USING IMAGE STATISTICS FOR AUTOMATED QUALITY ASSESSMENT OF URBAN GEOSPATIAL DATA

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1 USIG IMAGE SAISICS FOR AUOMAED QUALIY ASSESSME OF URBA GEOSPAIAL DAA WGoemn, LMrtnez-Fonte, RBellens, SGutm Dept elecommuncton nd Informton Processng, Ghent Unversty StPetersneuwstrt, B-9000 Gent, Belgum Unversty of Ghent KEY WORDS: Qulty ssessment, rdge detecton, performnce chrcterzton, rod extrcton, sptl ccurcy, GIS ABSRAC: In ths pper, frmework s proposed to ssess the qulty of urbn geosptl dt usng mge nformton An mportnt spect s the emphss on ccurcy nd relblty of the system he qulty of the mge nformton s quntfed by chrcterzng the rdge detecton performnce n terms of detecton rte Bsed on sttstcs of typcl rod nd ts mmedte surroundngs, predcton of the detecton performnce s mde nd the prmeter set for the optml performnce of the rdge detecton s derved he predcton s used to defne dsplcement qulty mesure Experments were conducted on IKOOS pnchromtc nd Quckbrd multspectrl stellte mges IRODUCIO Wthn the feld of geogrphc nformton systems, mor chllenge s the contnuous ssessment nd control of the qulty of the sptl dt he rpd growng number of sources of geosptl dt, rngng from hgh-resoluton stellte nd rborne sensors, GPS, nd dervtve geosptl products, poses severe problems for ntegrtng dt hs cn be especlly dffcult n n urbn or suburbn context, where the densty nd vrety of observed structures s very hgh Content provders fce the problem of contnuously ensurng tht the nformton they produce s relble, ccurte nd upto-dte Integrty constrnts re ble to resolve certn ssues n the dt, lke vld ttrbute vlues or reltonshps between dt obects he mn ssue s however the consstency of the dt wth respect to the current "rel-world" stuton Prt of ths problem s hndled usng mge nterpretton from erl photos nd very-hgh-resoluton stellte mges Although ths s stll mnly mnul process performed by humn opertors, utomted detecton of chnge nd nomles n the exstng dtbses usng mge nformton cn form n essentl tool to support qulty control nd mntennce of sptl nformton here re severl stndrds for sptl dt qulty t the ntonl, regonl nd nterntonl levels (FGDC, 995; ASPRS, 990; ISO, 999) In vew of tht, components of the qulty of sptl dt re defned, whch nclude postonl ccurcy, ttrbute ccurcy, logcl consstency, completeness, nd lnege Snce the postonl ccurcy component nd the completeness re the most relted components to ths study, the other three components of the sptl dt qulty re ntroduced shortly frst Attrbute ccurcy, the second component of qulty of sptl dt ddresses the qulty of the chrcterstcs of sptl dt nd how well tht mtches relty Logcl consstency s defned s the fdelty of reltonshps descrbed by the dt structure he lnege of dtbse ncludes reference to source mterls, dt collecton procedures, nd pre-processng ncludng geometrc trnsformtons ppled to the sptl dt Completeness refers to mppng rules ppled n equl wy to ll dt nd s sometmes referred to s exhustveness It dentfes gps n the dt progresson nd ndctes whether mssng vlues hve been encountered he Sptl Dt rnsfer Stndrd (SDS) dentfes four methods for ssessng the postonl ccurcy of dgtl dtset hese nclude deductve estmte, nternl evdence, comprson to source nd comprson to ndependent source of hgher ccurcy Deductve estmte s the prctcl estmte of errors n the source of sptl dt ncludng the ssumptons mde bout error propgton Internl evdence refers to ll possble sttstcs or dustments tht my be used on the sptl dt Comprson to the source mens comprng the derved sptl dt wth the orgnl source Among these sptl dt qulty stndrds, t s notced tht they ll ponted out tht comprson to n ndependent source of hgher ccurcy s the preferred method for ssessng postonl ccurcy of dgtl dtset (USGS, 999) Whle stndrd prctce stll reles on comprng control ponts, current pplctons put strcter demnds on shpe fdelty nd reltve ccurcy hs mens tht the postonl nd the geometrcl qulty of ther representtons should not