Research on Change Detection in Remote Sensing Images by using 2D-Fisher Criterion Function Method

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1 In: Wagner W., Székely, B. (ed.: ISPRS C VII Sympoium 1 Year ISPRS, Vienna, Auria, July 5 7, 1, IAPRS, Vol. XXXVIII, Par 7B Conen Auhor Index Keyword Index Reearh on Change Deeion in Remoe Sening Image by uing D-Fiher Crierion Funion Mehod Baoming Zhang, Ke Chen,Yang Zhou, Mingxia Xie, Hongwei Zhang Remoe Sening Informaion Engineering Deparmen, Zhen Zhou Iniue of Surveying and Mapping, Zhen Zhou, China, zbm@vip.371.ne, k17@163.om, zhouyang3d@163.om, xmx44@yahoo.n, hongwei691@163.om KEY WORDS: hange deeion, Fiher rierion funion, Image hrehold, wo-dimenion hiogram, remoe ening image ABSRAC: In hi paper, D-Fiher rierion funion wa inrodued o hange deeion in remoe ening image baed on lai one dimenion fiher rierion funion, and hi expanded he pae of grey value from one-dimenion o wo-dimenion and grealy improved he image noie-eniiviy. Meanwhile, in order o enhane he ompuing peed, we refined he oluion mehod of D hrehold in D-Fiher rierion funion hrough ranforming ompuing mehod from wo-dimenion hrehold o wo one-dimenion hrehold and grealy redued he deeion ime. Refined D-Fiher rierion funion mehod wa uiable no only for he hange deeion in remoe ening image, bu alo for oher ape in daa proeing. 1. INRODUCION he auo exraion of hange area i he key of he hange deeion of muli-emporal remoe ening image. I eay o ompue and ha a fa ompuaion peed. So how o find a hrehold finding mehod wih wide range of appliaion, good reul of exraion and good performane of ani-noie beome one of he main onen of he reearh on remoe ening image hange deeion. Unil now, domei and foreign holar have arried ou exenive reearh on hi problem and propoed kind of mehod o ele hrehold, for example,maximum variane beween-la, maximum enropy mehod and o on. However, wheher he maximum variane beween-la or he maximum enropy mehod, i rule funion only onider maximizing he variane beween-la, in oher word o maximize he degree of eparaion bu wihou onidering he diree level in la wihin. And he wo mehod are only uiable when pixel number of hange la and no hange la are no differen a lo. While he number of he wo kind of pixel i igfianly differen, neiher one mehod i appliable. A good remoe ening image hange deeion mehod hould no only maximize he eparaion degree beween hange la and no hange la, bu alo make he hange la and no hange la diperion degree mimum, ha i, imilariy of pixel in every la hould be maximal. A we all know, in he paern reogion heory, he Fiher rierion funion an be ued o ge he be projeion direion of feaure veor. In hi projeion direion we an ge he greae diane beween lae and he malle diane in la. A hi ime, value of Fiher rierion funion reahed he maximum. hu, Fiher rierion funion i a good rierion o analyze he degree of la eparaion. he laial Fiher rierion funion mehod i inrodued ino remoe ening image hange deeion and exended i original one-dimenional pae of gray value o he wo-dimenional pae, uh a he gray value mean neighborhood gray (G-Mean, gray value - he Medium value of neighborhood gray (G-Medium and o on. D-Fiher rierion funion mehod i bring forward o apply o he remoe ening image hange deeion. Beaue D-Fiher rierion funion mehod for olving adapive hrehold i omplex o ompue, we ry o improve remoe ening image hange deeion D-Fiher rierion funion mehod propoed in hi paper. So i an effeively de-noiing, and ahieve rapid hange deeion.. FISHER CRIERION FUNCION MEHOD he eene of olving Fiher rierion funion i o olve opimizaion problem, ha mean uing a few linear ombinaion (alled he diriminan or anoal variae y1 a 1 x, y a x,, yr a r x in p-dimenional x ( x, x,, x p (uually r i igfianly le x, x,, xp, in veor 1 han p o replae he original p variable 1 order o ahieve he redued-dimenional purpoe, and in he new projeion pae y ax, making he large diane beween he variou lae and he malle in one la. A i hown in Figure 1, for he wo aegorie ω and ω, auming ha all lae are haraerized by wo-dimenional diribuion (A, B par in Figure 1 and proje hem in raigh line Y1 and Y, you an learly ee ha he eparaion beween lae are pariularly good a he direion of raigh line. Y Y X B A ω ω n Figure 1. Projeion of wo-dimenional feaure veor in a raigh line he bi-objeive problem, namely la pae will be he large and he malle aegory from, i ranformed ino ingle-objeive opimizaion problem, ha make he formula 1 ge a maximum. Y 1 X 1 n 697

