E = N M α= = [( pα I α x ) 2 ( α qα + y ) 2 ] α r α r α I α α p α = P X α + P 2 Y α + P 3 Z α + P 4, q α = P 2 X α + P 22 Y α + P 23 Z α + P 24 r α =
|
|
|
- さや みのしま
- 7 years ago
- Views:
Transcription
1 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 rom multiple images based on our latest research results The main ocus o this paper is the handling o camera rotations and the eiciency o computation and memory space usage when the number o eature points and the number o rames are large An appropriate consideration o these is the core o the implementation o bundle adjustment Doing experiments o undamental matrix computation rom two images and 3-D reconstruction rom multiple images, we evaluate the perormance o bundle adjustment ),6),2),2) Department o omputer Science, Okayama University 2 Department o omputer Science and Engineering, Toyohashi University o Technolgy (X, Y, Z) (x, y) X x y A P Z A P 3 4 (u, v ) t R 4) P = KR / u / I t, K / v / A (2) I K 3) () P X + P 2 Y + P 3 Z + P 4 x = P 3 X + P 32 Y + P 33 Z + P, y = P 2 X + P 22 Y + P 23 Z + P (3) P 3 X + P 32 Y + P 33 Z + P 34 P (ij) P ij N (X α, Y α, Z α) M (x α, y α ) ( =,, M, α =,, N) P (3) Vol2-VIM-75 No9 2//2 x, y 3) = 6 c 2 Inormation Processing Society o Japan
2 E = N M α= = [( pα I α x ) 2 ( α qα + y ) 2 ] α r α r α I α α p α = P X α + P 2 Y α + P 3 Z α + P 4, q α = P 2 X α + P 22 Y α + P 23 Z α + P 24 r α = P 3 X α + P 32 Y α + P 33 Z α + P 34 (5) (x α, y α), α =,, N, =,, M (4) 3 (X α, Y α, Z α ) P 5),6),2),2) 3 3 (X α, Y α, Z α ) P (4) E 3 ( X α, Y α, Z α) P (2), (u, v ) t = (t, t 2, t 3) R,, u, v, t, t 2, t 3 R R 9 R R (4) = I 3 3 R 3 R 3 R R R R + R R = I R R = O ( R R ) = R R R R ω, ω 2, ω 3 ω 3 ω 2 R R ω 3 ω A (6) ω 2 ω 3 ω, ω 2, ω 3 3 SO(3) so(3) 6) a T a T a T 7) (6) ω = (ω, ω 2, ω 3) 6) I ω I (a I)b = a b, (a I)T = a T (6) R R = ω R (7) t t dr /dt ω (7) 7) 7),9) (7) 4 E X α, Y α, Z α, α =,, N,, t, t 2, t 3, u, v, ω, ω 2, ω 3, =,, M 3N + 9M ξ, ξ 2,, ξ 3N+9M ξ k ξ k 2 / ξ k (4) E E N [( )( ) I α pα = 2 xα p α r α r ξ k rα 2 α p α r α ξ k ξ k α= = ( qα + y )( )] α q α r α r α q α r α ξ k ξ k 9) 2 N 2 E ξ k ξ l = 2 α= = ( + I α r 4 α r α q α ξ k [( )( ) p α r α p α r α r α p α r α p α ξ k ξ k ξ l ξ l )] ξ l )( r α q α r α q α r α q α ξ k ξ l ξ k E E/ ξ k 2 2 E/ ξ k ξ l p α, q α, r α p α / ξ k, q α / ξ k, r α / ξ k Vol2-VIM-75 No9 2//2 (8) (9) 2 c 2 Inormation Processing Society o Japan
