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1 (2001) ( ) * Structure from motion, *
2 Image-Based Rendering, Virtualized Reality, Augmented Reality Mixed Reality structure from motion 3 structure from motion 3
3 Kanade-Lucas-Tomasi (Shi and Tomasi (1994)) (Xu and Zhang (1996)) image plane camera center pixel coordinate 3 1..
4 (camera coordinate) 2 (image coordinate) 2 XY Z optical axis Z X Y xy x y X Y x y X Y (X, Y, Z) T 3 (x, y) T (1.1) x = l X Z, y = l Y Z l (focal length) 3 (1.1)
5 (1990) 3 3 Tomasi and Kanade (1992) F P P 3 F FP FP 2 3 FP 2F P F 2F 3 P 3 3 P = Singular Value Decomposition; SVD
6 Necker Reversal Necker Reversal 2 3 (Christy and Horaud (1996)) f p X fp =(X fp,y fp,z fp ) T f p x fp =(x fp,y fp ) T l ψ! ψ! (2.1) x fp = l X fp x fp = l X fp Z fp Y fp l Z fp 3
7 paraperspective (Poelman and Kanade (1997)) scaled orthographic 2.2 Paraperspective (2.1) X f x f (G) X fp = X fp X f x fp = x fp x f (2.1) (2.2) ψ x fp l! l = Z f + Zfp (X f + X fp) ρ ff = l I 3 1 X f (0, 0, 1) X fp + l X f + O( X fp 2 ) Z f Z f Z f O( X fp 2 ) X fp x fp ψ! ψ! (2.3) x fp = l Z f 0 X f Zf 2 X fp + l X f = A para f X fp + x f 0 Z f Y f Z f Y f
8 paraperspective A para f paraperspective Zfp Z f 3 paraperspective 4 1. X fp Z = Z f X f l/z f 2.3 Scaled orthographic Paraperspective X f /Z f 0, Y f /Z f 0 paraperspective (2.3) ψ! (2.4) x fp = l X fp = A scaled f X fp Z f scaled orthographic weak perspective A scaled f scaled orthographic scaled orthographic 4 1. X fp Z = Z f l/z f 2.4 Scaled orthographic Z 1 Z, Z 2 Z,...,Z F Z (2.4) (2.5) x fp = l Z ψ l/z Y fp! X fp (2.6) Y fp = l Z X fp (2.5) (2.7) x fp = ψ ! Y fp = A ortho f Y fp A ortho f paraperspective scaled orthographic 4
9 scaled orthographic paraperspective (MAP; Metric Affine Projection) (Generalized Affine Projection) Mundy and Zisserman (1992) Mundy and Zisserman (1992) X fp x fp (2.8) x fp = A f X fp + u f (2 3) A f u f A f A f u f A f MAP 1997b scaled orthographic ψ! ψ! (2.9) x fp = l X fp x fp = l (tx fp ) (t>0) Z f tz f t t t Z f tz f t Z f λ f = tz f λ f = tz f A f λ f A f
10 λ f B f (2.10) A f = 1 λ f B f B f A f B f Bf T B f u f xf l = l λ f X f (Metric Affine Projection MAP) MAP (2.11) x fp = A f X fp = 1 λ f B f X fp, X f = λ f l A f A f MAP 2.6 MAP B f (2.12) B f = R f Σ f D f, R T f R f = D f D T f = I 2, Σ f = diag{p f,q f } B f R f Σ f D f (2.11) MAP (2.13) x fp = A f X fp = 1 λ f R f Σ f D f X fp D f =(c f, d f ) T ψ! (2.14) χ fp = D f X fp = fdf X fp χ fp X fp span{c f, d f } c f, d f A T f {c f, d f } e Y 2 3 Y =(Y1, Y 2 ) T 3 3 (Y 1, Y 2, Y 1 Y 2 ) T 1 (2.15) x fp = R f Σ f χ fp λ f 1 λ f χ fp X fp span{c f, d f } scaled orthographic {c f, d f } f Df 3 MAP span{c f, d f } scaled orthographic {c f, d f } R f Σ f (2.16) 1 χ fp = Σ 1 f Rf T x fp λ f ψ x f l!
