The Critical Sets of Lines for Camera Displacement Estimation : A Mixed Euclidean-Projective and Constructive Approach
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Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. The Critical Sets of Lines for Camera Displacement Estimation: A Mixed Euclidean-Projective and Constructive Approach Nassir Navab - Olivier D. Faugeras. N˚ 2305 Juillet 1994. PROGRAMME 4 Robotique, image et vision. ISSN 0249-6399. apport de recherche. 1994.
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(118) DE; 6 2 ;<AV C G{I HF}Kp JL$N M "O/) x{}pDiypH}ilpHypH#vn vlx{k#QPRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P S C GÁU T07p VWgxvlx{k#}L P,PRP,P,PWP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P X C G Y(nuoÈpHiln3x{y{nuHpHoÈpH#Z v P,PRP,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P [ C G q \k vlx{k#?n#}vÀil|}vÀ|}il^ p ]]ilk#o T=vÀk 2 T=x{pDHk#iliypHlfku}pH}Hp_ PRP,P,PRP,PRP,P,PRP,P 8dfB<; 6 AV g =@` :-1¡ a- 6 6#b ?%¡ a- gw }¡ % Au ;
(119) c# % ;<8 6 8edF% aA ¡ 2 ;²% ;]¡# B($ Au 3ih i G{I T07p VWgxvlx{k#}L P,PRP,P,PWP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P+H i GÁ jk#o1p0ilk#ApHivlx{pH k ]-vpDHixvlx{Hn Wx{}pHk PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P+u i G HF}px{}p3Hk#o1{)p lmnpoqPRP,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P+ i G q HF}p0iyp{nwvyx{kulx{ tfp v r(pHpH vpFx{}p0Hk#o1g{)p l}pHs m npo n#}v}pHixvlx{Hn Aypvj2k ]_x{}pHt g*H d8}+ v-2 A/w;<8:-$ B xyv:_ B<;^$ aAC9 B<z82 ;ª% aD 3{ u %¡ a- w ¡w% A#2 ;<cu g% ;
(120) 8 6 8d4% aA?¡ 2 ;ª% ;^¡# BK$ A#K iq G{| jk#o1p0yApHx{n AHn#lpH} P,P,PRP,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P+$ [ ~q G{ G{ 'HF}pÂ{nuRp Wx{FvÀ}p0g{nu}pÂn v x{ VWx v y RPRPKP,PRP,P,PRP,PRP,P,PRP,P+$ [ ~q G{ GÁ K 'HF}pÂ{nuRp Wx{k#}p!2k ]-vÀ}pDHkk#ilgx{}nwvÀpF{n#}pH 7C",72fP,PRP,P+H iq GÁ Y(kuoÈ{)p l\Hk#} p P,P,PWP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,PLw 8d(% aAB<; 6 A ¡ 8 6 z}2 :A 6 /¡ A_g 6 ~ B²% A# 6 % ; wA 6 ~ B!x-$ ;]+ >> C G{I {m#pHt}iln x{0pHzV|}n vlx{k#}(k ]-v}px{}p3Hku}m#il|pH}Hfp g P,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,PLu C GÁ 0iy}pHi(nu:{n#lFk ]-vpx{}p3Hk#}muiy|}pH}Hf p gPRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,PLwq F 4 B<B
(121) :-H % ;
(122) 8 6 8d(% aAB
(123) ; 6 A ¡ 8eDvB
(124) A/mnpo > {5 ; 6 A¡ 8 6 z}2 :A 6 /¡ A_g3¢ 6 :DEA#2 ;]¡u B^A/- DvB
(125) A > XCG{ #vpHilypHvlx{k#1k ]]^k#|}i(x{}pÂHkuoÈ{)p lpH PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,PL2 [ XCGÁU Tx{iypHvnu}ilk#nuÀ P,PWP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P uq XCG 0pHpHiln vlx{k#?n#} 0x{l|nwx ¡Hn vlx{k#?k ]#Y(ixvyx{Hnw ¢_x{}pHR P,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P g £ 8 6 /¡ B
(126) :-$ ;<8 6 u F & B<zA#-w ;]¡%¡ a- w }¡ % A#2 ;<cu % ;<8 6 8df¤ b + 8}2 9A# 6 9 /¡ B] }H u F. Û-Û ·¥HîÎ ß )(. .
