On the Geometry and Algebra of the Point and Line Correspondences between $N$ Images
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. On the geometry and algebra of the point and line correspondences between images Olivier Faugeras and Bernard Mourrain. N˚ 2665 October 1995. PROGRAMME 4. ISSN 0249-6399. apport de recherche.
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(90) = -UXle{ = 59 s-+_V~eYy;T` 8eY 0bj =-UXle{ jUJ_Q`bj + )#_V~ÅYÖY}y;`ky^P 0£UXOr|}PTlÅjQ_VOVUJ`blSQ_ ` = # =?4 M]aVf_V~eY}l _V~eY uOQjQ_ Y}ac?UJ_Q`bPTlÍ`bl»_UX2] 0bY jV~eNP ,Ójr_V~?UJ__V~eYÖ-_ ,rP _VOz7` 0±`bleYUAOz`¯_Q`bYÒj)UXOQY3U 0kRSY}]eOVUJ`b|U 0707) {eY}y^Y}le{eY}lS_Òf?-` 9¦;Y 9G_V~uUJ_%?` + PTlÅY)`kj A}Y}OQDP +8PTO%jVPTW Y _VOz`b2y 0bYP +y^PA`blS_V3j * = 70VfÅ_V~eY}l _V~eYËPA_V~eY}O%PTleY2`kj%`klDRSYÒlÅYÒOV3U 0U 0bjVP Q+8PTO'_V~eYÖjUXW Y _VOz`k=y 0kY;P +y^PX`klS_VNj 9Gp-~e_Y ,rPTOQ{ej `bl RSY}leY}OVU 0 W YUAl0 f +8PSOxY 8?UAW 2y 0bYAf_V~uUJ_x7` +
(91) = x`brj A}YÒOQP'_V~eY}lÖ`blRSY}leY}OVU 0X_V~eY|}P;Y g|h`bYÒlS_Vj P + 1'UXle{ UXOQYrlePX_]^PA_V~&Y}ac?U 0e_V P )UXle{&~eY}le|}Y-PSceOY}adcuU_Q`kPSl&`kW 2y 0¯`bYÒj_V~uU_
(92) = `bj23U 0bjVPY}adcu3U 0x_VP <9 PA_VY _V~uU_Ój`kle|}Y _V~eY2_VYÒOQW = #>=`bj-W2c 0¯_Q`k2y 0¯`bYÒ{,] )#_V~eOQY}HY +®UX|h_VPTOQj}fel?UAW Y 0?) 1Òf }fUAlÅ@ { * = #>= 0 f_V~`kj&jQ`¯_VcuUJ_Q`bPSl Wg!U ) UXyey^YUXO)`bl PX_V~eY}OÖ|UXjVY}Sj ,Ó~ÅYÒOQY _V~ÅPTjVY +®UX|h_VPTOQj ]^YÒ|}PSW Y 29 szl_V~eY |UXjVSY ,~eY}OQAY 134 M;f^`¯_)`kj YUAj?` 07) iSY}Oz` uY}{_V~?UJ_ _V~eY&-_ ,rP _VOz7` 0±`bleYUXOz`±_Q`bY}j#UAOQYÍlePA_#3U 0kRSY}]eOVU`k|3U 0?07) {eY}y^YÒlÅ{eY}lT_gjQ`ble|}YAhf +8PSO&Y 8?UXW 2y 0kYAf = 4 M UXle/{ 4 M&`bW 2y 0?)Í_V~uU_Ó|}P;Y : *
(93) = 0?4 M29%n l»_V~ÅYPX_V~eY}O-~uUXle{Í_V~eYÖ-_ ,rPg|UAjVY}j 4 M UXle{ * = # =;0 #{eP`bW 2y 07)+_V~?UJ_g_V~eYÍ-_ ,rP _VOz7` 0±`bleYUXOz`±_Q`bY}j»UAOQY,3U 0kRSY}]eOVUJ`b|U 0707) {eY}y^Y}le{eY}lSN_ 9
(94) xYh_-cejle P ,IjQ_Vce={ )#`klDW PTOQYË{eYh_UJ7` 0x_V~eY)`b2l +8PSOQW U_Q`bPTlD|}PTlS_U`kleY}{Í`klÍ_V~eY)_VOz7` 0¯`kleY3U / Oz`¯_Q`kY}Nj 9 O 20 20?) -) 30 ;+ . . . . . . . . . . . . . . . . . . .