11 MAP. MAP scaled orthographic scaled orthographic Xu and Sugimoto 1998 MAP λ f MAP λ f 2 1 λ f 1 {λ f } F f=1 {λ f } F f=1 (Xu and Zhang (1996)) 4 {λ f } F f=1 {λ f } F f=1 2 MAP MAP span{c f, d f } scaled orthographic span{c f, d f } (virtual image plane) MAP (Tomasi and Kanade (1992))
12 f t f f {i f, j f } k f C f =(i f, j f, k f ) T p s p f X fp (3.1) s p = t f + C T f X fp s s p = s p s, t f = t f s (3.2) s p = t f + C T f X fp X fp = C f (s p t f ) (2.11) MAP (3.3) x fp = A f X fp = A f C f s p, t f = λ f Cf T l (A f C f ) T 3.1 P F 2 (3.3) F f=1; P p=1 {C f } F f=1, {s p} P p=1 {λ f } F f=1 FP (3.3) F f=1; P p=1 {C f } F f=1, {s p} P p=1 {λ f } F f=1 W M S (3.4) W = M = 0 0 W 1. W F T M 1. M F 1 C 1 C (3.5) W = M A, W f =(x f1,...,x fp), ψ x f l A, M f = A f C f, S =(s 1,...,s P ) S (2F 3) (3 P ) (3.5) (3.3) F f=1; P p=1 M {C f } F f=1 {λ f } F f=1 S {s p} P p=1 W M S W M S C f 3 (3.6) M f Mf T = A f A T f = 1 B λ 2 f Bf T f λ f W (3.6) F f=1 M S!
13 W (3.5) 3 (3.7) W = ˆM Ŝ (2F 3) (3 P ) = 0 ˆM 1.. ˆM F 1 C A Ŝ Yokoya et al M, S, ˆM,Ŝ (3.8) M = ˆMA, S = A 1 Ŝ 3 3 A ˆM Ŝ 3 3 A A A Q = AA T (3.6) (3.9) ˆM f Q ˆM f T = A f A T f = 1 B λ 2 f Bf T f (3.9) F f=1 {λ f } F f=1 Q B f B f R f Σ f D f R f,σ f (3.10) ˆPf =(ˆp f, ˆq f ) T = R T f ˆM f, P f = R T f M f (3.9) (3.11) ˆPf Q ˆP f T = 1 Σ λ 2 f 2 f (3.11) (3.12) ˆp T f Qˆp f = p2 f, λ 2 ˆp T f Qˆq f =0, ˆqT f Qˆq f = q2 f f λ 2 f ˆpT f Qˆp f p 2 f λ f = ˆqT f Qˆq f q 2 f = 1, λ 2 ˆp T f Qˆq f =0 f (3.13) q 2 f ˆp T f Qˆp f p 2 f ˆq T f Qˆq f =0, ˆp T f Qˆq f =0 3 3 Q Q
14 Q = (G) (average depth) {λ f } F f=1 s (3.14) λ f = p 2 f ˆp T f Qˆp f = s q 2 f ˆq T f Qˆq f Q Q Q =(Q ij ) q =(Q 11,Q 12,Q 13,Q 22,Q 23,Q 33 ) T a, b (3.15) ω(a, b) T q = a T Qb 6 ω(a, b) (3.13) (3.16) ψ! qf 2 ω(ˆp f, ˆp f ) T p 2 f ω(ˆq f, ˆq f ) T ω(ˆp f, ˆq f ) T q = ˆ! T f q = 0 2 (3.17) Ω =(ˆ! 1,..., ˆ! F ) T (3F 6) 0 q ω(ˆp 1, ˆp 1 )=1 ψ! ψ! ω(ˆp (3.18) 1, ˆp 1 ) 1 q = Ω 0 2F (3.19) q = ψ ω(ˆp 1, ˆp 1 ) Ω! + ψ! 1 0 2F q 2 X + X s s p 2 f (3.20) λ f = ω(ˆp f, ˆp f ) T q = qf 2 ω(ˆq f, ˆq f ) T q Q Q Q Q Q (Quan (1996)) Q 3 Q Q = LL T A A = L T U( U O(3)) M, S (3.21) M = ˆML T U, S = U T LŜ U M S detu 2
