òàêæå îñíîâàííûå íà ìåòîäàõ ñåãìåíòàöèè èçîáðàæåíèé [9, 10]. Âî âñåõ ïåðå÷èñëåííûõ àëãîðèòìàõ îäèí èëè äâà íàñòðàèâàåìûõ ïà- ðàìåòðà è äîñòàòî÷íî âûñîêàÿ ýôôåêòèâíîñòü îáíàðóæåíèÿ ïîâðåæäåííûõ ïèêñåëåé. Ïðè ýòîì óäàåòñÿ ñóùåñòâåííî ñíèçèòü ïðîöåíò ëîæíûõ ñðàáàòûâàíèé. Ñëåäóåò îòìåòèòü, ÷òî ïåðå÷èñëåííûå àëãîðèòìû îáëàäàþò íå ëèíåéíîé, à êâàäðàòè÷íîé òðóäîåìêîñòüþ.
Öåëüþ äàííîé ñòàòüè ÿâëÿåòñÿ ðàçðàáîòêà àëãîðèòìà âûäåëåíèÿ ïîâðåæäåííûõ ïèêñåëåé íà îñíîâå ãðàôîâîãî ïðåäñòàâëåíèÿ èçîáðàæåíèÿ ñ ïîñëåäóþùåé åãî êëàñòåðèçàöèåé.
Èç ìåòîäîâ íà ñåãìåíòàöèè èçîáðàæåíèé ìîæíî îòìåòèòü ïðåäñòàâëåíèå èçîáðàæåíèÿ íà îñíîâå âçâå- øåííîãî ãðàôà ñ ïîñëåäóþùèì âûäåëåíèåì ñîîáùåñòâ (community) íà äàííîì ãðàôå [11, 12, 13]. Âûäåëåíèå ñîîáùåñòâ â áîëüøèíñòâå ñëó÷àåâ ðåàëèçóåòñÿ íà îñíîâå âûðàùèâàíèÿ îáëàñòåé íà èñõîäíîì èçîáðàæåíèè.
Äàííûé ïîäõîä èìåååò êâàäðàòè÷íóþ òðóäîåìêîñòü. Ïîâðåæäåííûå ïèêñåëè âûäåëÿþòñÿ êàê ñåãìåíòû, ñî- ñòîÿùèå èç îäíîé òî÷êè.
Copyright cby the paper's authors. Copying permitted for private and academic purposes.
In: Sergey V. Belim, Nadezda F. Bogachenko (eds.): Proceedings of the Workshop on Data Analysis and Modelling (DAM 2016), Omsk, Russia, October 2016, published at http://ceur-ws.org
1 Ïîñòàíîâêà çàäà÷è è àëãîðèòì ðåøåíèÿ
Èìïóëüñíîãîû øóì íà èçîáðàæåíèÿõ ïðîÿâëÿåòñÿ êàê îòäåëüíûå ñëó÷àéíî ðàñïîëîæåííûå ïèêñåëè ñëó-
÷àéíîãî öâåòà. Ïðè ýòîì èíôîðìàöèÿ î ïðåæíåì çíà÷åíèè ïèêñåëÿ ñòàíîâèòñÿ óòåðÿííîé. Îáîçíà÷èì îòíîøåíèå êîëè÷åñòâà èçìåíåííûõ ïèêñåëåé ê îáùåìó êîëè÷åñòâó ïèêñåëåé èçîáðàæåíèÿ ÷åðåçpè áóäåì íàçûâàòü ïðîöåíòîì çàøóìëåíèÿ.
Íà âõîäå àëãîðèòìà èìååì èçîáðàæåíèå ðàçìåðîìN×Mïèêñåëåé, íà êîòîðîì ïðèñóòñòâóåò èìïóëüñíûé øóì.Ïîëîæåíèå ïèêñåëÿ íà èçîáðàæåíèè ìîæåò áûòü çàäàíî äâóìÿ êîîðäèíàòàìè (x, y), ãäåx ïðèíèìàåò öåëûå çíà÷åíèÿ íà îòðåçêå [0, N −1], y ïðèíèìàåò öåëûå çíà÷åíèÿ íà îòðåçêå [0, M −1]. Äëÿ öâåòíûõ èçîáðàæåíèé êàæäîìó ïèêñåëþ ñ êîîðäèíàòàìè(x, y)ñîîòâåòñòâóåò òðè öâåòîâûå ñîñòàâëÿþùèå:r(x, y) êðàñíûé öâåò,g(x, y) çåëåíûé öâåò,b(x, y) ñèíèé öâåò.