depend only on the ndvdul ponts, whch re prt of ts representton, but on the nterreltonshps nd precse portrt of ll these ponts In the lterture, there s lttle publshed on how one cn verfy the shpe of lner dt set (eg rod network dt set) by nother set (of hgher ccurcy) Rmrez (000) ntroduced four postonl qulty mesures to express the smlrty between two lne presenttons: the generlzton fctor, the dstorton fctor, the bs fctor nd the fuzzness fctor he frst three qulty mesures bsclly use the segment lengths mesured long the two correspondng lne representtons to express n some wy ther resemblnce he lst mesure uses only the end ponts of the two lne representtons Another pproch for the ssessment of postonl qulty of lner fetures of prtculr nterest cn be found n (Goodchld nd Hunter, 997) nd (vete nd Lngs, 999) he two pproches use buffer overly concept he two lnes both get buffer t dstnce r By comprng the re of the dfferent zones, one s ble to clculte the verge dsplcement, the oscllton of the lnes nd n ndcton of the sptl bs hese qulty mesures re bsed on sttstcs, reltvely nsenstve to outlers nd do not requre mtchng of ponts between representtons

2 Fgure : Left: Rdge detecton result n stellte mge Rght: Correspondng rod vector dt However, the mn queston tht s ddressed here, s how system for qulty ssessment cn mke optml use of mge derved nformton, whch nherently s nccurte nd ncomplete he qulty mesures n the lterture re devsed to compre vector dt nd do not tke nto ccount the errors tht cn occur n mge derved nformton In our work, we explore wht sttements cn be mde to compre mge nd vector nformton Becuse t s dffcult to gurntee consstent qulty of mge nformton on n obect level, we focus on mkng relble sttements on regon level By chrcterzng the propertes of regons, qulty cn be descrbed n sttstcl sense nsted of usng comprson of ndvdul obects Whle ths somehow relxes the demnd for complete mge descrpton, t stll remns vtl to chrcterze the detecton n terms of ccurcy nd completeness Fg shows comprson between mge nd vector nformton Shdow, occluson nd vrety n ppernce ll gve rse to frgmented nd mprecse descrpton of the mge content For sttstc lke BOS to mke sense, the performnce of the detecton needs to be quntfed (e sptl ccurcy, number of flse segments, men true nd flse segment length) Wthout such performnce chrcterzton t becomes dffcult to mp the relblty of qulty mesures In next secton, we descrbe the rdge extrcton for rod detecton Secton 3 gves detls on the methodology for chrcterzng the performnce bsed on error propgton Secton dels wth the qulty ssessment of rod vector dt, bsed on mge nformton Secton 5 shows expermentl results performed on very-hgh-resoluton stellte mges Secton concludes the pper wth bref dscusson RIDGE DEECIO If we look t the ntensty mge s terrn model, lnes cn be dentfed s nrrow vlleys n the ntensty mge In (Steger, 998), dfferent pproches to lne detecton re revewed In ths work, lne detecton s performed bsed on polynoml nterpolton to determne pxels belongng to rod structures n the mge, the fcet model (Hrlck, 983) hs s stndrd method for rdge detecton he mge s regrded s functon I(, ) Lnes re detected s rdges nd rvnes n ths functon by loclly pproxmtng the mge functon by ts second order ylor polynoml he polynoml s used to pproxmte frst nd second order dervtves of the mge functon n ech pxel he drecton of the lne cn be determned from the Hessn mtrx of the ylor polynoml he grdent nd curvture nformton n ech pxel re used to clssfy pxel n number of topologcl clsses bsed on ther sgn or mgntude Lne ponts re mnly chrcterzed by hgh second drectonl dervtve, e hgh curvture perpendculr to the lne drecton he clculton of the prtl dervtves cn be done n vrous wys he fcet model determnes lest squres ft of polynoml F to the mge dt I over wndow of sze w wth wndow sze w he orgn s chosen n the centrl pxel of the wndow he vlue of the polynoml F n pxel (, ) s gven by: F + (,, ) wth m m () [ ] [ ] 3 5 he fcet model serches the