(95). . . . . %&. q'%(.
(96) R.
(97) !#"$! %!. |}P;Y5:
(98) * = 0
(99) = ?|}P;5Y :
(100) * = ) 0
(101) = ?|}P;5Y :
(102) * = 0
(103) = ?|}P;5Y :
(104) * 0
(105) = ?|}P;5Y :
(106) * = ) 0
(107) = ?|}P;5Y :
(108) * ) 0
(109) = ?|}P;5Y :
(110) * = ) #" 70 = L|}P;5Y :
(111) * = 0
(112) = ?|}P;5Y :
(113) * 0
(114) = ?|}P;5Y :
(115) * = ) #" 70 = L|}P;5Y :
(116) * ) #" 70 = L|}P;5Y :
(117) * = ) 0
(118) = )?|}P;5Y :
(119) * ) 0
(120) = )?|}P;5Y :
(121) * = ) 0
(122) = )?|}P;5Y :
(123) * = ) #" 70 = )L|}P;5Y :
(124) * ) #" 70 = )L|}P;5Y :
(125) * ) 0
(126) = )?|}P;5Y :
(127) * = ) 0
(128) = )?|}P;5Y :
(129) * = ) 0
(130) = )?|}P;5Y :
(131) * ) 0
(132) = )?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |}P;Y: *
(133) = $0 = L- 8* = # = 0 * = # =;0 |}P;Y : *
(134) = $0 = )L- 8* = # = 0 * = # =;0 |}P;Y : *
(135) = $0 = L- |}P;Y: *
(136) = ) ;" 80 * = #>=#0 |}P;Y : *
(137) = $0 L- |}P;Y: * # ) ;" 80 * = #>=#0 |}P;Y : *
(138) = $0 = )51>1|}P;Y: *
(139) = 0 * = #>= 0 |}P;Y : *
(140) = $0 )L- |}P;Y : * # ;" 80 * = #>=#0 |}P;Y : *
(141) = ;" 80
(142) = )L- 8* = >= 0= * = #>= 0 |}P;Y : *
(143) = $0 = L- |}P;Y : *
(144) = ) ;" 80 * = #>=#0 |}P;Y : *
(145) = $0 L- |}P;Y : * # ) ;" 80 * = #>=#0 |}P;Y : *
(146) = ;" 80
(147) = )51 V|}P;Y : *
(148) = 1 0 * = # = 0 |}P;Y : *
(149) = ;" 80 # )51 V|}P;Y : * # 1 0 * = # = 0 |}P;Y: *
(150) = ) $0 = )L- " 7* = ; =#0=;* = #>=#0 |}P;Y : *
(151) = ) $0 )51 " |}P;5Y :
(152) * ) 180 * = # =;0 |}P;Y : *
(153) = ) $0 = )51 |}P;5Y :
(154) * = ) 180 * = # =;0 |}P;Y : *
(155) = ) ; " 80
(156) = )51 " V|}P;Y : *
(157) = ) 1 0 * = # = 0 |}P;Y : *
(158) = ) ;" 80 # )51 V|}P;Y : * # ) 1 0 * = # = 0 |}P;Y : *
(159) = ) $0 )L- " |}P;Y : * # ) 80 * = #>=#0 |}P;Y : *
(160) = ) $0 = )L- " |}P;Y : *
(161) = ) 80 * = #>=#0 |}P;Y : *
(162) = ) $0 = )51>1|}P;Y : *
(163) = ) ;" 80 * = # =;0 |}P;Y : *
(164) = ) $0 )L- |}P;Y : * # ) ;" 80 * = #>=#0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . = 6
(165) = )L-
(166) = 6 = ) 1 8* = ; = 0 * = #>= 0. pUX]20kYÖ2d p%~eYÖOQY0£U_Q`bPTlej%P;+¨_V~eYÖY0kY}W Y}lS_Vj-`bl»_V~ÅYÖRTOQPScey s9. ô. qrq PsNtuu . 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M 4 M.