Ïðåäñòàâèì èçîáðàæåíèå â âèäå íåîðèåíòèðîâàííîãî âçâåøåííîãî ãðàôà G. Âåðøèíàìè ãðàôà áóäóò ñëóæèòü ïèêñåëè èçîîáðàæåíèÿ. Ðåáðàìè ñîåäèíèì òîëüêî âåðøèíû, ñîîòâåòñòâóþùèå áëèæàéøèì ñîñåä- íèì ïèêñåëÿì íà èçîáðàæåíèè. Âåñ ðåáðà áóäåò îïðåäåëÿòüñÿ îòëè÷èåì öâåòîâûõ ñîñòàâëÿþùèõ êîíöîâ ðåáðà. Êàê ïîêàçàíî â ñòàòüå [14] íàèëó÷øèå ðåçóëüòàòû ìîãóò áûòü ïîëó÷åíû ïðè èñïîëüçîâàíèè ýêñ- ïîíåíöèàëüíîé ôóíêöèè. Âåñ ðåáðà, ñîåäèíÿþùåãî âåðøèíû vi = (xi, yi) è vj = (xj, yj), îïðåäåëèì â ñëåäóþùåì âèäå:
d(vi, vj) = exp(−1 h
q
(ri−rj)2+ (gi−gj)2+ (bi−bj)2).
Çäåñüri=r(vi, vj),gi=g(vi, vj),bi =b(vi, vj). Ïàðàìåòðhîïðåäåëÿåò çíà÷åíèå ðàçíîñòè öâåòîâûõ ñîñòàâ- ëÿþùèõ, äåòåêòèðóåìîå êàê ïåðåõîä ê ñîñåäíåìó ñåãìåíòó. Äàííûé ïàðàìåòð îïðåäåëÿåòñÿ ïîëüçîâàòåëåì è ÿâëÿåòñÿ îáùèì äëÿ âñåãî èçîáðàæåíèÿ.
Âûäåëåíèå èñïîð÷åííûõ ïèêñåëåé áóäåì îñóùåñòâëÿòü íà îñíîâå àëãîðèòìà ñåãìåíòàöèè èçîáðàæåíèÿ.
Ïðè ñåãìåíòàöèè âñå ïèêñåëè ðàçáèâàþòñÿ íà ãðóïïû ñõîæèõ ýëåìåíòîâ.  êà÷åñòâå ìåðû ñõîæåñòè âû- áèðàåòñÿ ¾öâåòîâîå ðàññòîÿíèå¿ ìåæäó ïèêñåëÿìèd(vi, vj).  ðåçóëüòàòå ñåãìåíòàöèè çàøóìëåííîãî èçîá- ðàæåíèÿ íåêîòîðûå ñåãìåíòû áóäóò ñîñòîÿòü èç îäíîé òî÷êè. Ñ âûñîêîé âåðîÿòíîñòüþ â êà÷åñòâå îä- íîïèêñåëüíûõ ñåãìåíòîâ áóäóò âûäåëåíû èìïóëüñíûå øóìû. Îäíàêî ñòîèò îòìåòèòü, ÷òî áîëüøèíñòâî ôîòîãðàôè÷åñêèõ èçîáðàæåíèé ñîäåðæèò ýëåìåíòû, êîòîðûå â îòñóòñòâèå øóìîâ òàêæå îïðåäåëÿþòñÿ, êàê îäíîïèêñåëüíûå êëàñòåðû. Íàëè÷èå òàêèõ ýëåìåíòîâ áóäåò ïðèâîäèòü ê ëîæíûì ñðàáàòûâàíèÿì.