ro-produ, i um of quare in group and um of ro-produ.

2 In: Wagner W., Székely, B. (ed.: ISPRS C VII Sympoium 1 Year ISPRS, Vienna, Auria, July 5 7, 1, IAPRS, Vol. XXXVIII, Par 7B Conen Auhor Index Keyword Index Where, SSR a Ba Δ ( a (1 SSE a Ea SSR yij SSE yij i he um of quare beween group of, i he um of quare in he group, i um of quare beween group and um of ro-produ, i um of quare in group and um of ro-produ. hi paper applie i o remoe ening image hange deeion proe, o ha pixel of hange la and no hange lae have he mimum diperion in la and he maximum diane beween lae (diane beween he ener of every la repreen diane beween lae, in hange deeion, we mu onider he priori probabiliy of hange pixel and no hange pixel, B E P( ω and P( ωn 1 P( ω,herefore, aking ino aoun of he priori probabiliy irumane, he defiion of Fiher rierion funion i: k k 1 g( x, y f( x+ m, y + n (4 k m k n k 1 x m,1 y n, m and n are he widh and heigh of he hanged image repeively, and generally ake 3. he value of he wo-dimenional hiogram of hanged image i expreed a he pixel gray value. he pixel number of he Neighborhood average gray value i (, i j,1,, k gxy (, j. hree-dimenional deripion i hown in Figure and i projeion o he plane i hown in Figure 3 J ( P( ω μ P( ω μ n n + P ωn σn P( ω σ ( ( J ( When i he be hrehold value, ge maximum value, eleion rieria of Fiher hrehold i: Figure. hree-dimenional deripion [ ] Arg J max ( (3 3. D-FISHER CRIERION FUNCION IN CHANGE DEECION OF REMOE SENSING IMAGES A he laial Fiher rierion funion mehod merely refle he diribuion of pixel gray value, when SNR (ignal o noie of he remoe ening image i mall, he one-dimenional grey level hiogram of he differene image will have no noieable wave re and rough, o he hrehold i diffiul o ele. hen if only aording o one-dimenional grey hiogram, he hange deeion, aording o Fiher rierion funion, will make a eriou miake. In view of hi iuaion, in hi haper he laial Fiher rierion funion will be inrodued ino he proe of hange deeion, while he one-dimenional gray-ale pae will be expanded. aking full advanage of he neighborhood pixel paial informaion, we pu forward remoe ening image hange deeion D-Fiher rierion funion mehod. 3.1 he bai priniple of he D-Fiher rierion funion mehod Suppoe wo-dimenional pae i a G-Mean pae, f ( xy, i he gray value a ( x, y poin of differen image, gxy (, i he average gray value in k k adjaen area, ( x, y i he ener, and Figure 3. wo-dimenional hiogram diplay on plane Differene image i divided ino wo par, pixel hanged and no hanged. And heir pixel gray value and he neighborhood average gray value i almo equal, o i i mainly diribued in he viiy of he diagonal and he luering phenomenon i apparen. Similarly, for noie in he differene image, he differene beween pixel gray value and he average gray value in pixel neighborhood area i large, o mainly in he non-diagonal par. In he differene image, he roughly diribuion of hanged pixel, no hanged pixel and noie area in wo-dimenional hiogram i hown in Figure 4. I an be een, regardle of high and low SNR of he differene image, eleing an appropriae hrehold value o eparae hange la and no hange lae, we an ge a beer e reul. So i fully embodie he ani-noie performane afer exending he original one-dimenional gray-value pae o wo-dimenional pae. 698