3 5 3 (5) p α, q α, r α (X β, Y β, Z β ) δ αβ p α, X β = δ αβ P q α X β = δ αβ P 2, r α X β = δ αβ P 3, p α, Y β = δ αβ P 2 q α 6 Y β = δ αβ P 22, r α Y β = δ αβ P 32, p α = δ αβ P 3 Z β q α Z β = δ αβ P 23 r α Z β = δ αβ P 33 () (2) P P AR I t AK KR I t A u v / AP = u v / AP / = P u P 3 / P 2 u P 32 / P 3 u P 33 / P 4 u P 34 P 2 v P 3 / P 22 v P 32 / P 23 v P 33 / P 24 v P 34 / A () p α, q α, r α λ p α = δ ( λ p α u ) q α r α, = δ ( λ q α v ) r α, λ λ 7 r α λ = (2) (2) P u ( ) ( ) P AR I t AK KR I t u A u v / AP = P 3 P 32 P 33 P A (3) / v ( ) P AR I t P v 3 P 32 P 33 P 34 A (4) p α, q α, r α (u λ, v λ ) p α = δ λr α q α r α, =, =, u λ u λ u λ p α q α =, = δ λr α r α, = (5) v λ v λ u λ 8 t (2) P 4 P 4 (R + u R 3 )t + (R 2 + u R 23 )t 2 + (R 3 + u R 33 )t P 24 A = KR t (R 2 + v R 3 )t + (R 22 + v R 23 )t 2 + (R 32 + v R 33 )t 3 A P 34 (R 3 t + R 23 t 2 + R 33 t 3 ) (6) P P t 24 A t 3 P 34 P P 24 P 34 A R + u R 3 R 2 + v R 3 R 3 R 3 + u R 33 R 32 + v R 33 R 33 t 2 P 4 P 24 P 34 A R 2 + u R 23 R 22 + v R 23 R 23 A A (7) (t λ, t λ2, t λ3 ) tλ (5) tλ p α = δ λ ( r + u r 3 ), tλ p α = δ λ ( r 2 + v r 3 ), tλ p α = δ λ r 3 r, r 2, r 3 r = R R 2 R 3 9, r 2 = R 2 R 22 R 32, r 3 = R 3 R 23 R 33 (2) P Vol2-VIM-75 No9 2//2 (8) (9) 3 c 2 Inormation Processing Society o Japan
4 P = K(ω R) ω 3 ω 2 ω 2 t 3 ω 3 t 2 I t = ω 3 ω ω 3 t ω t 3 A (2) ω 2 ω ω t 2 ω 2 t (ω R) = R (ω I) (ω I)t = ω t 7) P / ω, P / ω 2, P / ω 3 R P 3 u R 33 R 2 +u R 23 (t 2 R 3 t 3 R 2 )+u (t 2 R 33 t 3 R 23 ) R ω 32 v R 33 R 22 +v R 23 (t 2 R 32 t 3 R 22 )+v (t 2 R 33 t 3 R 23 ) A, R 33 R 23 (t 2 R 33 t 3 R 23 ) R P 3 +u R 33 R u R 3 (t 3 R t R 3 )+u (t 3 R 3 t R 33 ) R ω 32 +v R 33 R 2 v R 3 (t 3 R 2 t R 32 )+v (t 3 R 3 t R 33 ) A, 2 R 33 R 3 (t 3 R 3 t R 33 ) R P 2 u R 23 R +u R 3 (t R 2 t 2 R )+u (t R 23 t 2 R 3 ) R ω 22 v R 23 R 2 +v R 3 (t R 22 t 2 R 2 )+v (t R 23 t 2 R 3 ) A (2) 3 R 23 R 3 (t R 23 t 2 R 3 ) (ω λ, ω λ2, ω λ3 ) ωλ (5) ωλ p α = δ λ ( r + u r 3 ) (X α t ), ωλ q α = δ λ ( r 2 + v r 3 ) (X α t ), ωλ r α = δ λ r 3 (X α t ) (22) X α = (X α, Y α, Z α ) E 2 E (LM) 9) ( ) X α,, (u, v ), t, R E c = ( 2 ) 2 E/ ξ k, 2 E/ ξ k ξ l, k, l =,, 3N + 9M ( 3 ) ξ k, k =,, 3N + 9M ( + c) 2 E/ ξ 2 2 E/ ξ ξ 2 2 E/ ξ ξ 3N+9M 2 E/ ξ 2 ξ ( + c) 2 E/ ξ2 2 2 E/ ξ 2 ξ A 2 E/ ξ 3N+9M ξ 2 E/ ξ 3N+9M ξ 2 ( + c) 2 E/ ξ 3N+9M 2 ξ E/ ξ ξ 2 E/ ξ ξ 3N+9M = E/ ξ 3N+9M ( 4 ) X α,, (u, v ), t, R A (23) X α X α + X α, +, (ũ, ṽ ) (u, v ), t t + t, R R(ω )R (24) R(ω ) N [ω ] ω 8) ( 5 ) X α,, (ũ, ṽ ), t, R Ẽ Ẽ > E c c (3) ( 6 ) X α X α,, (u, v ) (ũ, ṽ ), t t, R R (25) Ẽ E δ δ E Ẽ, c c/ (2) (23) c = ξ k 3 R = I, t =, t 22 = (26) 3 2 Y t 2 = 2 Y X Z t 2 = t 23 = (23) ω, ω 2, ω 3, t, t 2, t 3, t 22 3N + 9M 7 (23) LM X α,, (u, v ), t, R (26) (26) X α, t, R X α, t, R X α = ) s R (X α t, R = R R, t = s R (t t ) (27) s = (j, R (t 2 t )) j = (,, ) Vol2-VIM-75 No9 2//2 exp(ω I) so(3) Lie SO(3) 6) 4 c 2 Inormation Processing Society o Japan