Ïðè ïðåäñòàâëåíèè èçîáðàæåíèÿ â âèäå ãðàôà ñåãìåíòàöèÿ ýêâèâàëåíòíà êëàñòåðèçàöèè ãðàôàG. Ãðàô Gðàçáèâàåòñÿ íà ïîäãðàôû, ðàññòîÿíèÿ ìåæäó âåðøèíàìè êîòîðûõ çíà÷èòåëüíî ìåíüøå, ÷åì ñ îñòàëüíû- ìè âåðøèíàìè. Òàêèå ïîäãðàôû îáðàçóþò ñîîáùåñòâà (community). Äëÿ êîëè÷åñòâåííîé îöåíêè ðàçáèåíèÿ ãðàôà íà ñîîáùåñòâà èñïîëüçóåòñÿ ôóíêöèÿ ìîäóëüíîñòè Íüþìàíà [15, 16].
Äëÿ âû÷èñëåíèÿ ôóíêöèè ìîäóëüíîñòè íåîáõîäèìî äëÿ ãðàôàGçàäàòü ìàòðèöó âåñîâE. Äèàãîíàëüíûå ýëåìåíòû ìàòðèöû âåñîâ Eii ïîêàçûâàþò âåñ i-îé âåðøèí. Íà íà÷àëüíîì ýòàïå âåñ âñåõ âåðøèí íóëåâîé.
Íåäèàãîíàëüíûå ýëåìåíòû Eij (i 6= j) èìåþò âåñ, ðàâíûé öâåòîâîìó ðàññòîÿíèþ ìåæäó ïèêñåëÿìè, ñî- îòâåòñòâóþùèì âåðøèíàì vi èvj. ÌàòðèöàE áóäåò ñèììåòðè÷íîé îòíîñèòåëüíî ãëàâíîé äèàãîíàëè, òàê êàê ó ðåáåð íåò îðèåíòàöèè. Äëÿ âû÷èñëåíèÿ ôóíêöèè ìîäóëüíîñòè ââåäåì ïðèâåäåííóþ ìàòðèöó âåñîâ e=E/m, ãäå
m=
M N
X
i,j=1
Eij.
 ïðèâåäåííîé ìàòðèöå âåñîâ ýëåìåíò eij ïîêàçûâàåò äîëþ âåñà çàäàííîãî ðåáðà â îáùåì âåñå ãðàôà.  äàëüíåéøåì áóäåì ðàññìàòðèâàòü òîëüêî ïðèâåäåííûé âèä ìàòðèöû âåñîâ. Î÷åâèäíî, ÷òî
M N
X
i,j=1
eij= 1.
Âåëè÷èíà ìîäóëüíîñòè îïðåäåëÿåòñÿ âûðàæåíèåì [15, 16]:
Q(G) =
K
X
i=1
eij−
K
X
i=1
aibi.
ãäå K êîëè÷åñòâî âåðøèí ãðàôà, ai ïðèâåäåííàÿ èñõîäÿùàÿ ñòåïåíü âåðøèíû vi (ai = PK
j=1,j6=ieij), bi ïðèâåäåííàÿ âõîäÿùàÿ ñòåïåíü âåðøèíû vi (bi =PK
j=1,j6=ieji). Òàê êàê ãðàôG íåîðèåíòèðîâàííûé,
âõîäÿùàÿ è èñõîäÿùàÿ ñòåïåíü äëÿ âñåõ âåðøèí îäèíàêîâû (ai =bi; i = 1, ..., K). Ôóíêöèÿ ìîäóëüíîñòè ïðèíèìàåò âèä:
Q(G) =
K
X
i=1
eij−
K
X
i=1
a2i.