15 Necker reversal. f M f V f = λ f Σ 1 f P f C f (3.22) C f =(f Af ) 1 g Mf =(f Df ) 1 f Vf t f (3.3) detu 2 MAP 2 MAP Necker Reversal Necker Reversal 6 2 Necker Reversal 2 MAP Necker Reversal S S S diag{ 1, 1, 1}S S C f S H f C f,h f 3 1 (3.23) A f C f = A f H f D f C f = D f H f (3.24) H f =(f Af ) 1 diag{ 1, 1, 1}f Af C f =(f Df ) T diag{ 1, 1, 1}f Df C f scaled orthographic paraperspective (3.25) H f = 8 >< >: diag{ 1, 1, 1}C f ψ 1 2x para f xpara T f gf 2 I 2 g 2 f 2lx para T f 2lx para f g 2 f 2u 2 f! C f scaled orthographic (paraperspective)
16 MAP Necker reversal S C f diag{ 1, 1, 1}S K f C f,k f 3 1 (3.26) A f C f = A f K f diag{ 1, 1, 1} D f C f = D f K f diag{ 1, 1, 1} (3.27) K f = H f diag{ 1, 1, 1} =(f Af ) 1 diag{1, 1, 1}f Af C f diag{ 1, 1, 1} =(f Df ) T diag{1, 1, 1}f Df C f diag{ 1, 1, 1} (3.28) K T f = diag{ 1, 1, 1}C T f (f Df ) T diag{1, 1, 1}f Df diag{ 1, 1, 1}X X 1 Xdiag{1, 1, 1} X 3 C T f K T f MAP Necker Reversal 3 ranks =3 4 rankm =2 {M T f } F f=1 F MAP
17 MAP 3 MAP 3 MAP MAP rankm =2 MAP 3 rankm =3 rankm = ranks =3 rankm = ranks =3 W (2F P ) = M(2F 3) S (3 P ) M S 1997a Q Necker Reversal Q 1 (3.11) Q 3 2 span{ˆp f, ˆq f } MAP 3 Q 2 j i span{ˆp j, ˆq j } span{ˆp i, ˆq i } 2 j Q i Q Q 1 (3.11) Q 6 2 Q 2 Q 6 Q 1997a Q Koenderink and van Doorn (1991) (1997a) 1
18 i, j 2 span{ˆp j, ˆq j } span{ˆp i, ˆq i } 1 span{ˆp j, ˆq j } span{ˆp i, ˆq i } λ i λ j ĉ ij span{ˆp i, ˆq i } span{ˆp j, ˆq j } ĉ ij 0 3 ˆP i T ˆP j T 2 ĥi, ĥj (4.1) ĉ ij = ˆP T i ĥi = ˆP T j ĥj (3.11) (4.2) λ i : λ j = Σ j ĥ j : Σ i ĥ i {λ f } F f=1 {λ f } F f=1 Σ f (3.11) (4.3) ˆVf =(ˆv f, ŵ f ) T = λ f Σ 1 f ˆP f, V f = λ f Σ 1 f P f (4.4) ˆVf Q ˆV T f = I 2 ( ˆV f ˆV f )cs Q =csi 2 cs (4.4) 2 MAP MAP (4.5) ˆV = ( ˆV 1 ˆV 1 ) T,..., ( ˆV F ˆV F ) T T, I = (cs I2,..., cs I 2 ) T cs Q = ˆV + I Q ĉ ij 2 2 1,2 ĉ 12 ĉ ĉ Q =1 â, ˆb (4.6) â = ĉ, ŵ 1 Qˆv 1 ĉ, ˆv 1 Q ŵ 1, (4.7) ˆb = ĉ, ŵ2 Qˆv 2 ĉ, ˆv 2 Q ŵ a 1999 â Q = ˆb Q = ĉ Q =1, â, ĉ Q = ˆb, ĉ Q =0, (4.8) â span{ˆv 1, ŵ 1 }, ˆb span{ˆv2, ŵ 2 }, ĉ span{ˆv 1, ŵ 1 } span{ˆv 2, ŵ 2 } span{ˆv i, ŵ i } = span{ˆp i, ˆq i }(i =1, 2) â {ˆv 1, ŵ 1, ˆv 1 ŵ 1 } {a, c, ˆv 1 ŵ 1 } ˆb 8 (4.8) 5 (4.4) f=1,2 5 â, ˆb Q Q â, ˆb 2 Q â 2 Q ˆb 2 Q =1 (4.9) â, ˆb Q = cos 2θ, 0 < 2θ <π
