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Building Extraction from Digital Elevation Model

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(1)Building Extraction from Digital Elevation Model Mathias Ortner, Xavier Descombes, Josiane Zerubia. To cite this version: Mathias Ortner, Xavier Descombes, Josiane Zerubia. Building Extraction from Digital Elevation Model. RR-4517, INRIA. 2002. �inria-00072071�. HAL Id: inria-00072071 https://hal.inria.fr/inria-00072071 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Building Extraction from Digital Elevation Model Mathias Ortner — Xavier Descombes — Josiane Zerubia. N° 4517 Juillet 2002. ISSN 0249-6399. ISRN INRIA/RR--4517--FR+ENG. THÈME 3. apport de recherche.

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(158)      C <D. C UD. C U. *D. ‡gVm,otfh]VdXOcK]0c_aŠqbace‹ 7k c‹ŒniXžVbacKgi]  fŒo W+fhoto}fŒ]qnVm|cKIgifh]`_

(159) Vb}g‡dXoto

(160) fhoE]Vg_EpVf k btXd_a‹¯¬ W+XceotŠqbacežV‹hXemªce]Vpjf¯_ao€WYXQceo}ŠVbacežqfŒ‹hfh_^¬jfŒo€pVX«V]VXp¦_tSVbtgiŠqniS?_tSVXWYXQcotŠVbtcežVfh‹Œf¯_^¬ geŸ ceqV‹ŒfhdQcx_afhgi]Vo   "§ š X{dQc‹Œ‹  _aSVX{otW+ce‹h‹hXo}_ 7k c‹ŒniXžVbac¨Ÿ btgeW  o}ŠVdlS _aSVc_ _aSVXotX‘ceqV‹ŒfhdQcx_afhgi]Vo¨ceb}X°WYXQceo}ŠVbacžV‹ŒX§  _lc · Xo¨f¯_ao|¤ce‹hŠVXo(fŒ]     § š X°dce‹h‹ " B”•2–  “  •  _aSVXVbtgež0cežVfh‹Œf¯_^¬?W+XceotŠqbtXfh]VpVŠqdXpOž`¬  gi. ]   §,z _aSVXgk btXW¢nifh¤eX] fŒ]  Mƒ  dgiWYV‹ŒX_aXo€_aSqXqbtX¤=fhgiŠVo{pVX«V]Vfh_tfŒge]Vo².  

(161)     #       2  #      – 

(162) . .    

(163)    . !   .  

(164) 

(165)  #"#   & " B”•2–  “  • %” $   &    •   "   ” — . . . C FD. &C. . . . . D. . . . .      . . . . . .  . . . . .     . . 

(166)  #  

(167) '2     

(168)      #" <C C>KD] NNNM CG DD 0#  (   

(169) 

(170)  #  C>K NNNO )G<D      #  

(171)  *G)+,   NNNO       

(172)   ! - . RTSVX±WYgioy_4ŸBceWYgiŠVoIgefŒ]`_Vbtg=dXoto„fho_tSVX'ugifŒo}otgi]Igifh]`_„Vb}g‡dXo}omipVX«0]VXpYceoŸ gi‹h‹hg;© ². %'&)(*%'+.

(173) †.   

(174)   

(175) # . . •.   . .

(176)   #   !   # "  

(177)       2    #     B”Q”   – ˜  ””        •   ”  •     $        2#   

(178)              0#!