(127) . Kp N )$. - "
(128) < (0 1vÀx{s VWmu|ilptDFn#}DE }n
(129) upvÀ}pFln#o1p(x{oÈnum#pHkk#ilx{nwvÀpHG1HF}pHilp7]]kuiyp^]^k#i vÀ}p ln#o1px{o1n#mup fk x{uv nwx{i3Hk#ililpHyAk#}}pHHp
(130) ZD'nu Dåv}pHiyp p)lgx{v n vå{pHn#v3v r(k lk {|vlx{k#}R + 0n#}y ^]^k#iFvÀ}pDviy|}v|}iypt]^iykuo oÈkwvyx{ku}iykutg{pHo nu tfp{kumu4vkvÀ}p0Hixvlx{Hn ¤y|}i ]]nuHp kGkPRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P q vx{^ VQ mu|}iy p 9Ân#} 9 > }n
(131) up3ilpHyApHvyxup vÀ}p0ynuoÈpx{o1n#m#p0Hkk#ilx{}n vpH4nut 9 nu 9 > GeHF}pHiy7p ]^k#iltp ]]kui(vÀ}p0ynuoÈpvÀix{{pvFk ]-x{o1n#mupx{}pHHk#ililpHyAk#}}pH
(132) pH 9 ~ 9 nuR 9 Ev}pHiypK)p lgx{v-nwvf{pHn#vf v r kykw{|gvlx{k#}s 2 2 _nu}k & K & W ! ]^k#iÂv}p viy|}v|}iy, p ]^ilk#oLo1k vlx{k#}ilk#t{pHoLnu tfp{kumu!vk\vp Hixvyx{Hnwjlpv32k ] x{}pH gKG PRP,PRP,P,PWP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P HF}p!upHvk#il 6 n#} B TypHpvÀ)p l7v )G^P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P S q HF}pÂilp{n vlx{k#}lx{\tfp v r pHpH g=n#} g !G P,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P+u !0ypH1x{vÀ}p0}iyk2k ]-k ]K}ilk#fkuxvlx{k#1i G PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P+Hq S !0ypH1x{vÀ}p0}iyk2 k ]-k ]K}ilk#fkuxvlx{k#1iq G PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P+ X !0ypH1x{vÀ}p0}iyk2 k ]](2k ]K}iykufk#xvlx{k#}jq n#}: P,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P+$ S [ ½{|}vÀiln vlx{k#?k ]-vp0x{}pÂHk#o1{)p lpH' m npo" e~ m npo#%$ e~ m n$%o & ~Qnu m no&'# ~ PRP,PRP,P,PRP,PLw #vpHilypHvlx{k#}j2k ]-vÀ}fp ]]ku|}iFHk#o1g{)p lÈHku}pH(n#}\v}pvix ]^kHn A{n#}2p GtP,PRP,PRP,P,PRP,P Q
(133) #vpHilypHvlx{k#}j2k ]-vÀ}fp ]]ku|}iFHk#o1g{)p lÈHku}pH(n#}\v}pv}iypH7p
(134) ]]kHnw T}n#}2p G P,PRP,P,PRP,P g # ½{|}vÀiln vlx{k#?k ]-vp0x{}pÂHk#o1{)p l&mn(ko PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P u / o1n#mupH(k ]*)6nu+ ) fx{ v r kvÀix{{pvÀ(2k ]KHn#o1pHiynu7 GpP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P S
(135) Y(ilk#l -,}|x{k#:vpHiypHkum#iln#oBk ]*)M~Qn y|}t}lpv(k ]#g Hk#ililpHyAk#}x{m0vÀ.k )# <VWm#|}iyp
(136) q )G X
