Robust Classification of Remote Sensing Data for Green Space Analysis

Transcription

1 Journal of Mahemacs and Sysem Scence 3 (03) D DAVID PUBLISHING Robus Classfcaon of Remoe Sensng Daa for Green Space Analyss Dyah E. Herwnda, Maman A. Djauhar and Luan Jaup 3. Faculy of Informaon Technology, Tarumanagara Unversy, Le.Jend. S. Parman No, Jakara 440, Indonesa. Deparmen of Mahemacal Scences, Faculy of Scence, Unvers Teknolog Malaysa, Skuda, Johor Bahru 830, Malaysa 3. Conservaore Naonal des Ars e Méers, 9 Rue San Marn, Pars 75003, France Receved: Feburary 9, 03 / Acceped: March 8, 03 / Publshed: Aprl 5, 03 Absrac: All of he Landsa 7 daa colleced afer 003 conans mssng pxels n he form of unsghly srpes across he mages. To recover mssng daa of a Landsa mage, dfferen mehods may be used. However, he gap fllng process creaes nconssences on pxel nensy values. The ncongruous pxel numbers are anomolous observaons and her classfcaon n he reference specer s challengng. In an effor o conrbue o hs need, we propose a relable robus approach o classfy nconssen pxels afer he gap fllng process. To esmae mulvarae locaon-scale parameers a new robus D (deph mnmum vecor varance esmaor) s presened. The D algorhm does no requre any marx nverson for s calculaon, consequenly s compuaonal me s hghly reduced. The resuls show ha has a hgh breakdown pon and s very effcen for large daa se. Landsa remoe sensng daa of Jakara Provnce across years 00 and 00 are used as case sudy. Key words: Deph funcon, mnmum vecor varance, covarance marx, Mahalanobs dsance.. Inroducon Landsa saelles daa are frequenly used o analyze land-use and land-cover changes, [, 9-]. A common approach of land cover change sudes usng Landsa daa has been o use mages o classfy land no dfferen caegores, and o quanfy changes n caegores across dfferen daes n me [4,, 6, 7, 9]. Snce 003, he, SLC (scan lne correcor), of Landsa 7 faled and he falure appears o be permanen. The non-funconng SLC causes large gaps a he edges of he mage. Amng o resore an mage, a gap fllng procedure s appled []. However, he gap fllng process arses he problem of nconssences on pxel nensy values. The ncongruous pxel numbers are anomolous observaons and her classfcaon n he reference Correspondng auhor: Dyah E. Herwnda, Ph.D., assocae professor, research felds: daa mnng. Emal: herwnda@unar.ac.d. specer s challengng because, requres daa processng mehods, capable o classfy nconssen pxels and produce conssen land-cover monorng. In an effor o conrbue o hs need, we have developed a relable robus approach o classfy dscordan pxels afer he gap fllng process for land cover change sudes usng Landsa daa. The cornersone of robus sascs s he robus esmaon of mulvarae locaon-scale parameers. Poneerng work n hs area has been can be found n [5, 8, 5]. In sascal leraure, we fnd several hgh breakdown esmaors for mulvarae mean and covarance marx. A well known and largely used robus esmaor s he MCD (mnmum covarance deermnan) [3]. Under regulary condons, Hawkns n Ref. [6] proposed he FSA (feasble soluon algorhm), whch ensured an opmal soluon for MCD. Aferwards, Rousseeuw and Van Dresen n Ref. [4] nroduced an mproved algorhm called he FMCD (fas mnmum covarance deermnan). The

