(a) (b) (c) Canny (d) 1 ( x α, y α ) 3 (x α, y α ) (a) A 2 + B 2 + C 2 + D 2 + E 2 + F 2 = 1 (3) u ξ α u (A, B, C, D, E, F ) (4) ξ α (x 2 α, 2x α y α,
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1 [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 ] [email protected] [email protected] Yasuyuki SUGAYA, Member (Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi-shi, Japan) and Kenichi KANATANI, Member (Graduate School of Natural Science and Technology, Okayama-shi, Japan). Vol. 92 No. 4 pp (b) 1(c) Canny (4),(5) 1(c) 1(d) 1(d) 2 CG 3. Ax 2 +2Bxy+Cy 2 +2(Dx+Ey)f 0 +F f 2 0 =0 (1) f 0 (1) (x α, y α ), α = 1,..., N (1) α = 1,..., N Ax 2 α+2bx α y α +Cy 2 α+2(dx α +Ey α )f 0 +Ff (2) A, B, C, D, E, F 3 A, B, C, D, E, F [II] 301
2 (a) (b) (c) Canny (d) 1 ( x α, y α ) 3 (x α, y α ) (a) A 2 + B 2 + C 2 + D 2 + E 2 + F 2 = 1 (3) u ξ α u (A, B, C, D, E, F ) (4) ξ α (x 2 α, 2x α y α, y 2 α, 2f 0 x α, 2f 0 y α, f 2 0 ) (5) 2 (b) CG (2) (u, ξ α ) 0, α = 1,..., N (6) a, b (a, b) F = 1, A + B = 1, A 2 + B 2 + C 2 + D 2 + E 2 + F 2 = 1 (3) u = 1 (1) ( 1) ( 1) u (x α, y α ) x α 302 Vol.92, No.4, 2009
3 (1) (conic) (1) (6) ( 2) 4. (6) u N (u, ξ α) 2 (least squares) 6 6 M LS M LS ξ α ξ α (7) (u, ξ α ) 2 = (u, ξ α ξ α u) = (u, M LS u) (8) u u M LS (8) (3) F = 1 A + B = 1 (8) (2),(9),(10),(11) 5. (1) 0 (8) α (u,ξ α )=Ax 2 α+2bx α y α +Cy 2 α+2(dx α +Ey α )f 0 +Ff 2 0 (9) 0 (x α, y α ) x, y 0 ( x α, ȳ α ) x α = x α + ɛ α, y α = ȳ α + η α (10) ɛ α, η α 0 σ 2 (9) ( x α, ȳ α ) (9) 0 (u, ξ α ) = 2(A x α + Bȳ α + Df 0 )ɛ α +2(B x α + Cȳ α + Ef 0 )η α + (11) (u, ξ α ) 0 4 ( (A x α +Bȳ α +Df 0 ) 2 +(B x α +Cȳ α +Ef 0 ) 2) σ 2 (12) ( 3) u 4σ 2 (u, V 0 [ξ α ]u) (13) 6 6 V 0 [ξ α ] x 2 α x α ȳ α 0 f 0 x α 0 0 x α ȳ α x 2 α + ȳ 2 α x α ȳ α f 0 ȳ α f 0 x α 0 V 0 [ξ α ] 0 x α ȳ α ȳα 2 0 f 0 ȳ α 0 f 0 x α f 0 ȳ α 0 f (14) 0 f 0 x α f 0 ȳ α 0 f (u, ξ α ) 0 4σ 2 (u, V 0 [ξ α ]u) (u, ξ α )/ 4(u, V 0 [ξ α ]u) 0 σ 2 J = 1 4 (u, ξ α ) 2 (u, V 0 [ξ α ]u) (15) ( 2) AC B 2 > 0 (7) ( 3) c c 2 [II] 303