(137) q Y(ilk#l -,}|x{k#:vpHiypHkum#iln#oBk ]*)²~Qn y|}t}lpvFk ]#g _Hk#iliypHlfku}gx{}m0vÀ.k ) <VQmu|}iypå
(138) )G [ / Y(ilk#l -,}|x{k#1vÀpHilpHk#muiynuoâk ]¤ny|}t}ypv 2k ]_Hixvyx{Hnwx{}pHL gKGiHFpF{7p ]²vjx{o1n#mup(x{s ]^iykuo v}pÂfkwx{#vF2k ]-Vx{7p r=k ]*/10G P,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P u S Y(ilk#l -,}|x{k#DvpHilpHk#m#iln#o2k ]ny|}t}ypv¤k ]Hixvlx{Hn wx{pH g #HkuiyilpHyAk#}x{}mEvkFy|}t}lpv 2k ]#gâilpHlpH#vÀpH x{ VWmu|ilpH1~{1 X ~nu}
(139) GHF}p{7p ]²v(x{o1n#m#px{' ]^iykuovpAk x{#vF2k ] Vx{7p r k ]*/,0 G PRP,P,PWP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P qu 1 X Y(ilk#l -,}|x{k#1vÀpHilpHk#muiynuoâk ]¤ny|}t}ypv 2k ]_Hixvyx{Hnwx{}pHL gKGiHFpF{7p ]²vjx{o1n#mup(x{s ]^iykuo v}pÂfkwx{#vF2k ]-Vx{7p r=k ]*/ G P,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P qQ [ Y(ilk#l -,}|x{k#DvpHilpHk#m#iln#o2k ]ny|}t}ypv¤k ]Hixvlx{Hn wx{pH g #HkuiyilpHyAk#}x{}mEvkFy|}t}lpv 2k ]#gx{& VWmu|ilpH0È~{% X1~Qn#}.H GeHF}p!{7p ]²vFx{oÈnum#px{^ ]]ilk#ov}p!Ak x{#v2k ]-Vx{7p r=2k ]*/, Gåqg
(140) Y(ilk#l -,}|x{k#1vÀpHilpHk#muiynuoâk ]¤ny|}t}ypv 2k ]_Hixvyx{Hnwx{}pHL gKGiHFpF{7p ]²vjx{o1n#mup(x{s ]^iykuo v}pÂfkwx{#vF2k ]-Vx{7p r=k ]*/1G P,PRP,P,PRP,PRP,P,PRP,PRP,P,PRP,PRPKP,PRP,P,PRP,PRP,P,PRP,P qu Y(ilk#l -,}|x{k#DvpHilpHk#m#iln#o2k ]ny|}t}ypv¤k ]Hixvlx{Hn wx{pH g #HkuiyilpHyAk#}x{}mEvkFy|}t}lpv 2k ]#gx{& VWmu|ilpH0È~{% X1~Qn#}.H GeHF}p!{7p ]²vFx{oÈnum#px{^ ]]ilk#ov}p!Ak x{#v2k ]-Vx{7p r=2k ]*/ Gåquq Y(ilk#l -,}|x{k#ÑvpHilpHk#m#iln#o 2k ]0Hx{pH
(141) ~K\x{pHåk ]tgnu} vpx{iDHk#iliypHlfku}gx{}m1 x{}pHt ]]ilk#o g
(142) GeHF}p!{7p ]²vFx{o1n#m#pFx{t ]^iykuovÀ}p0fkwx{#vk ]-Vx{7p rk ]-v}p VWiyvFHnuoÈpHil2n / 0 G$qg. É -ÛfÉ]Ú ; .
(143) .
(144) !"# $%&'()+*, -./")() '0'1 !(2 %. È K(:; < F HF}p pHvlx{o1n vlx{k# k] /T%oÈkwvyx{ku n#} viy|}v|ilp]^ilk#o"ypHzV|}pH}HpHk]Mx{oÈnum#pHx{,r(p V}kr.vÀk:tfp n6x 1H|vkup tApHHn#|}lpk]DxvÀ1x{vn#txxv t}|gv?k#}p r}k#lp ykw{|vyx{ku }nu\m#ilpHn v1Ak vpH#vyx{nw{k]]kui o1n#/Ñn#}x{Hn vlx{k#}G'!}p?fk#lx{tg{p1x{}p k]0n vlvÀnu ]]kui3vÀx{ }iykut{pHoLx{vk x{}pH#vyx ]!E]^pHn v|}iypHÂx{ v}pypHzg|pH}Hp?k ]0x{oÈnum#pH3vnwv x{ÈtApx{m.n#}nw i¡HpHA~4oÈn p:y|}ilp\vÀ}nwvv}7p 6tAp{k#}m vÀkvÀ}pln#o1p ix{m x{ 6o1kHVx{}m k#tpHv3x{Ðv}pÈlHpH}pw~¤nu}ÐvÀiln# vÀ}pHoLkHupHivyx{o12p GpHFx{3viynu #x{}m Hnu6tfp1|}ypH x{ilpHvy .vÀk pHvn#tx{yÑ|}y7p ]^|(Hk#}vÀiln x{uvÀDk#Ðv}p #x{}pHo1n vlx{ÈlHil7p r2k ]FvÀ}p\o1kHVx{}mk#tpHv3nuA~ lk#o1pvyx{o1pH
