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A Generic Concept for Camera Calibration

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(1)A Generic Concept for Camera Calibration Peter Sturm, Srikumar Ramalingam. To cite this version: Peter Sturm, Srikumar Ramalingam. A Generic Concept for Camera Calibration. 8th European Conference on Computer Vision (ECCV ’04), May 2004, Prague, Czech Republic. pp.1-13, �10.1007/9783-540-24671-8_1�. �inria-00524411�. HAL Id: inria-00524411 https://hal.inria.fr/inria-00524411 Submitted on 25 May 2011. 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..

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(217) ) +2MYÔ8Ô8)Y)Y58=GÔI)*7»=?ÔF7ç(cÕj)Y2B=G2B58)*58+Y)*=?(,Ó!Õ,(,ÚcÕ )*ÖA%(D$585F7:EG=?ã C9HF71%(,9  Ø:ÔI=G7/)YÕ 2»01Õj)$ׂ(Ó!ÔFE?EG=?7A(c58+cÛ!ÑÙ(Õn)Y5IÓ`>6)*ÖA(,=G+±Ó

(218) Ô@ÔI+Y9<=?7158)*(,Շ=G7»)*Ö1(TÝéÔIEGE?Ôê=G71H  ­2B5)Y+*=GèÆë G)X;$5G)FE9/,+ EF,;9)1. ,. +}/ 2)F,7. EF,+ / 97,.$/12V1. )FE . @. m M 9. Vr. [C\]^_. ]Ge]H. r. CY i[C ]^_. b Q. ]"e$]". &. K **KŠKK  *KK  *ŠKZ  *  *K  *   *K  * **KŠ* KK  *KK *  *ŠKZ*   * *  *K*   * *   *K *  * * => <   **YK  ** K **j  **8 **  *

(219)   *  * *Y* K  * K*  *j*   * *  **   ***   * *  * *  6 ¶éas· * * * * * * * * * ** * * * * * * * *    * * * í)*AÖAÚÆ(,ê2õÖAÖAÚ/=œÓ`(­ÔFÖÒ×AÓ!)YÔF=?582ME?=?EG7A=?ØA7A(cE?(,=G9M(c5FÕ6+*×/=GæM)j)*æBÖ1E?58(,Ó

(220) 5s)ÔIå@715F=?Õj7AEGE®)YH+YÕ*5FÔF0A=G0<×<7/)´)TâŠ9<ÔF2M(!7A)*(c(.(!58+Y+*712MÔÕTê =G7:)*Ö1585587/)))Y5%Õ6)YÖA)*Ô8=?=œÝ2MÕÕn2B(F= !Û 58( T)*+Y5F=]Ó`èBÖB12ÔFåÝÆ0:s)*Õj5F)ÖA7A(c×:Õn=œ(6Õn(.ÖvÔ8Ó!ÛvÝ&ÔFõ+Y+Y+*5FÖ1(c7A(!Õn>M+Y؂(gÔFEG(c7:5FÕ*+*9AÕT( Õ$)*;)*Ö1Ô»5FÔ875 Ý )*ê+YÖA=GE?ÔI=G71Õ*(,(58Ó

(221) +6Ô@(,(ø/01Ó

(222) 58=?)*(!=?7/ÔF)`7ÀÕ=?9<7ö(!؂؂(!ÔF71=?7/9)%ÔIÓ!74Ô/ÔI)YÖA+Y9A(=G712M58Ô8)*)*(c=?Õ.ÔF7;587:Ø19;5F+Y)*5FÖ@2M01Õ.(

(223) )*)*(,Ô;+YÕ,5BÛ )Y+*=GÝéÔ<Ó!58E$Ó!5FEG=?×A+`5)Y=GÔI7;)*(!7:ÕnÔI+ =G2M745s)*æ4õ&ÖA(%5FÔF×A×158EGÕ*ØA( (!؂+YåF(!HF7:(­=?9<åF)*=]Ö1(cèÕ¦58ÔF))*ÖAÝ )*(´ÖA(6Ó

(224) Ô@é)j(ä#ê´Û ÔgAÓ!ÔI)*=G(,+(!7I7:×:)`ÕnÔFÕvÔI)*+YÔFÖvÕÝ/Ú<)YÕ*íÖAÖ1»(®58+Yñ:ÔF(%0<+YÕnÕn))vÔIÔ82g)jÝê´(Ô.»Ó!Ó!Ô/5FÓ!( Ô@EG=?(×AÓ