(179)

(180)      #  

(181)        #       '2      #  

(182)   )      

(183)         

(184)      

(185)  

(186)    . LC1N,D. C FD. C FD. >KM NNN. C >KD]NNNNO. C. D. RTSVXOpVfŒoy_ab}fŒžVŠ‡_afhgi] geŸotŠqdlS c#IgefŒ]`_ Vbtg=dXoto

(187) ©,fh‹Œ‹¨ž7XOpVX]Vg_aXp ž`¬  "§

(188) €]VpqXb otgiWYXceoto}ŠVWYq_afhgi]Vom4f¯_fhoIgio}otfhžV‹hX+_tg?dgi]Vo}_tbtŠVd_7gifh]`_qbtg=dXo}otXo©,SVgio}X ‹ŒcQ©,oceb}X pVX«0]qXpjž`¬

(189) pqX]Vo}fh_tfŒXo(cen`cfŒ]Voy_T_aSVX)pVfho}_tbtfhžVŠq_tfŒgi]?geŸ4c+ugifhototge]jVb}g‡dXoto§ =fŒ]VdX©XcebtX¨©gib · fh]Vn+gi] ®m0geŠVb'Ÿ baceWYX©±gib · ¤iXbtf¯«0Xo{_aSVXotXceoto}ŠVWYq_afhgi]Vo§ % —V&– %  " • – ˜  ””  ” š X¨©±ce]`_€_tg+pqXQce‹ ©,f¯_aS btXd_lce]qni‹ŒXo²v_tSVXo}0cedX©XcbtX¨©±geb · fŒ]qngi] otSqgiŠV‹hpj]Vge_{ž7X 5§ €g2©X¤iXbm žVŠ‡_  ©,SVXbt X    ©±X)pVg‘]Vg_,ŠVotX)c‘7gifŒ]`_,Vb}g‡dXo}o{pqX«0]VXp?ge] TmqžVŠq_{c°W+ceb · Xp IgefŒ]`_,Vb}g‡dXoto,gi] ©,fh_tS´fh_|Wcb · o¨‹Œf¯¤=fŒ]qn

(190) fŒ]   5§¨RTS0c_¨WYXQc]Vo|_aSVc_ _aSVX(7gifh]`_TVbtg=dXoto}Xo,©±X)ceb}X(‹hg‡g · fh]VnYc_'cebtX¨ž7ge_aS Igifh]`_,Vbtg=dXoto}Xo,gi] ce]Vp

(191) gi] ²„_ag‘XQcdlS?7gifh]C_'geŸ ©Xc_t_acedlS c°Wcb · W+cepqX¨geŸce]gibtfhX]`_lcx_afhgi]ªm0c°‹hX]Vn_aS ce]Vp c ©,fŒpq_tSª§   &– '  š gib · fŒ]Vn

(192) ge] 'm ©±X°«Vbto}_(dgi]Vo}fŒpqXb)c W+ceb · Xp­ugifŒo}otgi]OVb}g‡dXo}o¨gi] ce]Vp 'mI©,f¯_aS fŒ]`_aX]Votf¯_^¬#WYXQcotŠVb}X   ©,SVXbtX  fho_aSqX  XžIXotniŠqX

(193) W+XceotŠqbtX

(194) gi] ce]Vp ! ¸fŒo±cVb}giž0cežVfh‹hfh_^¬+pVfho}_tbtfhžVŠq_afhgi]

(195) gi]  § š X€]Vge_t X „_aSVX|pVfŒoy_ab}fŒžVŠ‡_afhgi]EgeŸ _aSVfho{ugifhoto}gi]jVb}g‡dXo}o§ \ _fho · ]qg;©,]¶_aS0c_Y_tSVX?X"‡IXd_lcx_afhgi] geŸ€_aSVX bac]VpVgiW ¤ceb}f~cžV‹ŒX  °ŠV]VpqXb C1N,D. .  . . . U. . . . . .  . . ;. ;. !. . ;. ;.  '/),+

(196) '/01 34*),+ 347 a. '/*),+ '/017/.  34*),+c 3 01. a. . . . C. C1N,D. I. 6DOCN5D. UCN5D. C1N,D. C . ()(+* ,.-0/213. D. CN5D.

(197) eŽ.  