(167) }Z . ! Z @! S ;g.! % j 2 . #& (' # ^ Y~uUÑiTYgjVY}Y}l,_V~uU_)`?+ _V~eOQY}Y&`bW UXRSY y^PX`klS_Vj = UXOQY j«ce|~_V~?UJ_)_V~eY)>A}Y}OQP U,RX`±iSY}l _VOz`7±0 `bleYUXOz`±_-T) fh8+ PSOY?8 UAW y20bY
(168) = Òf`¯_ W YUXlej_V~uUJ__V~eY»PSy;_Q`b|U0OVU!) P;+ = `blS_VYÒOQj«YÒ|h_Vj _V~eY ¯0 `klÅYP+ `blS_VY}OQjVY}|Ñ_Q`bPSlP; + _-r, P»y2µ0 UAlÅYÒj)RSPX`kleR _V~eOQPTcÅRT~,_V~eY&PSy;_Q`k|U30OVU!) P+ UXle{ Ò fÅOQY}jVyCY}|h_Q`¯iTY0?)j6` jVY}Y uRSceOQYgac9 . d deÍ µ;
(169) xYh_cÅjleP ,!jVY}Yh,Ó~?UJ_~?UAyey^Y}lejx`7+e_V~eY_V~ÅOQYÒYy^PX`klS_VjUXOQYjVce|~Ö_V~uU__V~ÅY5)SA}Y}OQP)UAlÅPA_V~eY}O _VOz`70±`bleYUXOz`±_-)@9 tTYÑiSY}OVU0|UAj«YÒjÖUXOQY yCPSjVjQ`b]20bY;d uOQj_Ö_V~eY jVY}|}PTle{ _VOz`?0¯`klÅYUXOz`¯_V) |UXl]^Y`bl _V~eY jUXW Y RTOQPScey*fT`-9¦YshfPSOlePA_ÒfÅUXle{#jVY}|}PTlÅ{ `±_r|UXl#]CYOQY 0£U_VY}{#_VP = PSOlePXN_ 9n + |}PSceOQjVYAfÅ_V~eYRSY}PTW Yh_VOz`b|)`k=l +8PTOQWgU_Q`kPSl,|ÒPSlS_UJ`bleY}{Í`klD_V~e Y +®UA|h_-_V~?UJ_V_ ,rP _VOz7` 0¯`kleYUXOz`±_Q`bY}j UXOQYÖY}adcuU00_VP `bj-Y}adc;`±iA3U 0bYÒlS__VP&_V~eYÖPSleYÖ|}PTlS_U`klÅYÒ{ `klÍ_V~eYh`bOÓ3U 0kRSY}]eOVUJ`b|)OQY 0£U_Q`bPTle!j 9
(170) xYh_»cejÍ|ÒPSlejQ`b{eY}Og_V~eY|UXjVY,;P + = Ñf2U 0bjVP `kl RSOQPTcey+shf ,~;`k|~ `bj»OQY 0µUJ_VY}{ _VP
(171) = 59p%~eY PTy_Q`k|3U 0*OV!U );j%;P + ='UAlÅ{ '`klS_VY}OQjVY}|h1_ ,Ó~;`b|~ |UXl»3U 0kj«P]^Y)cele{eY}OQjQ_VP;P;{ 3U 0kRSY}]eOVU`k|3U 0?07)+] ) _V~ek Y +®UX|h_g_V~uU_g_V~eY,V_ ,rP _VOz7` 0±`bleYUAOz`¯_Q`bYÒjDUAOQY,OQY 0µUJ_VY}{ _V~eOQPSceRS~ _V~eY +8celÅ{uUAW Y}lS_U 0WgU_VOz7` 8 = }f^UAj%jV~e P ,l#`bl»_UX2] 0bYÖ< 9
(172) xYh_GcÅjle P , W PiSY-_VP)_V~ÅYÓ|UXjVY-P +
(173) = )ÒfU 0bjVP)`bl _V~eYRTOQPScey&sf;]ec_'cÅleOQY 0£U_VY}{ _VP
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