(225) +`5=?Ó

(226) (!)*=?7/=?(!ÔF)Y7/Õ,76)YÚ<Õ´)Y(F(!58Û 71H1+YÕ*(­Û,ÔF+ 5F+` Õ®EGêá¾5F5sEGæ<E Õ .,58(!+Y+Y(®Ô1ÛHI=G@ åI71(!Û 7 ( 3 Ú´5F719 3 ê´(

(227)  õ A Ö ç ( Y ) ! ( 1 7 * Õ F Ô ` + 4 Õ , Ó 8 5 7 ‚ × Ò ( c ( j Õ Y ) G = B 2 8 5 * ) , ( 9 @ × æ * Õ F Ô ? E @ å G = 1 7 H G E ? = A 7 c ( 8 5  + , ( / ø 1 0  5 Y ) G = I Ô 7 * Õ @ æ n Õ * ) , ( ; 2 åFáé0A(!Ø+Y=Gñ1)*(,ÔM9÷ÕYÓ!0:58ÕnE?=?(c7Aä´HÜ5F+*Õn=?(62ÔF0A×<Eœ)`558)Y=?(,7A9R(,9v+YÚ/5F=G71ݱ9<íFÔFî 2 ؂(!ÔFè@=?؂7I)`(!Õ´+Y=?Ýé2gÔF+(,7/Õ*)Y0 Õ»)*Ó

(228) Ö1=?58(!7/)g)*=?E?7ìæ2BHF(!58717@(!æB+`58ØAET=Gè<01(!7AEœ=?Õø/0Aá (ÀgÕ*5ÔF)E?0<E?(,)*=?5IÔFÕj7:)#Õä Ø158áé0A+Y58(»Ø+`585s)*2Måԏ58(

(229) ÕY=?)YE?Ó!(!5F5F+`×AEGÕ!(sE?Û (Fä# vÛ1ÛA(

(230) õôŠ7ö) ÖA+$()*ÖA) 5F(»EGHIÝéÔFÔF0 +YE?E?=]+ Ô)Y)ÖAê2 58=G7A71H:ØA9 Ú:+Y Ô<ê´Ó

(231) ()(! (cHI 9A=GåIÕ(»5F Õ´5F7Ò)ÝéÔI58 EGE?E?ÔHFêDÔI+*Õ!=GÛ )*F Ö1F2F '&MÝéÔI×:+%(»Ó!)*ÔFÖA2M(»ØA(,0<Õn)Y)*=G=?712BH5)*)*(cÖ19;(»)*2M(,71Ô8)YÕ*=GÔFÔI+`7 Õ J J @ J Û FÛ TÕn)*=?2M58)*(6Õ*Ó,58E?(ݾ5FÓ#)YÔF+`Õ!ë 0 +  J +  J +  J 58719 <Û ÔF2MØA0<)Y( +,)   58719 ) "!#$   % ; &  F F ; F '& 3  3 ; J ; íAÛ ÔF2MØA0<)Y( %Æ58719 % ¾ë . ; .

(232) j. &. b. M. k&. > NM9 s. &. D&. j. l. $M'.  {. M *h *h. . (*,+  ' ) ! -/.  + 3 -/. 87. +  + ! 3-4-/0 0 :9. <= + 1 + ! 5-6-/2 2  -/;. . (* 1 ' ) ! -7   + 3 - 7  -6-. !1- 9 + 3 - 9-4> . !?>6; + 8 >6;-4@. <=. A. 1Û êõÖAÖAÔF2M(!=œÓ`æBÖØAê0<=œÕ)Y=?(E?E‚HF0:71A58Ô85F+`)7158×:7/9 (%)* (,ÔF (,@+*9B×/)*Ö1æ»)YÔFÔMÕn7AÔIÖ1ÔIEG5så@+*åF2B=?7A(58H65gE:56=G0A7Õn7A)*HF=œ+`ø/(,580A7A=?HF((!Ö/+`Õn)n58ÔIÝéEOÔIEGÛI0A+*ÑÙê)*=?ÔF(587v+`n9%ÚAÓ!ÔFÕ*EG=?(!+Y7A+*( (c(c58Ó#)+±E?Æ(,)YÝé5FÖAÔIÕn=?+D)±ÕÕ*9<5Iø/(

(233) Õ01)`Õ*585FÖA=?+*E?Ô(cÕ,êÕ&Û 7Ø1+*=?ÔI7 ×AEG(,2;xÛÚ . & *h.  NM9. L M 9.