3 In: Wagner W., Székely, B. (ed.: ISPRS C VII Sympoium 1 Year ISPRS, Vienna, Auria, July 5 7, 1, IAPRS, Vol. XXXVIII, Par 7B Conen Auhor Index Keyword Index 1 1 ( i μ ( ( ( P ω j μ P ω i, σ 1 1 σ i ( i μ ( ( j ( i P ωi j μ P ωj i i, σ j σ i i j (14 (15 Aording o Equaion, we an derive ha D-Fiher rierion funion i: Figure 4. diribuion of hanged and no hanged pixel and noie area Differene image. he wo-dimenional join probabiliy deniy of Pixel gray value and i neighbourhood average gray-ale i a follow: J (, ( P( ω μ P( ω μ + ( P( ω μ P( ω μ i i i j P( ω σ + P( ω σ + P( ω σ + P( ω σ i i j j (16 p Ni (, j ij, pij, ij 1 N i p (5 J(, When reahe he maximum he orreponding Spli poin hould be he be hange deeion hrehold, hen he D-Fiher hrehold eleion rule i: Given any wo-dimenional hrehold value, he orreponding hanged la and no hanged la are ω andω. heir gray and average neighborhood gray are: n [ ] (, Arg max J(, (17 1 P( ω pij, j,1,, i 1 (6 P( ω pij, i,1,, L 1 (7 P( ωi pij, j,1,, L 1 (8 i P( ωj pij, i,1,, L 1 (9 he orreponding mean and variane veor: And μ μi μ μ (1 j n ( μ, μ (, (, i j σ σ σ 1 (, n σ σ σ 1 ip( ω jp( ω i μ, μ 1 1 i ip( ω jp( ω i μi, μ L 1 j i (11 (1 (13 3. he improvemen of D-Fiher rierion funion D-Fiher rierion funion an make ue of he gray informaion of a ingle pixel and relaed informaion of pixel neighborhood pae. he onidering ope i exended from a ingle poin gray value ino he poin and i neighborhood gray-paial informaion. Relaive o he laial one-dimenional Fiher rierion funion, ani-noie performane ha been grealy improved in he proe of image hange deeion. Aording o he bai priniple and formula of D-Fiher rierion funion, i an be known ha along wih he inreaing of oluion pae dimenion, he enire oluion pae need o ravere when o find he opimal hrehold i [, L 1] [, L 1].A hi ime, ompuing ime i oo long, and real-ime i bad. o ome exen, i limi he D-Fiher rierion funion mehod in he praial appliaion of remoe ening image hange deeion. herefore, he following onen will onider how o improve he imeline of D-Fiher rierion funion mehod. In order o improve he peed of remoe ening image hange deeion of D-Fiher rierion funion, i an be onidered from wo ape o improve he propoed D-Fiher rierion funion: for one hing, narrow he oluion pae of D-Fiher rierion funion; for anoher, ranform he wo-dimenional hrehold ino wo one-dimenional hrehold. he following will diu hee wo menioned-above ape. 1 Narrow he ope of he original oluion pae, o a o ahieve he purpoe of improving he peed of deeion. Sine he exraion of he hange area i imilar o he wo ype of luering problem, o maximize he diane beween lae, he iial luer ener generally ele he poin where he rule funion value i he large. Beaue i i wo ype of luering, he iial luer ener alway ele he wo poin where he funion ge wo large value. In peifi luering proe, he opimal hrehold value will fall 699

In: Wagner W., Székely, B. (ed.: ISPRS C VII Sympoium 1 Year ISPRS, Vienna, Auria, July 5 7, 1, IAPRS, Vol. XXXVIII, Par 7B Conen Auhor Index Keyword Index beween wo poin.