(198) . fŒo)²       RTSVfŒoVbtg=dXoto°©,fh‹Œ‹žIXgiŠVbb}XŸ XbtX]qdX

(199) Vb}g‡dXoto§ š XEcebtXnigifh]Vnj_ag?pVX«V]VXE_aSVX pVfŒo k _abtfhžVŠq_tfŒge]   |geŸ±geŠVb¨IgefŒ]`_)Vb}g‡dXoto)geŸfh]C_tXb}Xo}_ ŠVo}fŒ]qn _tSVXY€cpVgi]‡k  f · g=pq¬=W pVXb}fh¤c_tfh¤eX²  + 

(200)  >. C . D1BC. . 6DOC . D(. UC. D. FCN5D. .   C *D . +. . C *D. {Xb}Xem  fŒovc(o}dQce‹hX'ŸBced_agib§ ‡ŠVdlS+c(7gifh]C_„Vbtg=dXoto  ceo4_tSVXToaceWYXTpVfho}_tbtfhžVŠq_tfŒgi]‘_tS0ce] c 7gifh]C_Vb}g‡dXotopVX«0]VXp žC¬ im_aSVX+oaceWYXYŸ ŠV]Vd_afhgi] ¨ce]qp®ce]­ŠV]VpVXbt‹¯¬=fŒ]Vn ugifhoto}gi]

(201) Vbtg=dXoto'gŸ fŒ]`_tX]Vo}fh_^¬   ! §v\ _fho_aSqX]

(202) X CŠVf¯¤ce‹hX]`_'_agWŠV‹¯_afhV‹¯¬ Xf¯_aSVXb´ž`¬Ece]`¬+ŸBced_tgibLgib_tSVX|ŠV]qpVXb}‹h¬=fh]VnYfŒ]`_aX]Votf¯_^¬EWYXceotŠVb}X(ž`¬_tSVX|otceWYX|ŸBced_agib§ RTSVX?ŠqotŠ0ce‹'©±cQ¬ geŸ€pVX«0]qfŒ]VnKpVX]qotf¯_afhXo gŸ|7gifh]C_+Vb}g‡dXo}ofho+_tg´©,btf¯_aX_aSVXpVX]Votf¯_^¬ ŠV]VpVXb{f¯_ao  fŒžqžVoTŸ gibtW›² . . C1N,D. C. . &. . -DCN5D.   

(203) Q. P). IH LK NNN P+. C *D. . . .  

(204). . ©,SVXbtX   ,fho€_tSVXX]VXbtne¬geŸ_aSVXotX_(geŸ40ceby_afhd‹hXo „§±RTSVX‹Œg2©Xb€_tSVXX]VXbtne¬ems_tSVX W+gebtX+VbtgižVcežV‹hX+_tSVXdgi]q«0neŠVbac_tfŒge]ª§ERTSVXbtXŸ gebtXem_aSVXY«0]0c‹Lneg`ce‹vgeŸ±giŠVb)Ÿ baceWYX©gib · dgi]Vo}fŒoy_ao(fh]?«Vbto}_€žVŠVfh‹hpVfŒ]qn

(205) ce]jX]VXb}ne¬im7_aSVX]?«0]qpVfŒ]qnEdgi]‡«0niŠVbtc_afhgi]Vo,_aS0cx_|WYfh]VfŒWYfX fh_§ ' 1  – &B— š XYceb}X‘pVXQc‹Œfh]Vn©,fh_tS­7gifh]`_ao¨_aS0cx_)btXqbtXo}X]`__aSVXYotSVceIX‘gŸ'c

(206) žVŠVfh‹hpVfŒ]qnV§ š XY©±ce]`_ _ag°fh]`_abtg=pVŠVdX(fh]