Äëÿ âûÿâëåíèÿ ñîîáùåñòâ íà ãðàôå áóäåì èñïîëüçîâàòü ïðîöåäóðó îáðàçîâàíèÿ ñòÿæåê. Ïîä ñòÿæêîé ïîíèìàåòñÿ ïðåîáðàçîâàíèå, ïðè êîòîðîì íåêîòîðûé ïîäãðàôH ãðàôàGçàìåíÿåòñÿ îäíîé âåðøèíîévH. Åñëè êàêàÿ-òî èç âåðøèí ïîäãðàôàH áûëà ñâÿçàíà ðåáðîì ñ âåðøèíîévèç ïîäãðàôàG\H, òî âåðøèíàvH
òàêæå áóäåò ñâÿçàíà ðåáðîì òîãî æå âåñà ñ âåðøèíîév. Âåñ íîâîé âåðøèíû áóäåò ðàâåí ñóììå âåñîâ ðåáåð è âåðøèí, âõîäÿùèõ â ïîäãðàô H. Íîâûé ãðàô îáîçíà÷èì GH. ÏîäãðàôH áóäåì ñ÷èòàòü ñîîáùåñòâîì, åñëè Q(GH)> Q(G). Ñëåäóåò îòìåòèòü, ÷òî ïðè îáðàçîâàíèè ñòÿæêè óìåíüøàåòñÿ ÷èñëî âåðøèí ãðàôà K. Íàøåé çàäà÷åé ñòîèò ïîèñê âåðøèí ãðàôà, íå âõîäÿùèõ íè â îäíî áîëåå êðóïíîå ñîîáùåñòâî.
Áóäåì íàõîäèòü ñîîáùåñòâà ìåòîäîì âûðàùèâàíèÿ îáëàñòåé.
1. Âûáèðàåì ïðîèçâîëüíûé ïèêñåëü èçîáðàæåíèÿv, íå âõîäÿùèé íè â îäíî ñîîáùåñòâî.
2. Äëÿ âûáðàííîãî ïèêñåëÿvïîî÷åðåäíî ðàññìàòðèâàåì áëèæàéøèå ñîñåäíèå ïèêñåëèv(i)(i= 1, ...,8) è ïûòàåìñÿ îáúåäèíèòü èõ â ñîîáùåñòâî. Ïðè êàæäîì îáúåäèíåíèè âû÷èñëÿåì èçìåíåíèå ôóíêöèè ìîäóëü- íîñòè∆Qi (i= 1, ...,8).
3. Åñëè îáúåäèíåíèå äàííîé âåðøèíû â ñîîáùåñòâî ñ äðóãèìè ïèêñåëÿìè íå âûãîäíî (∆Qi < 0, i = 1, ...,8), òî ñîîòâåòñòâóþùèé ïèêñåëü îòíîñèì ê ïîâðåæäåííûì. Èíà÷å ñòðîèì ñîîáùåñòâî
Íà âûõîäå àëãîðèòìà ïîëó÷èì ñïèñîê ïèêñåëåé, îáðàçóþùèõ ñîîáùåñòâà èç îäíîãî ýëåìåíòà. Ñ áîëüøîé âåðîÿòíîñòüþ äàííûå ïèêñåëè ÿâëÿþòñÿ èñêîìûìè.
Èçìåíåíèå ôóíêöèè ìîäóëüíîñòè ìîæåò áûòü âû÷èñëÿíî äîñòàòî÷íî áûñòðî íà îñíîâå òåêóùèõ õàðàê- òåðèñòèê ãðàôà. Ïðè îáúåäèíåíèè âåðøèí vi èvj èçìåíåíèå ìîäóëüíîñòè áóäåò ðàâíî:
∆Q= 2(eij−aiaj).
Î÷åâèäíî, ÷òî ïðåäëîæåííûé àëãîðèòì èìååò êâàäðàòè÷íóþ òðóäîåìêîñòü îò ÷èñëà ïèêñåëåé.
2 Êîìïüþòåðíûé ýêñïåðèìåíò
 êîìïüþòåðíîì ýêñïåðèìåíòå îáðàáàòûâàëèñü è èñêóññòâåííûå èçîáðàæåíèÿ è ôîòîãðàôè÷åñêèå ôàéëû ðàçìåðîì N = 512, M = 512 ïèêñåëåé. Êîîðäèíàòû è öâåò pN M òî÷åê, ìîäåëèðóþùèõ èìïóëüñíûé øóì ãåíåðèðîâàëèñü ñ ïîìîùüþ ëèíåéíîãî êîíãðóýíòíîãî ãåíåðàòîðà ñ ðàâíîìåðíûì ðàñïðåäåëåíèåì.