4 In: Wagner W., Székely, B. (ed.: ISPRS C VII Sympoium 1 Year ISPRS, Vienna, Auria, July 5 7, 1, IAPRS, Vol. XXXVIII, Par 7B Conen Auhor Index Keyword Index beween wo poin. Aording o hi heory, he peifi olving ep are a follow: Sep 1:o obain wo-dimenional hiogram of differene image; Sep :Aording o wo-dimenional hiogram o Sele exreme poin from he differene image, a i hown in Figure 5 (uually make k 6 ; Sep 3:Obain he orreponding value of eah exreme poin in he D-Fiher rierion funion. Sep 4:Sele he wo exreme poin ( 1, 1 and (, orreponding o he large wo funion value, a he ener and (, (, 1 1 a he verex o make a reangle. A hown in Figure 6, namely, he area of red reangle, , 1 1 i he improved ope of he oluion pae. From he above analyi we an ge ha he improved oluion pae i he original oluion pae. 1 1, , 1+ 1, L 1, [ ] [ ] Figure 5. he eleion of maximum in wo-dimenional hiogram L 1 g( xy, ( 1, 1 (, L 1 f( x, y Figure 6. Improvemen of oluion pae ranform wo-dimenional hrehold ino wo one-dimenional hrehold, o a o ahieve he purpoe of improving he peed of deeion Repeively make ue of eah pixel gray value and neighbourhood paial informaion, aording o he laial Fiher rierion funion mehod, o olve he opimal gray k hrehold value and he be neighborhood hrehold, boh of whih oniue he wo-dimenional hrehold of remoe ening image hange deeion. hen (, (, aording o he wo-dimenional hrehold, do hange deeion of he differene image. In mehod 1, he improvemen of oluion pae of D-Fiher rierion funion i he original oluion pae 1 1, , [, L 1] [, ] However, we need o ravere he enire image o obain he wo-dimenional join probabiliy deniy of pixel gray value and i neighborhood paial informaion aording o he wo-dimenional hiogram. Afer ha, i ha nohing o do wih he image ize ielf. he number of run ime (one run mean he proe of alulaing all kind of probabiliy, he mean and variane eah ime of he original oluion pae for olving i ( ( (Auming gray-ale of he image i 56. Afer improved, he number 4. In he Inel Penium Dual. CPU, G i 1 1 memory environmen, he ime one run required i probably.384. Sine he wo exreme value fall moly on boh ide of he middle-la gray, uppoe ha i (19,19 (1,1 he maximum poin, and i he eond, he ime i he be wo-dimenional hrehold required. I an be known ha no maer how narrow he oluion pae i, he oluion ime an no aify he need of praial appliaion. herefore, we hoe mehod. 3.3 he peifi proe o improve D-Fiher rierion funion mehod. he peifi proe of remoe ening image hange deeion make ue of he improved D-Fiher rierion funion mehod (aking wo-dimenional pae of hooing G-Mean for example: Sep 1:Aording o he pixel gray value and formula 4, obain he grey level hiogram of he differene image and he hiogram of he mean value of gray ale in 3 3 neighbourhood area. Sep :On he hiogram, a well a neighborhood average gray hiogram, ake advanage of laial Fiher rierion funion mehod o ge he one-dimenional opimal hrehold and he wo-dimenional hrehold repeively. (, and Sep 3:Aording o wo-dimenional hrehold, analyze he variou elemen o generae he reul of image hange deeion. For ( x, y If (( f ( xy, && ( gxy (, hen ( xy, ω Ele ( xy, ωn (, i he opimal hrehold of image hange deeion. 4. EXPERIMEN AND ANALYSIS In he above eion, hrough he Fiher rierion funion in he paern reogion heory, we propoe he remoe ening 7

hen, we will ue he imulaion daa and real daa experimen o validae he effeivene of he hange deeion algorihm propoed in hi haper. he experimenal environmen i Inel Penium Dual. CPU, G memory.