lest-squres soluton, gven the mge dt x contnng the ntensty vlue I(, ) n ech pxel (, ): rgmn M x r ( ) wth r( ) M x () R x [ I(, ) I(, ] R ) x hs leds to the lner system M M M x wth the soluton 0 gven by 0 (M M) M x he mtrx M s ndependent of the poston of the wndow wthn the mge, menng tht the clculton of (M M) M needs to be performed only once for the processng of n mge wth fxed wndow sze w On the bss of the prmeters of the nterpolted surfce F, the grdent nd Hessn n certn pxel cn be clculted In our model we re only nterested n the grdent nd the Hessn n the centrl pxel of the wndow (e 0) I grdent( I) x I y I I Hessn (I) x x y I I 5 x y y 3 ERROR AALYSIS We wsh to gve more quntttve nlyss of the performnce of rdge detecton More specfclly, we wsh to be ble to predct the performnce of the detector for gven dtset nd the ccordng prmeter set tht gves optml results For ths, we nlyze the nfluence tht perturbtons on the ntensty vlues hve on the estmton of the prmeters by usng error propgton (Hrlck, 99) Addtve rndom perturbtons re ssumed on the nput x nd the perturbtons re descrbed by the covrnce mtrx x he propgton of the error on the nput x to the estmted prmeters s gven by: (3)

3 x x + x, +, ( M M ) M xm ( M M ) () he mtrx (M M) M cn be worked out to closed expresson Due to the lner system, the error propgton of x on s only dependent on the wndow sze w nd not on the nput ntensty vlues (nd consequently ndependent of the observed perturbed mge structure) For uncorrelted nose wth vrnce, Eq() smplfes to θ (M M) snce n ths cse x I However, n ths work, the generl cse s followed he prmeter covrnce mtrx θ llows estmtng the vrnce on the detected grdent nd curvture of the rdge detector he grdent mgntude nd egenvlues of the Hessn re gven by: G g, λ + ± he vrnce on these mesurements up to the frst order s gven by G G G Σθ λ λ λ Σ θ In combnton wth Eq(), ths gves the relton between the perturbtons on the mge dt nd the perturbtons on the detecton mesurements G nd hs relton llows estmtng the expected performnce of the detector for gven prmeter set n terms of detecton rte he bsc rdge detector opertes by settng threshold t on the frst egenvlue of the Hessn Pxels tht exceed ths threshold re selected s rdge pxels o predct the performnce of the detector, the egenvlue s regrded s stochstc vrble usng Gussn dstrbuton wth vrnce he probblty p( >t ) expresses when the curvture of pxel exceeds t hs dstrbuton s gven by the survvl functon (e the complement of the cumultve densty functon) of the Gussn: ( λ λ ) λ > λ λ π t ( λ ) p t e d erf λ λ λ Gven the survvl functon, clculted wth the pproprte sttstcs for the rod, predcton of the detecton performnce cn be mde n terms of true postve nd flse negtve detecton In ddton, f sttstcs for the nose structures n the surroundngs of rod (eg buldngs, trees) re mesured, predcton of the flse postve nd true negtve detecton cn be mde (5) () (7) QUALIY ASSESSME When dgtzng fetures, one lwys ntroduces uncertnty on the sptl ccurcy of the dgtzed representton becuse of problems wth mesurng methods, frmes of geodetc reference nd feture defntons In order to ssess the postonl ccurcy of feture s dgtl representton, one cn compre t s locton wth one derved from source wth hgher ccurcy It s ssumed tht the ccurcy of the reference source s suffcently hgh, such tht the dfference between t nd the truth cn be gnored he comprson results n some qulty metrcs, whch re property of the tested source only Buffer overly sttstcs In the lterture, (Goodchld nd Hunter, 997) nd (vete nd Lngs, 999) use buffer overly concept tht dffers from other methods, such s (Rmrez, 000), n tht t s bsed on sttstcs nd doesn t need correspondence between the two lner representtons In ths method, the two lnes both get buffer t dstnce r, see Fg By comprng the re of the dfferent zones (nsde both Q nd X, nsde Q outsde X,), one s ble to clculte the verge dsplcement, the oscllton of the lnes nd n ndcton of the sptl bs Fgure : he buffer overly sttstcs