19 θ 0,π P =(â, ˆb, ĉ) cos 2θ 0 B Q=P C cos 2θ 1 0A P 1 = P T K diag{2 cos 2 θ, 2sin 2 θ, 1}K T P 1, (4.10) K= 0 1/ 2 1/ 2 0 1/ 2 1/ C A (4.11) A = P T Kdiag{ 2 cos θ, 2sinθ, 1}U 3, U 3 O(3) X T =(X T ) U 3 U 3 I 3 O(3) {M,S } 1 θ (4.12) (4.13) M(θ) T = diag{ 2 cos θ, 2sinθ, 1}K T P 1 ˆM T, S (θ) = diag{1/ 2 cos θ, 1/ 2sinθ, 1}K 1 P T Ŝ M(θ) T = diag{ 2 cos θ, 2sinθ, 1}M(π/4) T, S (θ) = diag{1/ 2 cos θ, 1/ 2sinθ, 1}S (π/4) M(θ) T M(π/4) T diag{ 2 cos θ, 2sinθ, 1} S (θ) S (π/4) diag{1/ 2 cos θ, 1/ 2sinθ, 1}
20 θ = π/4. ĉ span{ˆv 1, ŵ 1 } span{ˆv 2, ŵ 2 } 2 (4.14) c = diag{ 2 cos θ, 2sinθ, 1}KP 1 ĉ =(0, 0, 1) T a span{ˆv 1, ŵ 1 } b span{ˆv 2, ŵ 2 } (4.15) a =( cos θ, sin θ, 0) T, b = (cos θ, sin θ, 0) T a = b, a c, b c c (4.16) u =(1, 0, 0) T, v =(0, 1, 0) T M(θ) T M(π/4) T u v c 2 cos θ 2sinθ 1 S (θ) S (π/4) u v c 1/ 2 cos θ 1/ 2sinθ θ c θ 4.3 MAP 2 3 Necker Reversal Q Necker Reversal r T Qr =1 λ f 2 λ f 2 10 a 2 MAP 3 10 b 3 MAP
21 MAP 1997b Ullman (1979) 3 ˆπ i (i =1, 2, 3) 11 2 (a) ˆπ 1 ˆπ 2 ˆπ 3 1 ê 1 ˆπ 2 ˆπ 3, ê 2 ˆπ 3 ˆπ 1, ê 3 ˆπ 1 ˆπ 2 ê i ( 0) (i =1, 2, 3) ê 1 Q, ê 2 Q, ê 3 Q, ê 1, ê 2 Q, ê 2, ê 3 Q, ê 3, ê 1 Q Q (b) ˆπ 1 ˆπ 2 ˆπ 3 ê ˆπ 1 ˆπ 2 ˆπ 3 ê i ˆπ i ê i ê ê i ê, ê i ( 0) (i =1, 2, 3) ê 3 = e 1 ê 1 + e 2 ê 2 e 1,e 2 0 ê 3 2 Q = e 2 1 ê 1 2 Q +2e 1 e 2 ê 1, ê 2 Q + e 2 2 ê 2 2 Q ê 1, ê 2 Q ê Q, ê 1 Q, ê 2 Q, ê, ê 1 Q, ê, ê 2 Q, ê 1, ê 2 Q Q 5. W MAP W 3 W (2F P ) = ˆM (2F 3) Ŝ (3 P ) MAP W
22 W 3 4 MAP W 3 3 MAP 3 3 MAP W W = MS W M,S W M, S AB BA AB BA 0 W T W 0 (M T M)(S T S ) 0 Φ (S S T ) 1 (µ) = det(m T M µ(s S T ) 1 )=0 M T M 0 W 0 W T W 0 W M T M S S T s p (5.1) Cov(s p)= 1 P S S T S S T M T M M 1 FX (5.2) M T 1 M = np o 2 f v f v T f + qf 2 T w f w f λ 2 f=1 f M T M {v f, w f } F f=1 {p f /λ f,q f /λ f } F f=1 S S T (S S T ) 1 M T M
23 W T W LMeds 1999b 6. MAP MAP MAP 2 (Christy and Horaud (1996) Strum and Triggs (1996) Ueshiba and Tomita (1998) (1998)) MAP 1 MAP Strum and Triggs (1996) Ueshiba and Tomita(1998) (1998) 2
24 Strum and Triggs (1996) Christy and Horaud (1996) paraperspective paraperspective Christy and Horaud (1996) paraperspective f p x per fp f p paraperspective x para fp 12 (6.1) x para fp x per fp = µ fpx per fp, µ fp = λ fp λ f = x per fp x f x para fp = x para fp x f Ueshiba and Tomita 1998 λ fp (projective depth) f p µ fp f p Christy and Horaud (1996) (6.1) paraperspective paraperspective W (6.2) W = 0 µ 11x µ 1P x 1P µ F 1x F 1... µ FPx FP x fp = x fp x f 1 C A 12. paraperspective.