4 (maximum likelihood estimation) V 0 [ξ α ] (14) ( x α, ȳ α ) (x α, y α ) (15) u u (15) (1) ( 4) (6) (15) Chojnacki (12) FNS 6. (15) ξ α N (u, ξ) = 0 u N ξ α ξ α (Euclidean distance) (Mahalanobis distance) ξ α ξ α ( 4) ξ α ξ α ξ α V [ξ α ] J = (ξ α ξ α, V [ξ α ] 5 (ξ α ξ α )) (16) ξ α ξ α ( ) 5 5 ( 5) (16) (u, ξ α ) = 0, α = 1,..., N (16) (15) V 0 [ξ α ] V [ξ α ] () (14) ξ α 7. Taubin (15) FNS (1) 4. Taubin (15) V 0 [ξ α ] N TB 1 N V 0 [ξ α ] (17) (15) J TB J TB = N 4 = N 4 (u, ξ α ) 2 (u, N TB u) = N 4 (u, M LS u) (u, N TB u) (u, ξ α ξ α u) (u, N TB u) (18) M LS (7) J TB (Rayleigh quotient) u ( 6) (generalized eigenvalue problem) M LS u = λn TB u (19) (10) (14) V 0 [ξ α ] (17) N TB N TB ( 7) ξ α u, V 0 [ξ α ] ( ξ, u) = 0 4 ( 4) ξ α x α V 0 [ξ α ] 3 3 V 0 [x α ] ( 5) 5 0 (8) (1) ( 6) (19) N TB λ u ( 7) A 0 x (x, Ax) > 0 (8) 304 Vol.92, No.4, 2009
![ξ α = ( V 0 [ξ α ] = z α f0 2 ( ), u = V 0 [z α ] 0 0 0 5 5 M LS Ñ TB M LS z α z α, z α z α z α, ) ( Ñ TB z 1](/docs-images/91/105754389/images/5-0.jpg "N v F ) (20) V 0 [z α ] (21) z α (22) (19) M LS v = λñ TBv, (v, z) + f 2 0 F = 0 (23) 1 (19) Ñ TB v 2 F Taubin")
5 ξ α = ( V 0 [ξ α ] = z α f0 2 ( ), u = V 0 [z α ] M LS Ñ TB M LS z α z α, z α z α z α, ) ( Ñ TB z 1 N v F ) (20) V 0 [z α ] (21) z α (22) (19) M LS v = λñ TBv, (v, z) + f 2 0 F = 0 (23) 1 (19) Ñ TB v 2 F Taubin 5 Taubin Taubin (13) Taubin 1990 (14) (16) 8. (1) u u û u û u ( 6) û V [û] = E[ u u ] (24) E[ ] KCR (KCR lower bound)) V [û] 4σ 2 M 5 (25) ( 8) σ 2 (a) u u O u^ u (b) 5 Taubin (11) 6 u û u u ( 8) A x (x, Ax) 0 (8) [II] 305
![(a) (b) 7 (9) M M ξ α ξ α (u, V 0 [ ξ α ]u) (26) ξ α V 0 [ ξ α ] ξ α V 0 [ξ α ] (x α, y α ) u (25) O(σ 4 ) KCR 7 (9) 9. Taubin 2 (1),, [I], vol.92, no.3, pp.229 233, March 2009. (2) K.](/docs-images/91/105754389/images/6-0.jpg "Kanatani, Geometric Computation for Machine Vision, Oxford University Press, Oxford, U.K. 1993. (3),,,, 2004. (4),,,, (D-II), vol.j85-d-ii, no.12, pp.1823 1831, Dec. 2002.")