Make linear ranformaion on he original image o imulae anoher phae of he remoe ening daa, and hen add wo airraf on he imulaion image o make he hanged area.

8 reul ompare of hange deeion wih noie (a Phae 1 Original imulaion image (b Phae Original imulaion image Figure 7.

Fiher, wo-dimenional Ou, and wo-dimenional Fiher, do hange deeion e on he image wih noie. he omparion i hown in Figure 8. From fig.

I ani-noie i uperior o he laial one-dimenional Ou, one-dimenional Fiher, and ha he prey ame performane a pre-d-fiher rierion funion mehod and wo-dimenional Ou mehod, namely, neighbourhood

From he reul of wo-dimenional Ou mehod we an ee ha hi mehod i no very omplee for he exraion of he airraf, namely, exiing problem of miing deeion.

5 In: Wagner W., Székely, B. (ed.: ISPRS C VII Sympoium 1 Year ISPRS, Vienna, Auria, July 5 7, 1, IAPRS, Vol. XXXVIII, Par 7B Conen Auhor Index Keyword Index image hange deeion mehod: D-Fiher rierion funion. hen, we will ue he imulaion daa and real daa experimen o validae he effeivene of he hange deeion algorihm propoed in hi haper. he experimenal environmen i Inel Penium Dual. CPU, G memory. Fir i he imulaion experimen. he remoe ening imulaion image of muli-phae are oniued by an airpor image and he orreponding hanged image, a hown in Figure 7. Make linear ranformaion on he original image o imulae anoher phae of he remoe ening daa, and hen add wo airraf on he imulaion image o make he hanged area. (e Reul of -D Fiher (before improvemen (, (19,73 (f Reul of -D Fiher (afer improvemen (, (18,67 Fig.8 reul ompare of hange deeion wih noie (a Phae 1 Original imulaion image (b Phae Original imulaion image Figure 7.he imulaion image a differen ime bu in he ame area he following plu noie (Gauian noiein he differene image of he original imulaion image, le SNR1,aording o One-dimenional Ou, One-dimenional Fiher, wo-dimenional Ou, and wo-dimenional Fiher, do hange deeion e on he image wih noie. he omparion i hown in Figure 8. From fig.8 we an ee ha improved D-Fiher hange deeion algorihm an effeively dee he hanged area in he differene image wih noie. I ani-noie i uperior o he laial one-dimenional Ou, one-dimenional Fiher, and ha he prey ame performane a pre-d-fiher rierion funion mehod and wo-dimenional Ou mehod, namely, neighbourhood informaion are obviou for Removal of Gauian noie. From he reul of wo-dimenional Ou mehod we an ee ha hi mehod i no very omplee for he exraion of he airraf, namely, exiing problem of miing deeion. he ime oupied by wo-dimenional hange deeion mehod i hown in able 1. Algorihm ime of deeion D-Ou D-Fiher (before improvemen D-Fiher (afer improvemen able 1 he ime of every wo-dimenional hange deeion mehod (a Differene image wih noie (SNR1 (b Reul of One-dimenional 8 Ou ( In order o furher verify he effeivene of he propoed mehod in hi haper, he aual remoe ening image in an area of wo-phae i hoen o do he experimen. he experimenal daa i SPO panhromai image wih regiraion and relaive radiomeri orreion, and i a region in 1987 and 199 provided by ERDAS. he paial reoluion i 1m, region ize pixel and 56 gray level. Experimen are arried ou uing he above mehod, in whih ele (gray value, neighborhood gray-ale median pae a wo-dimenional pae of D-Fiher rierion funion mehod. he reul i hown in Figure 9 ( Reul of wo-dimenional Ou (, (8,15 (d Reul of One-dimenional Fiher (aremoe Sening Image in 1987 (bremoe Sening Image in