Ýêñïåðèìåíòû ïðîâîäèëèñü ñ óðîâåíåì øóìà îò 0% äî 70%. Äëÿ êàæäîãî íàáîðà ïàðàìåòðîâ è êàæäîãî èçîáðàæåíèÿ ïðîâîäèëîñü ïî 100 íåçàâèñèìûõ ýêñïåðèìåíòîâ.
 êàæäîì ýêñïåðèìåíòå ãåíåðèðîâàëèñüpN Mêîîðäèíàò è öâåòîâ ïèêñåëåé. Ïîñëå ýòîãî îñóùåñòâëÿëîñü âûÿâëåíèå ïîâðåæäåííûõ ïèêñåëåé. Ðåçóëüòàòû ñðàâíèâàëèñü ñî ñãåíåðèðîâàííûìè äàííûìè. Äëÿ îöåíêè êà÷åñòâà ðàáîòû àëãîðèòìà èñïîëüçîâàëèñü äâå âåëè÷èíû. Ýôôåêòèâíîñòü ðàáîòû àëãîðèòìà:
ef f = N0 pN M,
ãäåN0 êîëè÷åñòâî âåðíî èäåíòèôèöèðîâàííûõ èñïîð÷åííûõ ïèêñåëåé. Óðîâåíü ëîæíûõ ñðàáàòûâàíèé:
err= Ne
N ,
ãäåNe êîëè÷åñòâî îøèáî÷íî èäåíòèôèöèðîâàííûõ èñïîð÷åííûõ ïèêñåëåé,N îáùåå êîëè÷åñòâî ïèêñå- ëåé îïðåäåëåííîå àëãîðèòìîì, êàê èñïîð÷åííûå.
Äëÿ èçîáðàæåíèÿ, ïðåäñòàâëÿþùåãî ñîáîé îáëàñòü ðàâíîìåðíîé çàëèâêè îäíèì öâåòîì ýôôåêòèâíîñòü ðàáîòû àëãîðèòìà ïðèp= 10%ñîñòàâëÿåòef f = 99.98%ïðè ïðîöåíòå ëîæíûõ ñðàáàòûâàíèéerr= 0.11%. Ýôôåêòèâíîñòü íèæå ñòà ïðîöåíòîâ, òàê êàê ïðè ñëó÷àéíîì âûáîðå öâåòà èñïîð÷åííîãî ïèêñåëÿ íåíóëåâàÿ âåðîÿòíîñòü ñîâïàäåíèÿ åãî ñ öâåòîì çàëèâêè. Ýôôåêòèâíîñòü ðàáîòû àëãîðèòìà îñòàåòñÿ âûñîêîé âïëîòü äî áîëüøèõ çíà÷åíèé óðîâíÿ øóìà. Òàê ïðè p= 70% ýôôåêòèâíîñòü ðàâíà ef f = 99.97% ïðè ïðîöåíòå ëîæíûõ ñðàáàòûâàíèéerr= 6.20%. Ðîñò ïðîöåíòà ëîæíûõ ñðàáàòûâàíèé ñâÿçàí ñ òåì, ÷òî ïðè âûñîêîì óðîâíå øóìà èñïîð÷åííûå ïèêñåëè äîñòàòî÷íî ÷àñòî îêàçûâàþòñÿ áëèæàéøèìè ñîñåäÿìè.
