[ ] T Journal of Software. Vol.13, No /2002/13(05)

Transcription

1 -985//(5)957-9 Journal of Software Vol, No5, (, 8) E-al: : ( ),,,,,,, : ; ; : P9 : A [,],,,Zhang [] ( ), ( ),, (hoograph), Zhang, (DVS) Zhang,,,, ( ), ( ),,,,,,, : = u,v, M = [ x,, z], ~ = [ u, v, t] M ~ = [ x,, z, t] ( t ),, M ~ s ~ = K[ R t]m, () [ ] : --5; : -4-4 : (6;69975) ; 97 (G9985) : (976 ),,,,,, ; (96 ),,,,,,,

2 958 Journal of Software,(5) s R t,k, ( ) α γ u, K = β v Fg Zhang s planar pattern Fg Proposed planar pattern Zhang, t =, ~, M ~ M = ω, (), ω K K,, ω,, X-Y, z =, R, (), x u x [ ] s = [ () v = K r r r t K r r t] t t, [ x,, z, t] [ x,, t], t = l l I (,,,), J (,,,) ( ) [8] ~, : I, J M ~ M =, I, J ω I, J I, J, I, J ω, I, J, I K K I =, J K K J = (), I, J,, K K : Re( I K K I ) =, I( I K K I ) =,, (,,,) x, r, x x + = r (4) t t l, l t = (4), x + =, = ± x, (,,),,, t, ± x [4],,, 4,, ( ), r

3 : 959 L L L X B (,,) L Y X C Z A L (,,) C Z C Y C Fg Model plane Fg4 Fro odel plane to age plane 4, B,,,,,, C A, ( A B, C) = B L A AC = (, A B C A, B,, C A A B C B l C A B B ),,, C C A B, B,, C,,,,,,,, A,,, A A C = B B C (5) ( A B ) C = (5),, C C, C A B,,,,,,, 5, l, : E = d (, l ),, d, l ) l ( E, l (5),,, C A I B,,,, J l A l B Fg5 Nonlnear case 5 l l C C I = [ I,I,I ], C = K K = C C C C C C C, (),

4 96 Journal of Software,(5) [,I,I ] C[ I,I ] I,I (6) = c = [ C, C, C, C, C, C] C, 6, (6) Ac =, (7) [ A = I I I I + I I, I I, I I + I I, I I + I I I I ] A, (7) :,, Re( A) c = (8) I( A) n, n (8), V c =, (9) V n 6, n, c ( γ =, c ), 5, [5/]=, (9) V V [8], c Cholesk C K [8], K K,, K, 4 I, ( x,,), = ± x ( x, ), ( J ) () si = K x [ r r t] ± x = x( Kr ± Kr ) () () s, s / x = a + b, r = λ K ( a *Re( I ) b*i( I )), r = λ K ( b*re( I ) + * I( I )) ( λ, λ ) a, b, r, r ( : r r = a, b, a a, b ), r = r : r [ K Re( I )] [ K I( I )] r = λ ( λ r r = ) t λ t, t = λt K,,,, : 4, C, C X CY C ZC, ZC X Y Z ( ),,, r, X Y, Z Z r r X C YCZ C, Z ( ), X, Y,,,, r 5 r [5,9], I () : I R, t,,, R,, ( x,,,) K [ r r t] x = K x αx + γ = β r r r

5 : 96 [ α x + γ, β, ], l L, E,,,,, 6,,, E, l L : Fg6 [8], 6,, 6, : (), ; (), ; E l L Vanshng lne and the lne at nfnt (),, ; (4) ( ), ( ) (5), ( ) 7,,, [,],,, Hough [], n { x } = {( x, )}( =,, n), Q ( x, ) = Ax + Bx + C + Dx + E + F A + B + C + D + E + F = F = Q ( x, ),,, [9,] n =, : α =, β =, γ =, u = v, = ( ) r,, ( :degree) t ( :c) :, : r = [ 7,5, ], 5, t [,, ] = ; r [ 4,5, 6] =, 5, t = [,, 5] ; [,7,7] r =, 5, t [,, ] =, 5, σ ( ), σ 4 ~,, 5 ( 7 9 ) σ 6,,

6 96 Journal of Software,(5) Pxels 8 u 5 6 v Pxels 5 f u f v Fg7 Standard devatons of u and v Fg8 Standard devatons of f u and f v 7 u,v 8 f u, f v (Pxels) Fg9 Standard devaton of s 9 s,,,, ( ) Nose level able Calbratng results at dfferent nose levels f u f v s u v :, 4, 8,, ( ), 6,

