boost_sine1_iter4.eps
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- へいぞう かむら
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1 3 (, 3D ) D 3D....,,. a + b = f, a, f. b a (.) b a.: b f (.2), b f., f.2.
2 2 Y y Q(X,Y,Z) O f o q(x,y) Z X x image plane.2:.2, O, z,. O..2 (X, Y, Z) 3D Q..2 O f, x, y X, Y. Q OQ q, q (x, y). x = f X Z, y = f Y Z (.3).3 Q (X, Y, Z) (x, y) (perspective transformation)...3, 3D,. 3D u = (u, u 2, u 3 ) t.4, q., t... [.] 3D u q. O q (x, y, f) u []. ( ) (X 0, Y 0, Z 0 ), u 3D t,. X = X 0 + tu, Y = Y 0 + tu 2, Z = Z 0 + tu 3 (.4),. x = f X Z = f X 0 + tu Z 0 + tu 3,
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3 .. 3D 3.3: 3D Y y q Z O u x X.4: t, (X 0, Y 0, Z 0 ). y = f Y Z = f Y 0 + tu 2 Z 0 + tu 3 (.5) x = fu /u 3, y = fu 2 /u 3 (.6).. (f u u 3, f u 2 u 3, f) (.7) O (u, u 2, u 3 ) t.
4 33 2,.,.,., ,., (pixel).,, (, ) A/D., 8bit, (a) (b) 2.:
5 ,,,. 2.2 (x, y), w(i, j), f(x, y), f(x, y). w 2.2: f(x, y) = Σ s s Σ i= s j= s w(i, j)f(x + i, y + j)/ Σ s s Σ i= s j= s w(i, j) (2.), s 2s +. w(i, j) =, Gaussian. Gaussian w(i, j). w(i, j) = exp( i2 + j 2 2σ 2 ) (2.2) σ 2., σ 2., 2.3(a) 2.3(b). 2.3(a) 2.3(b)., σ 2 Gaussian 2.4(b),(c). σ 2,. 2..2,.,,.,
6 (a) (b) 2.3: (a) (b) σ = 0.5 (c) σ = : Gaussian. (Sobel) x D x y D y j i (a) Dx (b) Dy. 2.5: g x (x, y) = Σ Σ i= j= D x (i, j)f(x + i, y + j)
7 05 3, 2,,,. 3. Bayesian Filter [33],,., [33] F. F x...x F. x i x i. x i, i =,..., F z i, i =,..., F. X : {x,..., x }, Z : {z,..., z }., p i p(x i x,..., x i, z,..., z i ).,. P = p(x :F Z :F ) = p(x Z )p(x 2 X, Z :2 )...p(x F X :F, Z :F ) = p p 2...p F (3.), t p i p t i. p t i p(x t i X t :i, Z t :i, p t i ) (3.2)
8 06 3,. P t = p(x t,...x t F z t,...z t F ) = p(x t Zt, pt )...p(x t F Xt :F, Zt :F, pt F ) = p t p t 2...p t F (3.3) Bayesian filter Bayesian filter p(x t Zt0:t )., x x i, i <. section. Bayesian filter hypothesis generation-hypothesis correction. (Hypothesis generation), dynamic model p(x t xt ) t p(x t Z t0:t ). p(x t Zt0:t ) = x t p(x t xt )p(x t (lielihood) hypothesis correction. (Hypothesis correction) Z t0:t )dx t (3.4) observation model p(z t xt ), t p(xt Zt0:t )., α t. p(x t Z t0:t ) = α t p(z t x t )p(x t Z t0:t ) (3.5) Bayesian filter Kalman filter particle filter.. a.kalman filter dynamic model p(x t xt ) observation model p(z t xt ). p(x t x t ) = N(H t x t ; Σ t,h) (3.6) p(z t xt ) = N(M t xt ; Σt,m ) (3.7), H t M t. Σt,h Σt,m white noise. 3.6, 3.7 Bayesian filter 3.4, 3.5, hypothesis generation hypothesis correction
9 [36], 2 2,,. Yuan [36]. 3 3 reference plane i, i =, 2,... 3D P (x, y, z) 3 P i (x i, y i, z i ), 2 p i (u i, v i, ). 2 i, i + reference plane Π i,i+. i =, 2., P Π 2 p 2 p Homography H 2 p H 2 p 2. intensity P reference plane Π 2 planar pixels. residual pixels. process 3.5, Initial detection Homography based detection. residual pixels Parallax filtering, process Epipolar Structure consistency 2. Epipolar motion regions., Structure consistency reference plane Π 2 Parallax pixels, motion regions. Structure consistency 3 p, p 2, p 3 Π 2, Π P(x, y, z) i 3 P i R i, T i P. P i = R i P + T i (3.77), R = I, T = 0.
10 22 3 Original image Planar pixels Y Homography consistent? N Epipolar consistent? Y Structure consistent? Y Parallax pixels N N Initial detection (Homography based detection) Motion regions Parallax filtering 3.5: P i p i. p i = K i P i /z i (3.78), K i i P 2 p, p 2 (Fundamental matrix)f 2. p T 2 F 2 p = 0 (3.79). p 3.79.,, 3.79 P,., P C, C P,.,,,, Structure consistency.
11 P P P l l p p 2 p p 2 2 C C 2 3.6: P P C C 2 l l 2 d epi. d epi ( l p + l 2 p 2 )/2 (3.80), l l = F2p T 2, l 2 2 l 2 = F 2 p. l p p l, l 2 p 2 p 2 l Structure Consistency 3D reference plane Π : N P = d (3.8)., N = (N x, N y, N z ) T Π, d Π. Π P Π H. γ H = N P d (3.82) γ H/z (3.83). Π P 0. P 0 γ γ 0. γ γ 0. projective depth. γ/γ 0 = z 0 H H 0 z (3.84)
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