method re( XB nsde QB) AvgDsplcement( X ) π b (8) re( XB) In Fg 3, typcl exmple of the verge dsplcement n relton to the buffer sze s gven, bsed on Eq(8) he grph must be expected to ncrese stedly wth ncresng buffer sze untl t reches the verge dsplcement of the lne dt set, then the grph should strt to fltten out he shpe of the grph therefore gves n ndcton of the verge dsplcement Fgure 3: he verge dsplcement rt buffer sze here re few remrks to ths pproch he results re reported n the form of tble or grph, whch s dffcult to nterpret nd to hndle becuse there s no quntttve expresson of the qulty vlble whch cn be used for further decson mkng ext, the buffer overly technque requres complete representton of the lner fetures n both dt sets Here, qulty ssessment of rod vector dt s performed usng mge nformton, whch s the result of rdge extrcton procedure, contnng certn degree of frgmentton ext to ths frgmentton, nose wll be

4 present nd should be, together wth the frgmentton, ccounted for when constructng the qulty mesures Frgmented rdge detecton D Fgure : Rdge extrcton result nd buffered vector dt n overly he exmple n Fg 3 gves the mpresson tht the rod vector dt hs n verge dsplcement between 50 nd 00 meters, wheres the experment ws conducted usng vector dt mnully plotted over the rods from Fg An verge dsplcement of less thn 0 meters s expected, provng the nfluence of the nose nd the frgmentton from the rdge detecton on the qulty mesure, whch s not relble nymore ew pproch Bsed on prevous remrks, we propose new qulty mesure whch tkes nto ccount these shortcomngs Our gol s to construct mesure whch ndctes how much the rod locton descrbed by the vector dt devtes from the rel world stuton whch s represented by the mge nformton Fg shows us rdge extrcton result used s reference source to verfy the rod vector dt he method s n tertve process wth ncresng buffer sze, consstng out of the followng steps: Crete buffer RB of sze r round the rod vector R Clculte the overlp re O between the buffered vector dt RB nd the rod detecton dt D Subtrct the prevous (smlle buffer sze overlp re from O ormlze the result by dvdng ths dfference by the ncrese n re of the buffer RB hs procedure trnsltes n the normlzed dfferentl overlp re F(: re( D RB) F( re( RB) B r B r Rod vector dt R wth buffer RB ose re( D RB) re( RB) B r B r A result of ths clculton s gven n Fg 5 o nterpret ths fgure, we mke predcton of the expected nose level nd detecton rte bsed on typcl rod smple, see 5 We cn now dstngush three regons n the fgure: he upper regon from one to the predcted sgnl level: due to ncompleteness of the rdge detecton the grph F( wll never rse bove the predcted sgnl level (9) he mddle regon from the mxmum sgnl level to the predcted nose level: frcton of the vlue of F( s result from overlp wth rod sgnl he lower regon under the nose level: from ths threshold we cnnot know whether the vlue of F( s due to nose or to rod sgnl, nd must be dsregrded he drk lne represents the del cse of rod vector perfectly correspondng to the mddle of the rod n the mge For ll buffer szes smller thn the wdth of the rod n the mge, the normlzed dfferentl overlp re F( s expected to be the predcted detecton performnce When the buffer exceeds the rod wdth, F( wll fll bck to the predcted nose level he grph n lght gry shows the cse of smll shft between the locton of the rod n the test source nd the reference source he grph wll now be chrcterzed by some ntervls locted bove the nose level, whch ndctes overlp wth rod sgnl t dstnce r hs dstnce wll be n underestmton of the true dstnce becuse only the shortest pth between the two rod representtons s consdered usng these buffers Idel F( Fgure 5: F( n relton to the buffer sze Blck: Idel cse Gry: ypcl exmple Bsed on ths nterpretton of the fgure, we defne the verge dsplcement of the rod vector dt s the verge buffer length of the gry flled regon n Fg 5, whch trnsltes to: F (' rdr AvgDsplcement, F (' dr F( oselevel, F( > ose