7 : u v 4 f u f v Fg Relatve error of u and v Fg Relatve error of f u and f v u,v f u, f v : ( e : e = ( b / a),, a b ),, ( ), u v Fg Relatve error of u and v 5 5 f u f v Fg Relatve error of f u and f v u,v f u, f v Zhang :,,,Zhang ( ) 4 5 u, f u,,,zhang 5 Author s ethod Zhang s ethod Fg4 Relatve error of u 4 u 5 Author s ethod 5 Zhang s ethod Fg5 Relatve error of f u 5 f u CCD, ,, c 4 ( 6 ), 4,

8 964 Journal of Software,(5) Fg6 wo of the 4 real ages taken b dgtal caera 6 4 able Calbratng results fro the 4 ages 4 α β γ u v Coputed value , ( 7 ) 8, 9 ( ), [6],, 8,, 9, 9 Fg7 wo ages of a calbraton rg taken Fg8 wo vews of the reconstructed calbraton rg b dgtal caera 7 8 Zhang,,,,,,,,,,, References: [] Brown, DC Close-range caera calbraton Photograetrc Engneerng, 97,7(8):855~866 [] Fag, Calbraton of close-range photograetr sste: atheatcal forulaton Photograetrc Engneerng and Reote Sensng, 975,4():479~486 [] Zhang, Z A flexble new technque for caera calbraton, IEEE ransactons on Pattern Analss and Machne Intellgence,,():~4

9 : 965 [4] Lebowtz, D, Zsseran, A Metrc rectfcaton for perspectve ages of planes In: Proceedngs of the IEEE Conference on Coputer Vson and Pattern Recognton Santa Barbara, CA:IEEE Coputer Socet, ~488 [5] Stur, P Crtcal oton sequences for onocular self-calbraton and uncalbrated eucldean reconstructon In: Proceedngs of the IEEE Conference on Coputer Vson and Pattern Recognton San Juan, Puerto Rco: IEEE Coputer Socet Press, 997 ~5 [6] Zhang, Z Moton and structure fro two perspectve vews: fro essental paraeters to eucldean oton va fundaental atrx Journal of the ptcal Socet of Aerca A, 997,4():98~95 [7] Yang, CJ, Hu, ZY Planar conc based caera calbraton In: Sanfelu, A, Vllanueve, JJ, Vanrell, M, et al, eds Proceedngs of the Internatonal Conference on Pattern Recognton Barcelona: IEEE Coputer Socet Press, 555~558 [8] Seple, JG, Kneebone, G Algebrac Projectve Geoetr xford: Clarendon Press, 95 [9] Ma, Y, Soatto, S, Kosecka, J, et al Eucldean reconstructon and reprojecton up to subgroups In: Proceedngs of the Internatonal Conference on Coputer Vson Kerkra: IEEE Coputer Socet Press, 999 9~9 [] Booksten, FL Fttng conc sectons to scattered data Coputer Graphcs and Iage Processng, 979,9:56~7 [] Kanatan, K Geoetrc Coputaton for Machne Vson xford: xford Scence Publcatons, 99 [] Xu, L, ja, E Randozed hough transfor(rh): basc echans, algorths, and coputatonal coplextes CVGIP: Iage Understandng, 99,57():~54 [] Roth, G, Levne, MD Extractng geoetrc prtve CVGIP: Iage Understandng, 99,58():~ [4] Ma, Song-de, Zhang, Zheng-ou Coputer Vson Coputng heor and Algorth Bass Bejng: Scence Press, 998 (n Chnese) : [4], :,998 A New Eas Caera Calbraton echnque Based on Crcular Ponts MENG Xao-qao, HU Zhan- (Natonal Laborator of Pattern Recognton, Insttute of Autoaton, he Chnese Acade of Scences, Bejng 8, Chna) E-al: xqeng@csuclaedu; huz@nlpraaccn Abstract: A new eas technque for calbratng a caera based on crcular ponts s proposed he proposed technque onl requres the caera to observe a newl desgned planar calbraton pattern (referred to as the odel plane herenafter) whch ncludes a crcle and a pencl of lnes passng through the crcle s center, at a few (at least three) dfferent unknown orentatons, then all the fve ntrnsc paraeters can be deterned lnearl he an pont of the proposed technque s that t does not need know etrc easureent on the odel plane and the correspondences between ponts on the odel plane and age one, hence t can be done full autoatcall he proposed technque s partcularl useful for those people who are not falar wth coputer vson Experents wth sulated data as well as wth real ages show that the new technque s robust and accurate Ke words: caera calbraton; crcular ponts; odel plane Receved Januar 5, ; accepted Aprl 4, Supported b the Natonal Natural Scence Foundaton of Chna under Grant Nos6,69975; the Natonal Grand Fundaental Research 97 Progra of Chna under Grant NoG9985