6 In: Wagner W., Székely, B. (ed.: ISPRS C VII Sympoium 1 Year ISPRS, Vienna, Auria, July 5 7, 1, IAPRS, Vol. XXXVIII, Par 7B Conen Auhor Index Keyword Index ( he differene image (ereul of wo-dimenional Ou (dreul of One-dimenional Ou (freul of One-dimenional Fiher D-Fiher rierion funion mehod i propoed. Remoe ening image hange deeion D-Fiher rierion funion mehod exended he one-dimenional gray value pae of he laial Fiher rierion funion o wo-dimenional pae, uh a (G-Mean, (G-Medium, e. Among hem, he hoie of wo-dimenional pae i baed on he peifi irumane of he aual image. For example, G-Mean ha a good effe of removing Gauian noie, while G-Medium are obviou for he al and pepper noie. In he proe of he oluion, he wo-dimenional hrehold, we pli i ino wo one-dimenional hrehold, and he deeion peed i grealy improved. he D-Fiher rierion funion mehod ake ino aoun of he ani-noie and deeion peed of he hange deeion proe, making he mehod muh more uiable for praial appliaion need of remoe ening image hange deeion. Experimen how ha he improved D-Fiher rierion funion mehod of remoe-ening image hange deeion i uperior o he laial one-dimenional Ou mehod, one-dimenional Fiher rierion funion mehod in he ani-noie, and i far uperior o he wo-dimenional Ou in he peed of hange deeion. 6. REFERENCE [1] Rihard O.Duda, Peer E.Har, David G.Sork.,3.Paern laifiaion, ranlae by Li Hong-dong, Yao ianxiang, Beijing: China Mahine Pre(Chinee. (g Reul of -D Fiher (before improvemen Fig.9 he reul of real image hange deeion he ime oupied by wo-dimenional hange deeion mehod in he image hange deeion proe i hown in able. Algori hm ime of deeion D-Ou min (h Reul of -D Fiher (afer improvemen D-Fiher (before improvemen D-Fiher (afer improvemen able he ime oupied by wo-dimenional hange deeion mehod in he image hange deeion proe Experimenal reul how he exellen of he hange deeion mehod baed on he improved D-Fiher rierion funion, whoe uperior ani-noie, and peed ould have been fully embodied, wheher in he imulaion experimen or on he aual image. And, i able o mee he need of praial appliaion of remoe ening image hange deeion in effe of real-ime and hange deeion. [] Zhao Feng, Fan jiu-lun, 7. One Image Segmenaion Mehod Combing D Ou' Mehod and Fuzzy Enropy. Appliaion Reearh of Compuer (Chinee, 4(6, [3] ong Ying, Qiu Xiao-hui,4. A new algorihm of image egmenaion uing wo-dimenional hiogram baed on Fiher rierion funion. eleommuaion for Eleri Power Syem (Chinee, 5(9, 36-39, 47. [4] Yu Jin-hua, Wang Yuan-yuan, Shi Xin-ling, 7. Image egmenaion wih wo-dimenion fuzzy luer mehod baed on paial informaion. Opo-elero Engineering (Chinee, 34(4, [5] Chen Guo, 3. he Fiher rierion funion mehod of Image hreholding. Chinee Journal of Sienifi Inrumen, 4(6, ,576. [6] Xie Mingxia, Chen Ke, Guo Jianzhong, 8. Reearh of FCM for image egmenaion baed on graph heory. Journal of Compuer Appliaion (Chinee, 8(11, [7] Zhong Jia-qiang,Wang Run-heng, 5. Muliemporal Remoe Sening Image Change Deeion Baed on Adapive Parameer Eimaion, Aa Geodaeia e Carographia Sia (Chinee, 34(4, SUMMARY he laial Fiher rierion funion i inrodued ino he remoe ening image hange deeion. he approah baed on 7

Intermediate Frequency (IF)

Intermediate Frequency (IF) Inerediae Frequeny IF Iage frequeny p. II-33 Apliude Modulaion: SSB DSB odulaion: By ixing wih a inuoidal arrier a rad/e, half of hi peral deniy i ranlaed up in frequeny and enered abou and half i ranlaed