(145) ~
(146) vkÂn#v|}n HkuoÈ}|vpEx1v GCHFgx{Mox{mu#vMtfp(Hnw{pHåv} p i1
(147) % % (n#}}iykun#n#}vÀ}p xvpHiynwvÀ|}ilpÂkuvÀ}p3l|}tpHvx{0m x{mun##vlx{ [~
(148) qg~_V~_/q Sg~fq}w~f
(149) GHF}pÂvÀiln# #x{}mÈN Hnun {lkÈtAp3|}ypHvk pHvÀnutx{yDHk#iliypHlfku}pH}HpWtfp v r pHpH!x{o1n#m#pHAk ]}vp lHpHpKvn wpH3n v-x ApHiypHuv-vyx{o1pEx{}vÀnu#v7 G%HFpHlp HkuiyilpHyAk#}}pH}pHjHnuvÀ}pHtAp3|}ypHvkÈpHvlx{oÈnwvÀpvÀ}pDgx{l{n#HpHo1pH#vk ]Kv}p3oÈkHVx{}m1k#tpHvk#i2k ] v}pÈHnuoÈpHilin G HFx{o x{m##vtApÈHnw{pH v}p .%)
(150) n#}}ilk#n# G }pH v}påvlx{o1px{#vpHi nwjtAp v r(pHpH v}px{o1n#mupHjtfpHHkuoÈpHKloÈnw{pHi~Vvp v r(k nu}ilk#nuÀ}pH4Hkwx{}x{2p GCÈvx{F}n#fpHi r(pDx{yH|}l(k# 1vÀ}p x{lHiypvpHn#l2p G HFp0Hn#lp0k ]-Ak x{#^ v ]^pHn v|}iypH }n#FtApHpHÈvÀ|}x{pH x{}pvÀnwx
(151) G~HF}p!}ilk#t{pHo x{Fnu' ]^k {$k r Wm xupH Ak x{#v Hk#iliypHlfku}pH}pHfx{1 v r(k3x{o1n#mupH~Vn#ll|o1pH3vk3tfpk# vpln#o1pFvn vlx{Fk#tpHv/~ x{jxvFAk#lx{t{p vkiypHHkHupHi¤v}pjHnuoÈpHiln(x{y{nuHpHoÈpH#1v G Ðp(}nHupFtfpHpHÂnut{pjvÀkFviynuHpEvx{Kilk#t{pHoât}nu !vRk Y(nu{pH S _n#} xv}n#jilpHHpxupHÈnmuiypHnwv(}pHn Ak ]-nwvyvpH#vlx{k# tfkwvÀ x{\}}k vk#muiynuoÈo1pÀvi
(152) ~Q/~}V~¤ e~ Xu~g#~ SV~QquV~W/q [ -n#}\x{HkuoÈ}|vpHiEVx{x{k# wqV~Wq#~ [
(153) G jkuoÈp0k ]_vx{^ r(kui ?nu(l$k r\v}n v(v}pHiytp r pHiyp HnuypH r}pHiypFlp#pHiln }lk {|vlx{k#}jHku|{tApFk#tvn x{}pH n#}vÀ}pF})p lgv(}nwvÀ|}iln zV|}pHvyx{kux{' r}pHåx{MvÀ}p lk {|vlx{k#\|}x{zV|}pw~g
(154) x G 2p Gir}pH\x{(xvfkuyx{t{p vk iypHHkHupHi(|}}n#otx{m#|}k#|} vÀ}p0Hn#o1pHiynDx{y{n#HpHo1pH#1v G ]^n#vFxvx{FvÀ}pDiypupHiylpÂzg|pHvlx{k#\v}n v}n#FilpHHpx#pH?vÀ}pÂo1k#vn vlvpH#vyx{ku g}kpH(vpHilp0)p lgx{v0lpvÀ 2k ]fAk x{#v ]^k# i rx{À }kÂo1n vlvÀpHi-}$k ro1n#/ Ak x{#v r(pFo1pHn#l|ilsp ]^ilk#o=vÀ}nwv4lp#v r(^p rFxAn r($n # VW lp#pHiln Mlk {|vyx{ku}!vkvÀ}p1Hn#o1pHiyn?gx{l{n#HpHo1pH#1v G HFgx{zg|pHvlx{k#.nu3tfpHpH.n#} r(pHilpH Ak#xvyxup /t ?vÀ}p0ynuoÈp v r(k1Hk#o1o|}xvyx{pH GCHFpD}kwvÀkum#iln#o1o pvypHilK}n