(234) Q ´W`V/W*lj–]o.’ f,V/o`WY\Ih®‘œf!l’$m!“WYlnm’$m,[—–—iIlnm

(235) hj–—fcV  ÕnÔIEG0<.Õ)Y=G*ÔI=G77AHB=?7;Õ*=GHF2»(,0A7AEœ(!5+`)*58=?ÔFEOÛ 7:Õ!Ú@ê´(6åI(!+Y=]ñ:(,94)*Ö158)´)YÖA(58E?HFÔI+*=G)*Ö12ÂHF=?åF(,Õ5g0A7A=œø/0A(58719Ó

(236) ÔI+*+Y(,Ó

(237) ) 4. . . dd. . .       KK K * * *YK     d * *  * K*  4    **  ** **.      K  *K a¢ K ** ** dd *j* * * * * *   K K . Š K K. Y  K. Š K K. Y . * * * *  * K. Y  K. *  K. Y  K * * * * * * a¢    *K  * * **K *j* **  *Š* **  *Y* K *KŠK j* *  *KZ*  *YKK  ¡ KK **K ** dd. Y*j* ** K KK * * d . * *      * KK  * * **K * *  * *  *YK *KŠK KŠ* *K  . *K* Y K *YK K ¡    **  **K ** *Š **Y* *KK  * * ** * K Y* K*j* * *KZ * Y* * K * * *KŠ* K * j* *  * bž  K ** ** Y* K  *  *dd *   * * * *Š j Š j *KZ j* *  *KZ*  *j ** ** * .  j   b     *  * * `d  * * *  dd    *  * * *Š * *  * *  j*  *KZ KZ* *   . *K* j   *jK ž  *K *. Yj* * K d aca'd4    **  **K ** *  *ŠY* * K  * * ** * K j*  ** * *K * Y* * K8* * *KŠ* K ** * . *KZK*  * `Y¢a  ** ** ** **  dd a    *  * * *  j** . Š* *  * *KK j**  aca,¢a    **  ** ** * * * *  *5* * * *  ** * * *K* *  * * * * *  **K * #`¡   K ** **  *. *** K * *KŠK  * *. *Š . *KZK asac¡     **  **K ** Y*j* ** K  **. ***Š** K  ** Y*j* ** K  **K8K. **KŠKZ** K  ** * * * *  * *   * * *   * * *   * K * K*   * ``bž  *** K * KŠ* K a *K *     **  ** **.         * * * * * *  o`*Š*–— W`Vhj^T f,‘¦* KZ*  hZ²$f6hŠlj–š‘?fo#m,[¦o`m,[—–—iIlnm!hj–—f,VMhjW`V/^Šf!lj^®‘?f,l´m6°cWYV/WYlnm![‚a Ž  * Ko# * m,* “ WY ln* Km8*   * * *. ’  f Y W  ¼ ©@¤ 1«      *   *    *   *    *     **       * 4   **  4%4   *  4   *  4   *  4   *  4   * 4   * 4     *  4    *  4    *     . . . $Ë1Ð?±ÉTÊ ÜÌ+D4Ê ;

(238)   nÐ >­Ë  ÊAÐjÌTÉ ÒÌTÉ­ÏACBDÊ. =ÔFßDc× 571)*5F(c=?EGÓ#ÔFÔI)Y7:HFÕ,ÕÔFÛ<0:ÑÙÔ8ÕnÝE?(æBÔF9<01)*(,+ÔMÕYÓ!Ó

(239) )Y+Y5FÖA=GEG(ׂ=?×A(6Ó,+`5F)*5Õ*ÖA)*(6=?(,ÔF2ÔF7÷Ý åIÓ!8ÔF(!îò+Y71æÓ!Ó,(!58×AØ<2M+Y)c=G(Úv(!1+`Ýé5FÔFæ¦Õ,+»ùAÚA9<Ó

(240) Ó#(

(241) (!Ýj)`7/Û 58)YY=?+YíAE?5FÕÚ1ET5FêÓ!+*(5F(%2g9<HF(,(,=?åFåF+Y(,5I(,7EGÕÔIØ:58=?7 7:(c99Ò=?Ø12MxE?Û5FØ:71ÔI58+n+)`58Ó,7/58).E?=GÕ*×1Ø:+Y(c58Ó

(242) )*=œ=?58ÔFEG7 â ã  ÓÔ8

(243) (!ÝD7/Õn)Y= (!!+( áé0A71 >/ 71çÔ58ê717:9ÜBä#Û+`ôŠ´587Ü71æ)Y> ØAÖA+Y=?<ÕgÔ<ڇÓ

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