25 Christy and Horaud (0) µ fp =1 paraperspective M (+),S (+) M ( ),S ( ) M (±),S (±) (6.1) µ (±) fp (1) W (±) paraperspective (2) W (±) 2 M (±),S (±) M (±),S (±) (3) M (±),S (±) (6.1) µ (±) fp (4) µ (±) fp ɛ (1) (5) M (±) ˆx fp M (+),S (+) M ( ),S ( ) X f, p ˆx fp x fp MAP Morita and Kanade Morita and Kanade (1997) (1998) (1998) Christy and Horaud (1996) (Fujiki and Kurata (2000)) 7.1 MAP W W W 3 P 2F 3
26 W 3 S W 3 (3.6) M l T 1, l T 2, l T 3 M = (l 1, l 2, l 3 ) T W W = MS, MM T = 0 l T 1 l 1 l T 2 l 1 l T 3 l 1 l T 1 l 2 l T 2 l 2 l T 3 l 2 l T 1 l 3 l T 2 l 3 l T 3 l 3 M M 3 I (3.5) 3 M M M M T M M M T M (sufficient statistic) M M (7.1) M T M = M T M M M (7.1) M 1 C A
27 M (7.2) M = FΛE E Λ M F ΛE F (7.3) M = ΛE M M T M = M T M M M 3 3 M 2F 3 M 3 3 X X T X = M T M X = U M U O(3) M 1 M ( ) (7.4) W = MS, MM T = Λ 2 F +1 (2F +2) P (W T,W T F +1) T 5 P (W T,W T F +1) T 5 MAP MAP W MAP W = MS W = MS (7.5) W T W = S T M T MS = S T M T MS = W T W W, W W T W, W T W MAP M 3 E Λ
28 MAP 1998 Christy and Horaud (1996) paraperspective (Fujiki and Kurata (2000)) 2 2 Sref,S ob SrefS ob T SrefS ob T = UDV T Sob Sref = ESob E 2 (7.6) E = UV T (0) 3 (1) 5 P (2) (1) MAP (1998) (0) k( 3) W (1) f( k) M [f] f W [f] M [f] M T [f] = Λ 2 [f] f +1 Wf+1 f W[f] f +1 W[f+1] W[f+1] =(W[f] T,Wf+1) T T f 1 f [f] (2) M [f+1] = (M T [f],mf+1) T T S [f+1] Q ˆM [f] Q ˆM T [f] = M [f] M T [f] = Λ 2 [f] = diag{λ [f],1,λ [f],2,λ [f],3 }, ˆV f+1 Q ˆV f+1 T = V f+1 Vf+1 T = I 2 ψ! ˆM[f] ˆV [f+1] = ˆM [f], I [f+1] = ˆV f+1 ˆV f+1 ψ! cs (Λ 2 [f]) cs I 2 cs Q = ˆV + [f+1] I [f+1] ˆM [f] =(ˆl [f],1,ˆl [f],2,ˆl [f],3 ) T Ω [f+1] L [f+1] Ω [f+1] =(ω [f],11,ω [f],22,ω [f],33,ω [f],12,ω [f],13,ω [f],23, ˆω f+1 ) T, ω [f],ij = ω(ˆl [f],i,ˆl [f],j ), L [f+1] =(λ 2 [f],1,λ 2 [f],2,λ 2 [f],3, 0 T 3, 1, 0, 1) T
29 q =Ω + [f+1] L [f+1] dets [f] S T [f+1] > 0 Q (1) 6 (Fujiki and Kurata (2000)) (Costeria and Kanade(1998) Gear(1998)) 1998 (Quan and Kanade (1997) Morris and Kanade (1998)) Christy, S. and Horaud, R. (1996). Euclidean reconstruction: From paraperspective to perspective, Proceedings of 4th European Conference on Computer Vision, 2, Costeria, J. P. and Kanade, T. (1998). A multibody factorization method for independently moving objects, International Journal on Computer Vision, 29(3), (2000). Paraperspective , D 12 50, p (1997a). PRMU 97 22, (1997b). PRMU , Fujiki, J. and Kurata, T. (2000). Recursive factorization method for the paraperspective model based on the perspective projection, Proceedings of 15th International Conference on Pattern Recognition, 1, (1998). PRMU , Gear, C. W. (1998). Multibody grouping from motion images, International Journal on Computer Vision, 29(2), (1993). J76-D-II (8), (1990). 3 (1998). PRMU 98 26, 1 8. Koenderink, J. J. and van Doorn, A. J. (1991). Affine structure from motion, J. Opt. Soc. Amer. A, 8(2),