Level F (' 0, F( < ose Level 5 EXPERIMES Incompleteness Sgnl ose (0) o test the method n prctce, we pply the expressons derved n the prevous sectons Frst we ll tke look t the performnce of the rod extrcton then the optml performnce wll be derved, nd fnlly qulty ssessment of the lner sptl dt set s conducted usng the dpted BOS he experments presented here, were conducted on zones of n IKOOS pnchromtc nd Quckbrd multspectrl stellte mge, dsplyng the cty of Ghent, Belgum A number of smll mge subsets hve been selected contnng strght exmples of typcl rods hese subsets hve been mnully rotted untl ech rod s postoned prllel to the vertcl xs Fg shows the selected mge subsets referenced R to R 5

5 () R (b) R (c) R 3 (d) R (e) R 5 equvlent to rod whch s completely detected wth no detecton of nosy structures (e perfect detecton) he pont on the curve closest to perfect detecton defnes the optml threshold t for the gven wndow sze In Fg 7, the emprcl nd predcted ROC curves for rod type R re plotted for wndow sze w nd w 3 he full curve shows the emprcl plot, where detected nd flsely detected rod pxels hve been mesured on the rod xs nd the poston x nose he dshed curve shows the predcted plot usng the covrnce mtrces mesured n these postons he smple pont closest to the upper rght corner defnes the optml threshold for ech wndow sze he dfference between the emprcl nd predcted ROC curve for gven wndow sze s mnly due to less ccurte estmton of the true nose survvl functon Fgure : Rod dt sub set 5 Performnce chrcterzton he poston x rod of the centrl xs of the rod s used to mesure the covrnce mtrx Σ x nd the men curvture E[λ ], by smplng x nd λ for gven wndow sze w Usng Eq (7) we cn mke predcton of the expected detecton rte for tht type of rod hs equton gves rse to dstrbuton tht only gves nformton bout the useful sgnl, e the rod tht needs to be detected hs gves n upper bound to the threshold t A lower bound s defned by the propertes of the nose, e undesred structures n the mge whch re flsely detected If the threshold s chosen too low, the detecton of these flse negtves wll ncrese he performnce of the detecton for ech threshold cn be summrzed n Recever Opertng Chrcterstc (ROC) curve Senstvty nd specfcty re defned s follows: P senstvt y P + FP specfcty detected rod pxels rod length detected nose pxels () P + FP nose length where {P,,F, FP} stnds for true postve etc rue postves nd flse negtves re mesured on the rod where x s x x rod nd re normlzed usng the totl rod length n the mge rue negtves nd flse postves re mesured long vertcl xs x x nose representtve for the nosy structures n the vcnty of the rod he poston of ths xs s determned utomtclly by tkng the poston of the second lrgest pek n the men curvture profle of the rod nd ts vcnty ormlston s performed usng the totl length of the xs, whch n ths cse equls the totl rod length Fg 8 llustrtes the poston x x rod nd x x nose for rod type R he reson for ths pproch s tht t cn be menngful to chrcterze flse detectons n the drect surroundngs of rod Snce for some pplctons rough regstrton between mge nd GIS dt s known, regons-of-nterest cn be defned where rods re expected n the mge Rod detecton n ths cse should then be med t dstngushng the useful sgnl from nose n the mmedte surroundngs In our exmple we mesure the nose sttstcs of the structures besde the rod nd use ths to model the expected flsely detected nose pxels usng Eq(7) In ths cse Σ x nd E[λ ] re mesured for x x nose for the sme wndow sze w s the sgnl Usng the ROC curve, the optml performnce for ths curve s defned s the pont on the curve closest to the upper rght corner (, ) he upper rght corner s specfcty predcted w emprcl w3 predcted w3 emprcl w w 3 t 075 w t senstvty Fgure 7: Emprcl nd predcted ROC curves for rod type R for wndow sze w nd w 3 he emprcl nd predcted pont of optml performnce re mrked by the rrows 5 Spectrl bnd qulty he performnce chrcterzton of the prevous secton cn be used to mke n ssessment of the