Àíàëîãè÷íûå ýêñïåðèìåíòû äëÿ èñêóññòâåííûõ èçîáðàæåíèé ïðàâèëüíûõ ãåîìåòðè÷åñêèõ ôèãóð ñ ÷åò- êèìè ãðàíèöàìè è ïðèñóòñòâèåì îáëàñòåé ãðàäèåíòíîé çàëèâêè ïðè ñ óðîâíåì øóìà îòp= 10%äîp= 70%
ïîêàçàëè ýôôåêòèâíîñòü îòef f = 99.97%äîef f = 99.95%. Ïðîöåíò ëîæíûõ ñðàáàòûâàíèé, ïðè ýòîì, òàê- æå ñíèæàëñÿ îòerr= 7.81% äîerr= 4.15%. Îñíîâíîé âêëàä â âåëè÷èíó ïðîöåíòà ëîæíûõ ñðàáàòûâàíèé âíîñèëè ÷åòêèå ãðàíèöû, ðàçäåëÿþùèå îáëàñòè èçîáðàæåíèÿ.
Ýêñïåðèìåíòû íà ôîòîãðàôè÷åñêèõ èçîáðàæåíèÿõ ïîêàçàëè, ÷òî ýôôåêòèâíîñòü âûÿâëåíèÿ ïîâðåæäåí- íûõ ïèêñåëåé îñòàåòñÿ äîñòàòî÷íî âûñîêîé è ìåäëåííî óáûâàåò ñ ðîñòîì óðîâíÿ øóìà. Äàæå äëÿ ïðîöåí- òà çàøóìëåíèÿ p= 50% ýôôåêòèâíîñòü ef f = 83.85%. Çíà÷åíèå ïðîöåíòà ëîæíûõ ñðàáàòûâàíèé òàêæå óáûâàåò, ÷òî ñâÿçàíî ñ åãî îòíîñèòåëüíûì õàðàêòåðîì. Ïî àáñîëþòíîé âåëè÷èíå êîëè÷åñòâî îøèáî÷íî îïðåäåëåííûõ ïèêñåëåé îñòàåòñÿ ïðàêòè÷åñêè íà îäíîì óðîâíå.
3 Àíàëèç ðåçóëüòàòîâ è âûâîäû
Ïðåäëîæåííûé ìåòîä âûÿâëåíèÿ ïèêñåëåé, ïîâðåæäåííûõ èìïóëüñíûì øóìîì, îáëàäàåò äîñòàòî÷íî âû- ñîêîé ýôôåêòèâíîñòüþ äàæå äëÿ ñèëüíî çàøóìëåííûõ èçîáðàæåíèé. Ïðè÷åì êîëè÷åñòâî ïèêñåëåé, îøè- áî÷íî îòíåñåííûõ ê ïîâðåæäåííûì, ðàñòåò î÷åíü ìåäëåííî ñ óâåëè÷åíèåì çàøóìëåíèÿ, ÷òî ïðèâîäèò ê óìåíüøåíèþ óðîâíÿ ëîæíûõ ñðàáàòûâàíèé. Ïðîâåäåì ñðàâíåíèå ñ ðåçóëüòàòàìè äðóãèõ ðàáîò. Íàèáîëåå ðàñïðîñòðàíåííûé àëãîðèòì SD-ROM ïîçâîëÿåò îáíàðóæèâàòü èñïîð÷åííûå ïèêñåëè â ñðåäíåì ñ ýôôåê- òèâíîñòüþ 71% è óðîâíå ëîæíûõ ñðàáàòûâàíèÿ 5% ïðè èíòåíñèâíîñòè øóìà 10% [1]. Ýòîò æå ìåòîä ìîæåò äåìîíñòðèðîâàòü ýôôåêòèâíîñòü äî 96% ïðè óðîâíå çàøóìëåíèÿ 30%, íî íà øóìàõ òèïà ¾ñîëü è ïåðåö¿.
