I-08- IIS-08- Construction of Overead View Images by Estimating Intrinsic and Extrinsic Camera arameters of Multiple Fis-Eye Cameras Sota Kase, Ryota Okutsu, Hisanori Mitsumoto (Cuo University) Yoei Aragaki, Noriko Simomura (Nissan Motor Co.,Ltd.) Kenji Terabayasi, Kazunori Umeda (Cuo University) Abstract In recent years, active safety tecnologies of cars are becoming important and te cases tat cameras are mounted in cars are increasing. Since te perception of te distance of a usual image is difficult for drivers, metod to construct overead view images and assist drivers are proposed. In tis paper, we propose metods for estimating camera parameters of multiple cameras and construct overead view images wit small errors. Effectiveness of te metods is examined by experiments. (overead view images, fis-eye lens, wide-angle lens, camera calibration, camera paramater ).,., ( ), ()., () ().,,.,,., () (), () (8),,.,.,,..,, ()r f [pixel], (9).,. r f δ ( ) () r f δ sin ( ) () Optical δ rojection plane p Image rp (a) erspective projection Fig.. Optical ' δ rojection plane p p' Image (b) Fis-eye Difference of projection r f δ tan(/) ( ) () r f δ sin(/) ( ) () δ f/w, f : [mm], w : [mm],, r p δ tan ( ) ()..,, p.,, p. rf,, () ()., (8),. /
() (),, sin tan. sin, tan. (0) r f k + k + k + k + k (). k, k, k, k, k (radial distortion)., (Sift of optical ). (, ) m f [ v f ] T., c [c u c v ] T., c m f mf, m f v f γ 0 0 c u v f c v ()., γ, v f., CCD, γ. (), r f q + v f φ arctan v f.! (8),. (),. (), I [k k k k k c u c v] T (9)..,., (, ).,.,.,. Zw Zw Yw Yw ' k Normalized perspective projection image yp δp Fig.. xp Fis-eye image xp vf c φ φ uf erspective projection image vp mp mf mi ui up Coordinate systems Xi Zi Yi vi Overead view image δi, m p [u p v p ] T, m f [ v f ] T., r p δ p tan (0)., q r p u p + vp (). (0), (), p! u p + vp arctan (m p) () δ p, m p., c [c u c v ] T φ r f r p u p + c u, v f r f r p v p + c v (). (), (), (), () m f v f r f (m p ) p u p + v p u p + c u r f (m p ) p u p + v p v p + c v /
F u (m p, I) F v (m p, I) (), m f m p., m i [u i v i] T, m p [u p v p] T.,.,, Y p, X p Z p.,, Z w.,,,, m p X p u p v p X p Y p Z p, x p x p y p,, X w., Y w Z w m p A p x p ()., A p. δ p 0 c pu A p 0 δ p c pv () 0 0,, c p [c pu c pv ] T 0.,, 0 0 0 x p [J 0] X p 0 0 0 X p () 0 0 0., X p p M w (8)., p M w. () (8),, m p A p [J 0] p M w p (9) φ s (a) oint Fig.. n Spere model s (b) Line (). p,. p i p i, Z w 0, (9) s X w i Y w m p p p p p p 0 i p p p X w Y w s H p x w (0), H p., m i [u i v i ] T m i H i x w (), (0), () m p H ph i m i (), m p m i.,,.,.,,..,, (8). (a), φ i T s sin cos φ cos sin sin φ ()., (b) /
s, s i T n n x n y n z (). (), () n s n x sin cos φ + n y cos + n z sin sin φ 0 (). ξ i LX X l (n l s i) () l i I., L, l l., Gauss- Newton. m fi [i v fi ] T, () Brent (), (). s i. n, s, s, n s s s s () (, s s 0). n l, n l µ µx k s k s k s k s k (8). µ,, s k, s k, k., i m fi [i v fi ] T X wi [X wi Y wi Z wi ] T. cam, α cam, β cam., [X cam, Y cam, Z cam ] T,,, E [X cam Y cam Z cam cam α cam β cam] T (9), (8) p M w. X wi m wi, (), (9) m wi m wi (E, X wi ) (0) E, X wi. ξ e NX {m fi m wi (E, X wi )} () i E. N., Gauss-Newton.,,. Yw Zw Fig.. Camera Camera Camera Camera World Coordinate system and camera position (0), I m wi m wi (E, I, X wi ) ()., I, E NX ξ c {m fi m wi (E, I, X wi )} () i,..,.,,.,,. CCD oint Grey Researc Dragonfly, TVM. TVM., 0[pixel] 8[pixel], [pixel] 8[pixel].., cam. cam, Y w 0[deg]. α cam, 0[deg],. Z w 00[mm].,,..,,. Camera, /
(a) Camera (a) Witout optimazation (b) Camera Fig.. Fis-eye images., α cam 0[deg]., β cam 0[deg]. (a), (b).,.,. k, k Camera.. (a) k, k (b) k, k. Camera. α cam 0[deg]. 8.. (b) Wit optimazation Fig.. Effect of simultaneous optimazation Table. camera parameters of camera X cam [mm] Y cam [mm] Z cam [mm] 8.0 909.. 8.9 909.9. α cam [deg] cam [deg] β cam [deg] -.90 8. -.88 -.98 8.0 -.99 k k k.89 0.0 8.88 -..9 k k c u c v 0 -.9.00 0.0-0. 0.9.0 9.90.,,,.,.. /
(a) Witout k, k (b) Wit k, k Fig. 8. Fig.. Effect of Fis-eye camera model cange 8 overead view after integration of four images,,,. K.Asari,Y.Isii,H.Hongo,and H.Kano: A racticable Calibration Metod for Top View Image Generation, SSII0,IN- (00) :,, IN- (00) K. Oizumi: Development of All-Around View System, Sae Tecnical aper Series (00) M.Suzuki,S.Cinomi,and T.Takano: Development of Around View System, JSAE roceedings, No.-0, pp.-(00) :,, No.-0, pp.-(00) :,, pp.-8, (999) Z. Zang: A Flexible New Tecnique for Camera Calibration, IEEE Transcations on attern Analysis and Macine Intelligence, Vol., No., pp.0- (000) H.Komagata,I.Isii,A.Takaasi,and D.Wakatsuki: A Geometric Calibration Metod of Internal Camera arameter for Fis-Eye Lenses, IEICE D-II, Vol.J89-D- II, No., pp.-(00) :, D-II, Vol.J89-D-II, No., pp.-(00) M.Nakano,S.Li,and N.Ciba: Calibrating of Fiseye Camera for Aquisition of Sperical Image, IEICE D- II, Vol.J88-D-II, No.9, pp.8-8(00) :, D-II, Vol.J88- D-II, No.9, pp.8-8(00) 8 M.Nakano,S.Li,and N.Ciba: Calibrating Fiseye Camera by Stripe attern Based upon Sperical Model, IEICE D, Vol.J90-D, No., pp.-8(00) :, D, Vol.J90-D, No., pp.-8(00) 9 :, industrial, pp.-0, (00) 0 S.Kase,H.Mitsumoto,Y.Aragaki,N.Simomura,and K.Umeda: A Metod to Construct Overead View Images Using Multiple Fis-Eye Cameras, JSME ROBOMEC,Nagano(008) :,, (008) :, (CG-ARTS ), (00) W.H. ress,s.a. Teukolsky,W.T.Vetterling,and B.. Flanery ( ),,,, ( ): Numerical Recipes in C,, pp.-, (99) /