(207) giŠVb±WYg=pVX‹7_aSVX · ]Vg2©,‹ŒXpVniX¨©±X|S0cQ¤iX¨gi] _tSVX(ž7XS0cQ¤=fhgib'geŸžVŠqfŒ‹hpVfh]Vnio fŒ] ŠVbtžVce] cebtXceo§ RgYpVg+otgVmV©X)ŠVotXc =_abtceŠVo}o{WYg=pVX‹  otXX  i  ªŸ gebTW+gebtX)pVX_acefh‹Œo  § ¹4fŒb}o}_YgeŸ|ce‹h‹5mv©X · ]qg;©¢_aS0c_YžqŠVfŒ‹hpVfh]VnioYpVgO]Vge_Yg2¤eXbt‹Œceª§#RTSVc_+fŒo°©,S`¬#©X fh]`_ab}gk pVŠVdX)fh]?geŠVbTWYg‡pVX‹c ” 5• ˜ – _tXb}W msco{XWYV‹Œg2¬eXp¦fh] ¯!† c]Vp ¯† A ². ?C *D.  . . .   . . . *),+!#"%$2C*D '  &P)5+!#"$. E C*D. %'&)(*%'+.

(208) ‡†.   

(209)   

(210) #. ,© SVXb}X  ,fho(ce] fh]C_tXniXb|dgiŠV]`_afh]VnEfh]?_tSVXdgi]q«0niŠqbac_tfŒgi]  _tSVX]CŠVWžIXb(geŸ40cefhbto geŸ(b}Xd_ace]Vni‹hXoY_aSVc_+fŒ]`_aXbto}Xd_§& !#"$+fho+c­b}XQce‹,0cebtceWYX_tXbmdQce‹h‹hXp •  • B—& •  –x”  ˜e• § ³ \fŒ]qŸ d& btX!ce#"%ot$ Xo{_tqSVmCX)fhX]C]V_tXXb}btotneX¬d_agfhgiŸ]V_tSVoTX)cbto}X{¬=o}W_tXcWpVX€§ b}XVŠq‹Œo}fh¤eX(otfh]VdX€XQcedlS]VX© fh]`_aXbtotXd_tfŒgi] ³ \otŸfh]V& dX'!#"Ÿ %ge$ b4dgeq]qm«0fŒ]`ni_aŠVXbtbtco}_aXfhdgi_t]VfŒgeo]V©,ovfh_tceSb}XLc€W+‹~ceceb}pqniX'X'c]C_}ŠV_aWbacžId_aXf¯b ¤iX§ ge±ŸsŠ‡7_ gifŒ ]`_tfŒoomi]V_ageSq_X']VXgi]Vb}XW+btnece¬‹ŒfhoadcgižVŠq‹Œ‹ŒXp m X¤egi‹h¤eXfh] Q§ 9E C D. . P)5+. . .  . . c),+. . . c),+. [. [ ;. . . . .   . . RTSVXcfŒW SqXbtXfho,_tgŠqotX)_aSVXdgioy_,Ÿ ŠV]Vd_tfŒge]jpVXotdb}fŒž7XpjžIXŸ gibtXce]Vp_aSqX¡|£¥ fŒ]?ce] X]VXbtne¬E_tXb}W §¸RTSVfho{X]VXbtne¬

(211) fho{nifh¤eX] ž`¬O² 1 ! C D.  . $. & %CP) D. RTSVXp0c_ac°_aXb}W & |S0ceoT_tgY_ac · X)fh]`_agceddgiŠV]`_,_aSVX¨Ÿ gi‹h‹Œg2©,fh]Vn+Igifh]`_ao)² †i§T_aSVX´WYfh]VfhWŠVWYojgŸ & ?o}SVgiŠV‹hp ž7X´btX‹ŒX¤ce]`_?SqgiŠVotXo?ge] _tSVX­¡(£L¥K§,RTSVfho fho X]Vo}ŠVbtXpjž`¬E_tSVX)dgi]Voy_ab}ŠVd_tfŒgi]?geŸ_aSVX)dgeo}_,Ÿ ŠV]Vd_afhgi]ª§ ‡§ & {otSqgiŠV‹hpjž7X CŠVf¯_aX)o}W+g=ge_tS?fh]?gebtpVXb'_agYXQceo}X_tSVX)giq_tfŒWYfQc_tfŒgi] § RTS0c_LfŒo¸©,S`¬im=ŠVotfh]Vn_aSVb}XX{Igio}fh_tfh¤eX€b}XQce‹0]CŠVWžIXbto mC©X{Vbtgi7gio}X{_tSVXTŸ gi‹Œ‹hg2©'k fŒ]Vn‘Ÿ ŠV]qd_afhgi] & €‹Œf¯¤=fŒ]qnfh]. 5²  (