6 (a) (b) 7 (9) M M ξ α ξ α (u, V 0 [ ξ α ]u) (26) ξ α V 0 [ ξ α ] ξ α V 0 [ξ α ] (x α, y α ) u (25) O(σ 4 ) KCR 7 (9) 9. Taubin 2 (1),, [I], vol.92, no.3, pp , March (2) K. Kanatani, Geometric Computation for Machine Vision, Oxford University Press, Oxford, U.K (3),,,, (4),,,, (D-II), vol.j85-d-ii, no.12, pp , Dec (5),, 14 (SSII08), IN1-14, pp.1 6 June (6) A. Fitzgibbon, M. Pilu and P. B. Fisher, Direct least square fitting of ellipses, IEEE Trans. Pattern Anal. Mach. Intell., vol.21, no.5, pp , May (7),,, (8),,, (9) Y. Kanazawa and K. Kanatani, Optimal conic fitting and reliability evaluation, IEICE Trans. Inf. & Syst., vol.e79-d, no.9, pp , Sept (10) K. Kanatani, Statistical Optimization for Geometric Computation: Theory and Practice, Elsevier Science, Amsterdam, The Netherlands, 1996; Dover, New York, (11),,,,, no.2006-cvim , pp , May (12) W. Chojnacki, M.J. Brooks, A. van den Hengel and D. Gawley, On the fitting of surfaces to data with covariances, IEEE Trans. Pattern Anal. Mach. Intell., vol.22, no.11, pp , Nov (13) G. Taubin, Estimation of planar curves, surfaces and, non-planar space curves defined by implicit equations with applications to edge and range image segmentation, IEEE Trans. Pattern Anal. Mach. Intell., vol.13, no.11, pp , Nov (14) N. Tagawa, T. Toriu, and T. Endoh, Un-biased linear algorithm for recovering three-dimensional motion from optical flow, IEICE Trans. Inf. & Syst., vol.e76-d, no.10, pp , Oct (15) N. Tagawa, T. Toriu, and T. Endoh, Estimation of 3-D motion from optical flow with unbiased objective function, IEICE Trans. Inf. & Syst., vol.e77-d, no.10, pp , Oct (16) N. Tagawa, T. Toriu, and T. Endoh, 3-D motion estimation from optical flow with low computational cost and small variance, IEICE Trans. Inf. & Syst., vol.e79-d, no.3, pp , March IEEE 306 Vol.92, No.4, 2009
, ( ξ/) ξ(x), ( ξ/) x = x 1,. ξ ξ ( ξ, u) = 0. M LS ξ ξ (6) u,, u M LS 3).,.. ξ x ξ = ξ(x),, 1. J = (ξ ξ, V [ξ ] 1 (ξ ξ )) (7) ( ξ, u) = 0, = 1,..., N
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1,,.,.. Maximum Likelihood Estimation for Geometric Fitting Yasuyuki Sugaya 1 Geometric fitting, the problem which estimates a geometric model of a scene from extracted image data, is one of the most fundamental
IPSJ SIG Technical Report Vol.2009-CVIM-168 No /9/ Latest Algorithm for 3-D Reconstruction from Two Views Kento Yamada, 1 Yasu
2 3 2 3 2 3 Latest Algorithm for 3-D Reconstruction from Two Views Kento Yamada, Yasushi Kanazawa, Kenichi Kanatani 2 and Yasuyuki Sugaya 3 This paper presents a new algorithm for reconstructing the 3-D
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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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Vol.-CVIM-7 No.7 /3/8 RANSAC M Subspace fitting via robust Jacobian kernel PCA Jun Fujiki and Shotaro Akaho The subspace fitting method based on the original kernel principle component analysis (PCA),
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3 2 3 2 3 undle Adjustment or 3-D Reconstruction: Implementation and Evaluation Yuuki Iwamoto, Yasuyuki Sugaya 2 and Kenichi Kanatani We describe in detail the algorithm o bundle adjustment or 3-D reconstruction
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![1 Kinect for Windows M = [X Y Z] T M = [X Y Z ] T f (u,v) w 3.2 [11] [7] u = f X +u Z 0 δ u (X,Y,Z ) (5) v = f Y Z +v 0 δ v (X,Y,Z ) (6) w = Z +](/thumbs/81/83701592.jpg "1 Kinect for Windows M = [X Y Z] T M = [X Y Z ] T f (u,v) w 3.2 [11] [7] u = f X +u Z 0 δ u (X,Y,Z ) (5) v = f Y Z +v 0 δ v (X,Y,Z ) (6) w = Z +")
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Random Forests 2013 3 A Graduation Thesis of College of Engineering, Chubu University Proposal of an efficient feature selection using the contribution rate of Random Forests Katsuya Shimazaki [1] SBS
Fig. 3 Flow diagram of image processing. Black rectangle in the photo indicates the processing area (128 x 32 pixels).
Fig. 1 The scheme of glottal area as a function of time Fig. 3 Flow diagram of image processing. Black rectangle in the photo indicates the processing area (128 x 32 pixels). Fig, 4 Parametric representation
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Journal Article / 学術雑誌論文 ベイズアプローチによる最適識別系の有限 標本効果に関する考察 : 学習標本の大きさ がクラス間で異なる場合 (< 論文小特集 > パ ターン認識のための学習 : 基礎と応用 On the limited sample effect of bayesian approach : the case of each class 韓, 雪仙 ; 若林, 哲史
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