2 Robus Classfcaon of Remoe Sensng Daa for Green Space Analyss 8 FMCD s a robus procedure wh hgh breakdown pon, bu as ndcaed n Ref. [8], mgh be neffcen for large daa ses. To mprove hs aspec, Herwnda e al. n Ref. [7] proposed he (mnmum vecor varance), whch s effecve for huge daa ses. has he same breakdown pon as FMCD bu s compuaonal aspecs are by far advanageous. Ths paper proposes a relable algorhm for robus supervsed land-cover classfcaon n remoe sensng. To esmae mulvarae locaon-scale parameers, a new robus deph funcon s presened. Is calculaon does no requre any covarance marx nverson [], whch s a valuable asse when one deals wh huge daa ses. The supervsed green space classfcaon s done wh a convenonal wo phase process: ranng ses and mage cell classfcaon. The sample areas for he ranng sep are seleced by human assessors. The oucomes of ranng ses are he specral references of green space,.e. he waer cachmen and vegeaon areas. Then specral reference values are used o classfy he enre mages from Landsa saelle. The area under nvesgaon s Jakara Provnce. In order o make hs paper self conaned, n Secon we provde a background summary of remoe sensng daa and preprocessng for classfcaon. In Secon 3 we descrbe he mehods and he algorhm used o classfy land-cover no dfferen caegores. Then, monorng resuls of green space areas of Jakara Provnce across years 00 and 00 are presened n Secon 4. The paper concludes wh addonal remarks and references.. Remoe Sensng Maerals Landsa saelles have been provdng mulspecral mages of Earh connuously snce early 970 s. The purpose of he Landsa program s o provde world s scenss and applcaon engneers wh a connung sream of remoe sensng daa for monorng and managng earh s resources [0, ]. A common approach usng Landsa daa has been o use mages o classfy land no dfferng caegores, and o quanfy changes n caegores beween dfferen daes [, 6, 9]. Land cover and land use changes are mporan ndcaors of human acves and clmac change. In Jakara Provnce proeced area publc polces and her managemen by Governor s offce are cenral o undersand he recen land cover changes [4].. Sudy Area The case of research s Jakara mulspecral magng from Landsa 7 saelle. Jakara s he capal of Indonesa ha s spread over an area of around 700 km wh populaon up o 9.5 mllon n 00. The supervsed classfcaon s done for change deecon of Jakara green space areas. The area under nvesgaon s covered by coordnae 5 9' " - 6 3' 54"S laude and 06 ' 4" ' 8"E longude.. Daa Ses Tff formaed mages across years 00 and 00 are used as npus. Daa s capured by sensors havng 7 bands nvolvng he vsble specral, NIR, and MIR. The spaal resoluon of bands n -5, and n 7 are 30 m, he resoluon of he sxh band s 60 m. On May 3, 003, SLC of Landsa 7 ETM+ (Enhanced Themac Mapper Plus), faled. Snce ha me all Landsa ETM+ mages have wedge-shaped gaps. The mpac of falure resuls n approxmaely 0% daa loss. The gap fllng s he preprocessng echnque used o fll mssng pars of remoe sensed magery. e do he gap fllng procedure wh he mul source. Fg. reveals he Jakara mulspecral mage wh SLC n year 00, and Fg. shows he recovered mage afer he gap fllng process. 3. Mehods of Classfcaon and Algorhm 3. Robus Mnmum Vecor Varance Le n X, X,..., X be a random sample from a p-varae dsrbuon wh locaon parameer μ and

3 8 Robus Classfcaon of Remoe Sensng Daa for Green Space Analyss The esmaors of mulvarae locaon-scale T,S parameers are defned as he par ( ) whch mnmze ( ) Tr S among all possble sample Fg. Mulspecral Jakara 00 mage wh SLC. n+p+ subses H of sze h=, wh T = X, (4) H h S ( ) ( ) = X H -T X -T (5) h p p Tr ( S ) = s + s s pp + s (6) j = j s an effcen robus esmaor mnmzng he square of parallelogram dagonal lengh. I was proposed n Ref. [7], n order o mprove FMCD algorhm. By usng Cholesky decomposon, we fnd O p compared ha effcency of s of order ( ) 3 wh FMCD whch s of order O( p ) [7]. 3. The Deph Funcon Fg. Mulspecral Jakara 00 mage afer gap fllng process. covarance marx Σ. Sample mean vecor and sample covarance marx are defned respecvely by n X= X () n = and n S= ( X )( ) -X X -X () n- = λ λ... λ 0 be egenvalues of Le p sample covarance marx S. VV (The vecor varance), of S s defned by Tr S = VV = ( ) λ + λ + + λ p (3) The advanage of VV consss n he fac ha measures mulvarae dsperson even f he covarance marx S s sngular. d e noe he sample Mahalanobs dsance defne by d ( ) - = X -X S ( X -X) (7) The sample verson of Mahalanobs deph of X, noed MD s defnes as; MD = (8) - + ( X -X) S ( X -X) from Eq. (7) and Eq. (8) we have he followng equaon. MD = (9) +d Par of MD denomnaor s Mahalanobs dsance, whch requres he nverson of sample covarance marx S for s calculaon. Amng o reduce he complexy of FMCD and algorhms, Djauhar and Umbara n Ref. [3], nroduced a new deph funcon noed M gven by ( X -X) M = (0) ( X -X ) S M s a marx of sze ( p+) ( p+) where assocaed o sample X, X,..., X n. By usng he propery of paroned marx deermnan, we have:

4 Robus Classfcaon of Remoe Sensng Daa for Green Space Analyss 83 d =- M S () From Eq. (0) and Eq. () we can wre; S MD = () S-M where S and of S and M. 3.3 Algorhm M are respecvely he deermnans The supervsed green space classfcaon s done wh a convenonal wo phase process: ranng ses and mage cell classfcaon. The sample areas for he ranng sep are seleced by human assessors. The oucomes of ranng ses are he specral references of green space area,.e. he waer cachmen and vegeaon areas. To conduc he ranng process, D esmaor s proposed. D s a modfed verson of based on deph funcon gven n Eq. (0). Is calculaon does no requre he nverson of covarance marx, whch s a valuable asse when one deals wh large daa ses. D s a robus esmaor ha has he same breakdown pon as [7]. The algorhm o conduc he ranng phase s as follows: Sep (): Collec mages of he vegeaon area n sze ( a a) pxels based on red-green-blue mulspecral vsual and Normalzed Dfference Vegeaon Index [3]. Le { X, X,..., X n} be he ranng daa se; Sep (): Le H0 { X, X,..., Xn} such as card { H 0 } = h wh n+p+ h =. Sep (3): Compue mean vecor X H and covarance O marx SHO of H O. Sep (4): Compue M = for =,,..., n. ( ) H O ( ) X -X X -X S Sep (5): Sor { M / =,..., n } n decreasng HO M M... M. order, ( ) ( ) ( n) Sep (6): Defne HO { ( ) ( ) ( h) } H = X, X,..., X. X H Sep (7): From Eq. () and Eq. () calculae and S respecvely mean and covarance marx of H. H Sep (8): If Tr ( S H ) Else, f Tr ( SH ) Tr ( SH ) = 0 he process s sopped. repea from Sep o Sep7, unl a soppng rule s sasfed: eher accordng o number of eraons k or by he Tr S - Tr S ε, where dfference ( H,k) ( H,k+) ε s a small consan. Sep (9): Le T VV and S VV be he locaon and covarance marx calculaed a Sep 7. Based on T VV and S VV from Eq. () calculae robus squared dsances d VV, for =,,, n. Sep (0): Deermne he range of each green space specral area as c dvv, c where c s he frs quarle and c s he hrd quarle of d VV, for =,,, n. Fg. 3 dsplays he scaer plo of d VV, for green space specral and Fg. 4 shows he scaer plo of d VV, for green space reference specral nsde he nerval c d c. VV, 4. Resuls 4. Case Sudy Tff formaed mages across years 00 and 00 are used as npus. Daa s capured by sensors havng 7 bands nvolvng he vsble specral, NIR, and MIR. The spaal resoluon of 6 bands (n -5, and n 7) are 30 m, he resoluon of he sxh band s 60 m. The area under nvesgaon s Jakara Provnce covered by coordnae (5 9' " - 6 3' 54")S laude and (06 ' 4" ' 8")E longude. The classfcaon sep s done for Jakara Provnce mages by usng he reference specral from he he ranng sep. Assume ha Y, Y,..., Y M are he pxels of whole Jakara Provnce mage. The dsance dvv, ( Y, T VV ) ( =,,..., M) s calculae. Then each pxel s classfed n one of hree classes: waer O