(155) up3x{lHk
(156) upHilpHÈvnwv(x ]KvÀ}pDfk x{uvÀj{$n ku um#7p ] n#}ix{}p ,- nuÀ}pH ÂvÀ}pHvpHil^p r(pHilp0n r($n n v({pHnuvM v r(klk {|vyx{ku} H~QwV~A/
(157) GHFx{(}nu tApHpHÈilpHx{yHkHupHiypH1/t ?Hk#o1|vpHi-Vx{x{kulx{pH#vyx{v4{n vpHi uV~¤ Sg~Q [g~Q2 S~}#qg~Q g~_% XV~# ^~n#}1vÀ}p um#7p ] n#}ix{}p ,- n#}pH ilpH}n#o1pHÈHixvlx{Hn Ay|}i ]]nuHpH ^lpHp ,¤x{mu|}iyp1 )G HFp?Hn#lp\2k ]x{}& p ]^pHn v|}iypHD}n# }k v ilpHHpx#pH6o|}6n vlvÀpHuvyx{ku vkJku|}i V}k rF{pH}mup ]^iykuoIvÀ}p }}k vk#muiynuoÈo1pÀvi 0HkuoÈo|}x v 3nu lk#o1p(n vlvpH#vyx{kuK ]]ilk#o=v}pFHk#o1|vpHifVx{x{k#1Hk#o1o|}gx v q~}#~ uV~VVu~V}
(158) GHF}p(}ilk#t{pHo=x{4nu ]^k {$k r Vm xupH vÀix{{pHE2k ]Qx{}pHk#ililpHyAk#}}pH
(159) pHQx{vÀ}ilpHpjx{o1n#m#pH
(160) ~ nuyl|}oÈpHvk3tfp0k# vÀ}pln#o1pvn vlx{kutpHvH~#x{jxvFAk#lx{t{pFvkiypHHkHupHi4vpHnuoÈpHilnÂx{lg{nuHpHoÈpHuvÀ G HF}ilpHpVx{7p rnuiyp0iypHzg|gx{ilpHtApHHn#|}ypF v r kågx{7p r2k ]Kviln x{m#uv(x{}pH}k }k vFx{o1fkuypn# Hk#}vÀiln x{uvÀ |}fkuvÀ}pHnuoÈpHiln gx{l{n#HpHo1pH#v7 G\JkuvDk ] vKp r k#i }n#0tfpHpHvk rixvÀp}$k r vÀ}pHk#}vÀiln x{uvÀ v}n vHkuoÈp ku|vk ]åvÀ}pk#t}lpHiwn vlx{k#2k ]k#}p x{}pJx{ v}iypHpgx{7p rn#}Ëvk6}ilk#fkuyp nw{m#kuixv}oÈ ]^k#ilk Vx{}mp 1x{pH#vl v}pÈ vÀpHo k ]}k#x{}pHn#i3pHzg|nwvyx{ku}3iypHl|vyx{}m ]^iykuoLvp1k#t}lpHiwnwvyx{ku 2k ] y|}Ðx{}pH /~HV~(u#~(wV~jw~4u~4qg#~jq X
(161) G'HF}pzg|pHvlx{k#62k ]FvÀ}p\Hixvlx{Hn FlpvÀ2k ]Fx{}pH}nu kug ÑtfpHpH.t}iyku|}m##vå|ÑiypHHpHuvy /t _HF}k#o1n# (|}À}n#}n# q~M
(162) GsHF}p1}iykutg{pHo"Hn#Ñtfp1}iln#lpH x{ n r($n Ðv}n vx{ x{ox{nui3vÀk vnwv k ]Ak x{#v ]]kuinJmwx#pH nw{m#kuixv}o~-}kpH3vÀ}pHilpÈ)p lgx{v lpvÀ2k ] x{}pH1y|}À6v}n v/~4}k o1n vlvpHi3}k ro1n# Ðx{}pH r p k#t}lpHiup\x{ vÀ}pHlp\lpvÀ
(163) ~ r p rFx!nw r($n + VW lp#pHiln Eykw{|gvlx{k#}^ ]^k#iFvpåHn#o1pHiynx{lg{nuHpHoÈpHuvÀ GsW11% & C k . (f-~7
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The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide
Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to