(212). f¯Ÿ & f¯Ÿ 4 Ÿ gibc nefh¤eX]®b}Xd_ace]Vni‹hX  ce]qp®cSVXfhniS`_Ÿ ŠV]qd_afhgi] "§ERTSVfhop0c_ac_tXb}W S0ceo žIXX]Ogižq_acefŒ]qXp´ž`¬¦_ab}f~c‹„ce]Vp´Xbtb}gib¨ce]Vp´fho CŠVf¯_aX‘btgežVŠVo}_§\^]OVbtced_tfŒdXemª©X‘ŠVotX°_tSVX . . .

(213) KM . . . .  C ? ]=D(. ()(+* ,.-0/213. C. .  KD] . C ; ;  K/ . ;. . .  KD . . . .     C ? ]=D. . ;. ;. . . YC ? ]=D

(214) . 2)5+. YC ? ]=D. 2)5+. =C1N,D.

(215) i.  

(216) . Ÿ gi‹Œ‹hg2©,fŒ]qn0cbaceWYX_tXb}o². . . 7. .

(217) N  . .

(218) N. ; K. . -. 2*),+. )W . ¨W ¹0gib,cY‹Œg2© ¤egi‹ŒŠqW+Xbacx_aX  fhXe§‹ŒXoto€_tS0ce]-  _aSVXbtXd_lc]Vni‹hXfho,btXqŠV‹Œo}fh¤eXe§ ±Š‡_{_tSVX d‹hgiotXb - fŒoTŸ btgeW - qmV_aSVX)‹hXo}o€b}XVŠV‹hotf¯¤iXfh_,fho  o}W+g=ge_tS _tXbtW¢fŒ]-  §¸RTSVX]ªm0©,SVX] _aSVX,¤igi‹hŠVWYX|btc_aX,fho‹Œceb}niX€X]VgiŠVneSªm=_tSVX{SVgiWYginiX]VXf¯_^¬+bac_tX€c]Vp_tSVX€o}ŠVb}ŸBcdX{bac_tX|ceb}X fŒ]`¤ige‹h¤eXp¦fh] _tSVX¨p0c_acY_tXb}W § RTSVX)otŠVbyŸBcedXbac_tX¨W+c · Xo€žVfhniniXb,otfh‹ŒSVgeŠVX_}_aXo{ž7XWYgib}X¨¤ec‹ŒŠ0cžV‹ŒX§ RTSVX±gi]q‹h¬fhW+7giby_lce]`_0cebacW+X_aXbtovceb}X _tS0c_4otSVgiŠq‹Œp‘c‹h©±cQ¬‡o4žIXLX CŠ0ce‹=_ag#Xb}gVm otfh]VdX‘f¯_(nif¯¤iXo(_aSVX°ceŠq_aSqgibtfXp´Xbtb}gibm Ece]Vp 4§ ce]qp c‹Œ‹hg2© _tgEž7giŠV]Vpj_tSVX X]VXbtne¬geŸ„ce]jgež‡wyXd_Q§'RTSVfho{fŒo{fŒWY7gib}_ace]`_€Ÿ geb{W+c_tSVXW+c_tfŒdce‹btXceotgi]qo|ceo{pVXotdb}fŒž7Xp ‹~c_tXbTfh] _tSVfho{b}X7gib}_§ =

(219) *),+. .  . . N. _*),+. 2),+. R;.

