ISSN -9825, CODEN RUXUEW E-mail: jos@iscasaccn Journal of Software, Vol7, No5, May 6, pp959 967 ttp://wwwjosorgcn DOI: 36/jos7959 Tel/Fax: +86--62562563 6 by Journal of Software All rigts reserved, +, ( )8) A Vision Based Metod for Aircraft Approac Angle Estimation ZHU Hai-Jiang, WU Fu-Cao +, HU Zan-Yi (National Laboratory of Pattern Recognition (Institute of Automation, Te Cinese Academy of Sciences), Beijing 8, Cina) + Corresponding autor: Pn: +86--826452, Fax: +86--6255993, E-mail: fcwu@nlpriaaccn, ttp://wwwiaaccn Zu HJ, Wu FC, Hu ZY A vision based metod for aircraft approac angle estimation Journal of Software, 6,7(5):959 967 ttp://wwwjosorgcn/-9825/7/959tm Abstract: An algoritm for estimating aircraft approac angle using computer vision is proposed in tis paper During te landing of an aircraft, te descent of te aircraft may be approximately considered as a pure translation motion In tis case te epipole as te same coordinates in all images and is called te Focus-of-Expansion (FOE), and te vanising line of te ground plane is termed te Horizon Furtermore, ow te Focus-of-Expansion and te Horizon are extracted from a few calibrated sequential images is first introduced, ten te aircraft approac angle is derived from tese parameters Simulated and real experiments validate tis algoritm Key words: : aircraft approac angle; FOE (focus-of-expansion); orizon,,, FOE(focus-of-expansion) Horizon FOE Horizon, : ;FOE(focus-of-expansion);orizon : TP39 : A (unmanned aerial veicle UAV) [,2] [3] GPS(global positioning system) INS(inertial navigation system), [5] GPS Supported by te National Natural Science Foundation of Cina under Grant Nos6754, 62759 ( ); te National Hig-Tec Researc and Development Plan of Cina under Grant No2AA42223 ( (863)) Received 4-7-2; Accepted 5--
96 Journal of Software Vol7, No5, May 6,,, [6], 3 : (principal point),,,,,,, (epipole) ( ) FOE(focus-of-expansion), (principal axis, ), FOVC(field of view center) Horizon P P n, FOE W ; P n V, VP V, VP ( ); P,P,,P n t,t,,t n ; FOVC α Camera centre Time t t P t n P P n FOE FOVC VP Image plane W α Ground plane V Fig Geometry of te aircraft approac angle
: 96 2 2 2,P n ;Horizon ;FOE ;VP α β β [],, β FOE VP Horizon P n (Camera centre) FOE β VP Ground plane W α Fig2 Measurement of te approac angle α 2 α V Image plane K, w=k T K, FOE VP e v β T T T e ( K K ) v e w v cos( β ) = = () T T T T T T e ( K K ) e v ( K K ) v e w e v w v β α 2 FOE VP [2] 2, FOE, VP FOE VP, () [3,4] FOE FOE VP X x 2 x, :sx =Hx,H, 3 3 ;s H = 2 3 2 22 32 3 23 33 u s v = 2 3 2 3 22 23 32 33 u u v u 2 + v 2 + v 22 + 3 + 23 x = u, v, x=[u,v,] T [ ] T uu uv 3 3 vu vv i 32 32 u v 33 33, H H 2 n, x x (i=,2,,n) : i i = = A = (2) [ ] T = ; 2 3 2 22 23 3 32 33
962 Journal of Software Vol7, No5, May 6 u v uu vu u u v uv vv v A = M M M M M M M M M u n vn unun vnun un u n vn unvn vnvn vn A, H,, 4 H 4, 4 3, H [5] 3 u l ;l u [] u u 3 l u 2 Fig3 Geometry of Homograpy H H H U=U V U = u, 3 H : [ u ] 2 u3 λ V = λ2 λ 3 (u i U i );V 3 3,λ I (i=,2,3) H λ 2 =λ 3, λ u FOE; λ 2,λ 3 u 2 u 3 l Horizon [5],, w l p v p, l p =w v p (3) Horizon (3) VP :, 4 3 4, 4 P4P [6] FOE VP 4, π Z=, 4 H π, H π =K[r,r 2,t] :K ;r,r 2 R ;t H π R t R,R 2 t,t 2 2
: 963 : T e = K ( R2R ) ( t2 R2R t), e = K ( t R R ) 2 2 2 t R R 2, e =e 2 =K(t 2 t ), FOE VP 3 (), [2] ; (2) (2) H; (3) FOE Horizon;, (3) VP; (4) 2 () 4 4 f u =, f v =,s=,u =3,v =24 (), 4 A,B,C,D 4 Z=, 4 X A =[,,] T,X B =[4,,] T,X C =[5,,] T,X D =[,3,] T r=(8568, 3549,374) T θ =5325π ( r θ R) α [5,75 ], α =,r=z/tan(α),z= C =(77r,77r,z) T t = R C ; 2 C 2 =(47r,47r,667z) T t 2 = R C 2 6 6 σ( ), FOE VP, P4P 4(a) 4(b), RMS(root mean square), 5(a) 5(b) P4P RMS ; RMS, RMS P4P (2), 6 2,3,,6, 5 6, 6(a) 6(b) 5,3,45 RMS,, RMS
964 Journal of Software Vol7, No5, May 6 Mean of te approac angle 8 6 4 Mean of te approac angle 8 6 4 2 4 6 8 2 4 6 8 2 25 Fig4 Noise (pixel) (a) Our metod (a) 2 4 6 8 2 4 6 8 2 Noise (pixel) (b) Based on P4P metod (b) P4P Te averages of te estimated approac angle under different noise levels 4 25 RMS error 5 RMS error 5 5 5 2 4 6 8 2 4 6 8 2 Fig5 Noise (pixel) (a) Our metod (a) 2 4 6 8 2 4 6 8 2 Noise (pixel) (b) Based on P4P metod (b) P4P Te RMS errors of te estimated approac angle under different noise levels 5 RMS
: 965 Mean of te approac angle (degree) 6 55 5 45 4 35 3 25 5 Fig6 2 25 3 35 4 45 5 55 6 Te number of images (a) Te averages of te estimated approac angle (a) RMS errors (pixeeels) 35 3 25 5 5 2 25 3 35 4 45 5 55 6 Te number of images (b) Te RMS errors of te estimated approac angle (b) RMS Te averages and te RMS errors of te estimated approac angle under different number of images 42 6 RMS,, 7 6 5 ; 8 2 6, 35 [2] Canny, 4 ( ); FOE Horizon, 537 2 358, Fig7 Te st image sequence of te lab scene 7
966 Journal of Software Vol7, No5, May 6 Fig8 Te 2nd image sequence of te lab scene 8 2,, 726, 3 9 ( ),FOE Horizon; 7249 Fig9 Te 3rd image sequence of te lab scene 9 3 5,,,, References: [] Suter D, Hamel T, Maony R Visual servoing based on omograpy estimation for te stabilization of an x4-flyer In: Proc of te 4st IEEE Conf on Decision and Control, Vol3 2 2872 2877 ttp://wwwdsengmonaseduau/suter_publications/cdcps
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