5 84 Robus Classfcaon of Remoe Sensng Daa for Green Space Analyss Table Percenages of green space areas of Jakara on years 00 and 00. Green space area Year aer cachemen area Vegeaon area Toal %.096% 0.57% %.55%.46% Fg. 3 Scaer plo of green space specral. Fg. 5 Jakara pxels classfcaon on 00. Vegeaon area green color; waer cachmen area yellow color; mpervous area grey color. Fg. 4 Scaer plo of green space reference specral. cachmen area, vegeaon area and mpervous area. The mpervous area s defned as surface mpenerable by waer ncludng sde walks, srees, hghways, parkng los and roofops. Observaon Y s classfed as mpervous area f dvv, ( Y, T VV ) s no n he c;c. nerval [ ] Fgs. 5 and 6 dsplay Jakara pxels classfcaon on he years 00 and 00, respecvely. Vegeaon area s labeled wh green color, waer cachmen area s colored n yellow, and mpervous area s presened wh grey color. On year 00, he percenage of Jakara green space was around 0.569%. I was ncreased up o.4568% on year 00. Table shows percenages of green space areas on years 00 and 00. aer cachmen area on year 00 s sgnfcanly greaer han on 00. The bgges ncrease has happened a Jakara Halm Perdana Kusuma dsrc. Fg. 7 shows land use changes. The blue color Fg. 6 Jakara pxels classfcaon on 00. Vegeaon area green color; waer cachmen area yellow color; mpervous area grey color. represens ncreased waer cachmen area and he red color represens decreasng one. Jakara Halm Perdana Kusuma dsrc s rounded by he whe crcle. 4. Vsualzaon of Area Fg. 8 shows real vsual of Jakara Halm Perdana Kusuma borough afer foresaon and reforesaon by Google Earh. The governmen of Specal Capal

6 Robus Classfcaon of Remoe Sensng Daa for Green Space Analyss 85 projec budge was sgnfcanly ncreased and he Governor s offce deermned also specal rules for he managemen and he mplemenaon of proeced area polces. For furher nformaon on specal rules general program, we refer he reader o auhenc offcal documen The Specal Rules Capal Regonal Dsrc Jakara Provnce Number 8 of 007, [4]. 4.3 Comparsons of Compuaonal Tmes n Tranng Process Fg. 7 Change vegeaon area of Jakara, durng perod 00-00: ncreased waer cachmen area blue color; decreased waer cachmen area red color. Fg. 8 Jakara Halm Perdana Kusuma dsrc afer foresaon and reforesaon by Google Earh on 0. The D s an effcen esmaor for classfcaon of large remoe sensng daa. Fg. 9 shows graphcal represenaon of mes o esmae green space specral reference n ranng phase for and D esmaors. D has sgnfcanly lower compuaon me han. I s neresng o noe ha larger s he daa se greaer s he dfference n calculaon me beween and D. Compuaons were operaed by MATLAB 8.00 n an Inel Core 7 CPU RAM 4.00 GB processor. 5. Remarks M The advanage of as a deph measure s ha does no requre any marx nverson n s compuaon. Is calculaon only needs he compuaon of he deermnan of a symmerc marx. The modfed mnmum vecor varance wh deph funcon, D s an effcen and effecve robus esmaor ha should be consdered for classfcaon of large daa ses. The emprcal resuls provde srong evdence ha D s able o reduce sgnfcanly compuaonal me n ranng sep and has a hgh breakdown pon. References Fg. 9 Compuaon me n ranng process for and D esmaors. Regon of Jakara and s former Governors durng he perod from year 000 ll year 008 made sgnfcan effors o repar and develop Jakara. The green land [] H. Bagan, Y. Yamagaa, Landsa analyss of urban growh: How Tokyo became he world s larges megacy durng he las 40 years, Remoe Sensng of Envronmen 7 (0) 0-. [] M.A. Djauhar, A robus esmaon of locaon and scaer, Malaysa Journal of Mahemacal Scences () (008) -4.

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