(220) K. 2*),+. . L=

(221) ),+. .  .  . .   

(222)   . . ;.     . . .     . RTSVX‘‹~co}_)o}_tXOgeŸ¸_aSqX‘dgi]Voy_ab}ŠVd_tfŒgi]­geŸ¸_aSqX‘Vbtgi7gio}XpOWYg‡pVX‹„dge]Votfho}_tofh]OŠVotfh]Vnfh]‡k _aXbtced_tfŒge]Vo{ce]Vp_aSVX)p0c_ac°_aXb}W fh]?gi]qX¨X]VXbtne¬e§ š X)dQce‹h‹ ³ Vbt•fhgi b –  m —&   & " _tSVX(0cb}_TgeŸ _tSVX¨X]qXbtn¬EbtX‹~cx_aXp

(223) _tg_aSVX¨fh]`_aXbaced_afhgi]Vo  fhXe§„_tSVX ³  •  – —&   & " _aSVX)X]VXb}ne¬

(224) btX‹~cx_aXp_agY_aSqXpVc_lc°_aXbtWm ³ ce]Vp •    –;—q• – _aSqXdg‡<X +dfhX]`_  ² . . . . ?C*D$. . . #. CPN 1 !.  C. RDMN *),+!#"%$]D. ,© SVXb}X fŒo+_aSVX¦o}WYg‡ge_tSVfh]Vn BŸ ced_agib+_aS0c__aŠV]qXoESVg2© fhW+7giby_lce]`_ _tSVX¦p0cx_lc­_tXb}W fŒo¨¤iXbto}ŠVo_tSVXfh]`_aXbt]0ce‹„«VX‹hpª§ RTVS fho · fh]Vp­geŸ±©XfhniS`_afh]Vn?fŒo)¤iXb}¬OdgeW+WYgi]­fh] fhWcniX Vbtg=dXototfh]VnV§ %'&)(*%'+.

(225) eZ.   

(226)   

(227) #.    T¨.  ]qdXT©±X,S0cQ¤eX€pVX«0]VXp+_tSVX,W+g=pVX‹5m`_aSqXT]VX=_Lo}_tX+dgi]Vo}fŒoy_aoLfŒ]+pVX«0]Vfh]Vnc¨Vb}g‡dXpVŠqbtX _aS0c_{c‹Œ‹hg2©,o{Šqo{_tgY«V]Vp _tSVX)dgi]‡«0niŠVbtc_afhgi]WYfŒ]VfhWYf!fŒ]qn_aSqXX]VXb}ne¬i§ €Xb}Xem±_tSVfhoX]VXb}ne¬ fŒo+btX‹~c_tXp _ag®cOpVX]Votf¯_^¬ gŸ¨cOIgifh]`_ qbtg=dXo}omTo}gK_aSqX?gi‡_afhWc‹ dgi]q«VniŠVbacx_afhgi]fŒoT_aSqXge]VX¨_aS0c_,W+cx‡fhWYf!Xo€_tSVfho{pqX]Vo}fh_^¬e§ RTSVfŒo)S0co¨žIXX]­pVg2©,]Ko}X¤iXbace‹v_tfŒWYXomXot7Xdf~c‹Œ‹¯¬OfŒ]OfhW+ceniX‘Vb}g‡dXoto}fŒ]qn  otXX ¯†im„† ‡m †;Aˆ   § ¥?gio}_YgŸ{_tfŒWYXomLVbtgi7gio}Xp ce‹hnigibtf¯_aSqW+o°cebtX ¥?ge]C_tXk $'cebt‹hgOoaceWYV‹hXb}o+dgiŠVV‹hXp#©,f¯_aS otfhWŠV‹Œc_aXp¦ce]q]VXQce‹hfh]VnV§ š X)S0cQ¤eXpqXdfhpVXpj_ag‘Ÿ gi‹h‹Œg2© _aSVfho,fŒpVXcq§   

(228)         

(229)  

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