30 ,, (1999a). 40(8), ,, (1999b). PRMU , Morita, T. and Kanade, T. (1997). A sequential factorization method for recovering shape and motion from image streams, IEEE Trans. Pattern Analysis and Machine Intelligence, 19(8), Morris, D. D. and Kanade, T. (1998). A unified factorization algorithm for points, line segments and plane with uncertainty models, Proceedings of International Conference on Computer Vision 98, Mundy, J. L. and Zisserman, A. (ed.) (1992). Geometric Invariance in Computer Vision, MIT press Cambridge, Massachusetts. (1998). J81-D-II 3, Poelman, C. J. and Kanade, T. (1997). A paraperspective factorization method for shape and motion recovery, IEEE Trans. Pattern Analysis and Machine Intelligence, 19(3), Quan, L. (1996). Self-calibration of an affine camera from multiple views, International Journal on Computer Vision, 19(1), Quan, L. and Kanade, T. (1997). Affine structure from line correspondences with uncalibrated affine cameras, IEEE Trans. Pattern Analysis and Machine Intelligence, 19(8), Shi, J. and Tomasi, C. (1994). Good features to track, Proceedings of Computer Vision and Pattern Recognition 94, Sturm, P. and Triggs, B. (1996). A factorization based algorithm for multi-image projective structure and motion, Proceedings of 4th European Conference on Computer Vision, 2, Tomasi, C. and Kanade, T. (1992). Shape and motion from image streams under orthography: A factorization method, International Journal on Computer Vision, 9(2), Ueshiba, T. and Tomita, F. (1998). A factorization method for projective and Euclidean reconstruction from multiple perspective views via iterative depth estimation, Proceedings of 5th European Conference on Computer Vision, Ullman, S. (1979). The interpretation of visual motion, MIT Press, Cambridge, Massachusetts. Xu, G. and Sugimoto, N. (1998). A linear algorithm for motion from three weak perspective images using Euler angles, Proceedings of Asian Conference on Computer Vision 98, Xu, G. and Zhang, Z. (1996). Epipolar Geometry in Stereo, Motion and Object Recognition A Unified Approach, Kluwer, Dordrecht. Yokoya, N., Takemura, H. and Hwang, K. (1998). A factorization method using 3-d linear combination for shape and motion recovery, Proceedings of International Conference on Pattern Recognition 98,
31 Proceedings of the Institute of Statistical Mathematics Vol. 49, No. 1, (2001) 107 3D Reconstruction from Sequences of 2D Images under Point Correspondences An Mathematical Analysis of the Factorization Method Jun Fujiki (National Institute of Advanced Industrial Science and Technology) Recovering the camera motion and the object shape from multiple images is a fundamental and important problem in the field of computer vision. Especially, the problem under point correspondences is the most fundamental and most important. To solve this problem, many methods are presented and among them, the factorization method is an excellent method because it is stable in numerical computation and it gives good reconstruction although it is based on the affine approximation of the perspective projection. The factorization method is useful not only for solving the problem, but also for understanding the mathematical meaning of the problem under affine approximated projection. In this paper, the mathematical analysis of recovering the camera motion and the object shape from multiple affine approximated projection images under point correspondences by the factorization method is considered. The way to recover the camera motion and the object shape from perspective images by estimating the affine approximated projection images from perspective images and the recursive factorization method are also considered. Key words: Structure from motion, factorization method, recursive, Metric Affine Projection, perspective projection.