Ñëåäóåò îòìåòèòü, ÷òî çàäà÷à àíàëèçà èçîáðàæåíèé ñ øóìîì ¾ñîëü è ïåðåö¿ ÿâëÿåòñÿ áîëåå ïðîñòîé, òàê êàê â íèõ èíòåíñèâíîñòü öâåòà èñïîð÷åííûõ ïèêñåëåé èìååò ëèáî ìàêñèìàëüíîå, ëèáî ìèíèìàëüíîå çíà÷å- íèå. Ïðè÷åì äîñòèæåíèå ìàêñèìàëüíîé ýôôåêòèâíîñòè âîçìîæíî ëèøü ïðè îïðåäåëåííîì íàáîðå ÷åòûðåõ ïàðàìåòðîâ, ïîäáèðàåìûõ âðó÷íóþ. Ïðè óâåëè÷åíèè óðîâíÿ øóìà óðîâåíü ëîæíûõ ñðàáàòûâàíèé â àë- ãîðèòìå SD-ROM ðàñòåò î÷åíü áûñòðî è óæå ïðè èíòåíñèâíîñòè øóìà 30% äîñòèãàåò 73%. Àíàëîãè÷íûå àëãîðèòìû, îñíîâàííûå íà àíàëèçå ëîêàëüíîãî îêðóæåíèÿ êàæäîãî ïèêñåëÿ, äåìîíñòðèðóþò áëèçêèå ðå- çóëüòàòû. Òàê ìåòîä, èñïîëüçóþùèé ïîñòðîåíèå àññîöèàòèâíûõ ïðàâèë äëÿ íàáîðîâ ñîñåäíèõ ïèêñåëåé, ïðè èíòåíñèâíîñòè øóìà 30%, ïîêàçûâàåò ýôôåêòèâíîñòü 77% è óðîâåíü ëîæíûõ ñðàáàòûâàíèé 35% [6, 7].
Àëãîðèòì, îñíîâàííûé íà ìåòîäå àíàëèçà èåðàðõèé ïîçâîëÿåò îáíàðóæèâàòü èìïóëüñíûé øóì ñ ýôôåê- òèâíîñòüþ 85% è ëîæíûìè ñðàáàòûâàíèÿìè 55% [8]. Ñóùåñòâåííûì íåäîñòàòêîì äàííûõ ìåòîäîâ ÿâëÿåòñÿ àíàëèç äîñòàòî÷íî íåáîëüøîé îáëàñòè èçîáðàæåíèÿ âîêðóã êàæäîãî ïèêñåëÿ, êîòîðûé íå ïîçâîëÿåò âûÿâ- ëÿòü è àíàëèçèðîâàòü ïðîòÿæåííûå îáëàñòè íà èçîáðàæåíèè. ×àñòè÷íî äàííûé íåäîñòàòîê áûë óñòðàíåí â ìåòîäå âûÿâëåíèÿ èìïóëüñíîãî øóìà, îñíîâàííîì íà êëàñòåðèçàöèè èçîáðàæåíèé [9, 10], äëÿ êîòîðî- ãî ýôôåêòèâíîñòü îáíàðóæåíèÿ èñïîð÷åííûõ ïèêñåëåé 82%, à óðîâåíü ëîæíûõ ñðàáàòûâàíèé 23% ïðè çàøóìëåíèè íà 10%. Ïðè óâåëè÷åíèè ïðîöåíòà èñïîð÷åííûõ ïèêñåëåé ýôôåêòèâíîñòü ïàäàåò è ïðè 30%
çàøóìëåíèÿ ñîñòàâëÿåò 68%, à óðîâåíü ëîæíûõ ñðàáàòûâàíèé 11%.
Òàêèì îáðàçîì, ïðåäëîæåííûé â äàííîé ñòàòüå àëãîðèòì ïîçâîëÿåò ïîëó÷àòü çàìåòíûé âûèãðûø êàê â ýôôåêòèâíîñòè îáíàðóæåíèÿ èñïîð÷åííûõ ïèêñåëåé, òàê è â óðîâíå ëîæíûõ ñðàáàòûâàíèé ïðè çíà÷è- òåëüíîì çàøóìëåíèè èçîáðàæåíèÿ, âûøå 30%.
Ñïèñîê ëèòåðàòóðû
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Algorithm of an Impulse Noise Detection on an Image
Sergey V. Belim, Stanislav B. Larionov
In article the algorithm of of an impulse noise detection is suggested. The image is presented as a graph.
On the graph communities are looked for. Communities from one point are read by the defective pixels. The computer experiment is made. The algorithm shows high eectiveness.