qulty of dfferent mge sources for rod extrcton purposes In ble rod smple ws extrcted from the spectrl bnds of Quckbrd mge he qulty metrc used s the dstnce to the perfect detecton, mesured n the ROC curves From ths tble we conclude tht the blue bnd s the most nterestng for rod extrcton, nd the pnchromtc bnd performs the worst hs s explned by the ppernce of the rod n the severl bnds In the blue, green nd red bnd we fnd drk rods surrounded by hgher ntensty pxels, wheres n the IR-bnd we fnd the opposte Integrtng the ntensty over the dfferent bnds wll result n lower contrst Rod sttstcs Spectrl Bnd rue rod pxel Flse rod Dst pxel Pn 77% 9% 037 Blue 9% % 0 Green 9% 7% 07 Red 8% 3% 033 IR 83% % 07 ble Rdge detector performnce of mult spectrl stellte mge

6 53 GIS qulty ssessment o test the dsplcement qulty mesure, we ppled the proposed methodology to Quckbrd test zone, dsplyng suburbn prt of Ghent, shown n Fg he rod vector dt correspondng to ths regon ws mnully plotted nd rtfclly shfted to ntroduce some deformtons he experment ws performed two tmes wth dfferent detector prmeter set Rod sttstcs Qulty Mesure Shft P FP Dsp 0 m m m m m m m m ble Results showng the nfluence of the dsplcement between vector dt nd mge dt on the dsplcement qulty mesure From ble, t s cler there s lwys n underestmton of the dsplcement, except for the frst nd ffth mesurement, whch s due to n occsonlly hgher nose level thn predcted he underestmton cn be explned by consderng shft of the vector dt long the drecton of the rod In tht cse no mentonble dsplcement wll be detected usng buffer overly sttstcs Fnlly, only the shortest dstnce between rod vector dt nd mge dt s consdered usng ths technque COCLUSIO Wheres n other reserch the mn focus s on dt producton, n ths pper we focus on how mge nformton cn be used to ssess the qulty of n lredy exstng rod vector dt bse In the lterture, only few technques re presented to verfy lner vector dt set by comprng wth nother Usng buffer overly sttstcs, we cn mke some qulty sttements bout the tested rod vector dt wthout the need of fndng n exct correspondence between the tested source nd the reference source But the need for complete representton of the rod vector dt s dsdvntge when usng mge nformton, becuse the rdge detecton result s nherently bound to frgmentton nd mscodng herefore, we propose frmework whch sets up the optml prmeters for the rdge detecton nd mkes predcton bout the frgmentton nd the nose n the detecton result Bsed on these predctons, dsplcement qulty mesure s defned whch quntttvely expresses the dsplcement of the tested source compred to the mge source () (b) (c) Fgure 8: Detected result on rod type R usng optml prmeter settngs he orgnl mge shows the poston x x rod nd x x nose () orgnl (b) predcted (c) emprcl 7 REFERECES References from Journls: Goodchld FM nd Hunter J Gry, A smple postonl ccurcy mesure for lner fetures Hrlck, R, 983, Wtson, L nd Lffey,, he topogrphc prml sketch, Interntonl Journl of Robotcs Reserch ():50 7 Hrlck, R, 99, Propgtng Covrnce n Computer Vson, Interntonl Journl on Pttern Recognton nd Artfcl Intellgence 0(5):5 57 Rmrez, J 000, Qulty Evluton of Lner Fetures, A whte pper submtted to IMA Steger, C, 998, An unbsed detector of curvlner structures, IEEE rnsctons on Pttern Anlyss Mchne Intellgence 0():3 5 References from Other Lterture: Amercn Socety for Photogrmmetry nd Remote Sensng (ASPRS) 990, Accurcy Stndrds for Lrge-Scle Mps, Photogrmmetrc Engneerng nd Remote Sensng, 5 (7), pp Federl Geogrphc Dt Commttee (FGDC) 995, Content Stndrds for Dgtl Geosptl Metdt Workbook, USA Federl Geogrphc Dt Commttee (FGDC) 998, A common set of termnology nd defntons for the documentton of dgtl geo-sptl dt, Content Stndrd for Dgtl Geosptl Metdt (CSDGM), USA Interntonl Stndrd Orgnzton (ISO) 999, ISO-50: Geogrphc Informton, Prt 3: Qulty prncples, ISO/C, Doc o 78 References from webstes: Unted Sttes Geologcl Survey (USGS) 999, tonl Mp Accurcy Stndrds Fct Sheet FS-7-99, (09/5/00)