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28 Horizontal angle correction using straight line detection in an equirectangular image 1170283 2017 3 1 2 i Abstract Horizontal angle correction using straight line detection in an equirectangular image
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1 1 1 1 2 1. Visual Recognition of Wire Harnesses for Automated Wiring Masaki Yoneda, 1 Takayuki Okatani 1 and Koichiro Deguchi 1 This paper presents a method for recognizing the pose of a wire harness
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[II] Optimization Computation for 3-D Understanding of Images [II]: Ellipse Fitting 1. (1) 2. (2) (edge detection) (edge) (zero-crossing) Canny (Canny operator) (3) 1(a) [I] [II] [III] [IV ] E-mail sugaya@iim.ics.tut.ac.jp
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Vol. 1 No. 2 41 49 (July 2008) 3 1 1 3 2 1 1 3 Person-independent Monocular Tracking of Face and Facial Actions Yusuke Sugano 1 and Yoichi Sato 1 This paper presents a monocular method of tracking faces
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Curved Document Imaging with Eye Scanner Toshiyuki AMANO, Tsutomu ABE, Osamu NISHIKAWA, Tetsuo IYODA, and Yukio SATO 1. Shape From Shading SFS [1] [2] 3 2 Department of Electrical and Computer Engineering,
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a) Change Detection Using Joint Intensity Histogram Yasuyo KITA a) 2 (0 255) (I 1 (x),i 2 (x)) I 2 = CI 1 (C>0) (I 1,I 2 ) (I 1,I 2 ) 2 1. [1] 2 [2] [3] [5] [6] [8] Intelligent Systems Research Institute,
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IP 06 16 / IIS 06 32 3 3-D Environment Modeling from Images Acquired with an Omni-Directional Camera Mounted on a Mobile Robot Atsushi Yamashita, Tomoaki Harada, Ryosuke Kawanishi, Toru Kaneko (Shizuoka
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21 Edge Feature for Monochrome Image Retrieval 1100311 2010 3 1 3 3 2 2 7 200 Sobel Canny i Abstract Edge Feature for Monochrome Image Retrieval Naoto Suzue Content based image retrieval (CBIR) has been
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a) Extraction of Similarities and Differences in Human Behavior Using Singular Value Decomposition Kenichi MISHIMA, Sayaka KANATA, Hiroaki NAKANISHI a), Tetsuo SAWARAGI, and Yukio HORIGUCHI 1. Johansson
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形状変形による古文書画像のシームレス合成
Use of Shape Deformation to Seamlessly Stitch Historical Document Images Wei Liu Wei Fan Li Chen Sun Jun あらまし 1 2 Abstract In China, efforts are being made to preserve historical documents in the form
IPSJ SIG Technical Report Vol.2014-DPS-158 No.27 Vol.2014-CSEC-64 No /3/6 1,a) 2,b) 3,c) 1,d) 3 Cappelli Bazen Cappelli Bazen Cappelli 1.,,.,.,
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24 Depth scaling of binocular stereopsis by observer s own movements 1130313 2013 3 1 3D 3D 3D 2 2 i Abstract Depth scaling of binocular stereopsis by observer s own movements It will become more usual
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(MIRU2008) 2008 7 525 8577 1 1 1 E-mail: matsuzaki@i.ci.ritsumei.ac.jp, shimada@ci.ritsumei.ac.jp Object Recognition by Observing Grasping Scene from Image Sequence Hironori KASAHARA, Jun MATSUZAKI, Nobutaka
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1 Abstract n 1 1.1 a ax + bx + c = 0 (a 0) (1) ( x + b ) = b 4ac a 4a D = b 4ac > 0 (1) D = 0 D < 0 x + b a = ± b 4ac a b ± b 4ac a b a b ± 4ac b i a D (1) ax + bx + c D 0 () () (015 8 1 ) 1. D = b 4ac
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IS1-09 第 回画像センシングシンポジウム, 横浜,14 年 6 月 MI-Hough Forest () E-mail: ym@vision.cs.chubu.ac.jphf@cs.chubu.ac.jp Abstract Hough Forest Random Forest MI-Hough Forest Multiple Instance Learning Bag Hough Forest
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1 1 1, Extraction of Transmitted Light using Parallel High-frequency Illumination Kenichiro Tanaka 1 Yasuhiro Mukaigawa 1 Yasushi Yagi 1 Abstract: We propose a new sharpening method of transmitted scene
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