5 2 (8), (9) N MN α= = E/ ξ k (8) ξ k β X β () δ αβ N α= α = β ξ k λ λ, (u λ, v λ ), t λ R λ (2), (5), (8), (22) δ λ = = λ (8) N α= = α α α 2 E/ ξ k ξ l (9) ξ k, ξ l (9) N α= ξ k, ξ l (9) = ξ k, ξ l N α= = E/ ξ k, 2 E/ ξ k ξ l 2 2 E/ ξ k ξ l H(k, l) (3N + 9M 7) (3N + 9M 7) N, M 3N 3 E, 3N 9M F 9M 9 G E 2 E/ X 2 α, 2 E/ X α Y α 2 F 2 E/ X α, 2 E/ X α u 2 G 2 E/ 2, 2 E/ u 2 27NM + 9N + 8M H(k, l) (k, l) 3 3N +9M 7 (23) (3N +9M 7) (3N +9M 7) N, M LU 2) 2 27NM + 6N + 4M I α = 3 (23) (23) E (c) F ( ) ( ) ξ P d P E (c) N F N ξ F F F N G (c) ξ P ξ 3 3N ξ F 9M 7 d P, d F (23) 3N 9M 7 E (c) α, α =,, N α (X α, Y α, Z α) E (c) ( + c) F α α (X α, Y α, Z α ) α E 2 3 (9M 7) G (c) E 2 (9M 7) (9M 7) ( + c) (28) E (c) E (c) N ξ P + F F N = ξ F = d P, d F ( F (28) ) F N ξ P + G (c) ξ F = d F ξ P 2 ξ F 9M 7 ( N G (c) F α E α (c) F α ) ξ F = α= N α= F α E (c) α α E d F, α (29) E/ X α E/ Y α A (3) E/ Z α ξ F (29) 2 ξ P α X Y α A = E (c) α (F α ξ F + α E) (3) Z α 4 Vol2-VIM-75 No9 2//2 5 c 2 Inormation Processing Society o Japan
6 2 4) σ = LM ɛ LM δ δ = nɛ 2 / 2 n = N α= = Iα ɛ = = = 6 x, y (Hartley 8 3) ) 22),, ) (u, v ) (4) e N = 9 E e = (32) N 7 N 7 7 7) σ e 2 / 2 σ 2 N 7 χ 2 N 7 (32) e σ 4) 4) xyx y 3 4 EFNS 3) ) 22) 3 22) Oxord 2(a) P 5266 (23) (b) % P (u, v ) t R A 3 A2 n = N Iα 6432 (4) α= = (32) E e = 2n (3N + 9M 7) Vol2-VIM-75 No9 2//2 (33) 6 c 2 Inormation Processing Society o Japan
7 Vol2-VIM-75 No9 2//2 情報処理学会研究報告 4 ま と め 本論文では多画像からの 3 次元形状復元を行うバンドル調整のアルゴリズムを最新の研究 に基づいて詳細に記述した 本論文で着目したのはカメラ回転の適切な取扱い方 および特 徴点と画像数が多いときの計算とメモリの効率化である まず 2 画像からの基礎行列の計 算に応用し 金谷 菅谷4) の方法と同じ解が得られ 彼らの方法が最適であることを実証 した ただし バンドル調整は効率において彼らの方法に劣る 次に英国 Oxord 大学の実 測データを用いて 3 次元を行った これは特徴点数が非常に多く バンドル調整をその原理 (a) 回 再投影誤差 (b) 回 (d) 通りに実装することは困難であるが ここに述べた工夫によって実行できることを示した (c) 理論的にはバンドル調整は任意の 3 次元復元に適用できる万能手法であるが 椋木ら9) 再投影誤差 が検討したような単純な形状 例えば球面 と単純なカメラ配置 例えば同心円上 から出 発して複雑な形状に収束させることには無理があり 初めに精度のよい近似的な 3 次元復 元を行うことが必要である 近似的 3 次元復元の代表はアフィンカメラ近似による因子分 解法2),5),),2) であるが 透視投影モデルによる自己校正法),),8) のほうが精度が高い バンドル調整はそのような高精度の復元を行った後の最終的な補正を行う手段とみなすのが よいと思われる 謝辞: バンドル調整についてご助言頂いた東北大学の岡谷貴之准教授に感謝します 本研究の一部は文 部科学省科学研究費基盤研究 ( 2572) の助成によった 参 (e) 考 文 献 ) ハノ アッカーマン, 新妻弘崇, 金谷健一, 自己校正法のための射影復元の計算量削減, 情報処理学会研究報告, 27-VIM-6- (27-9), ) 浅原 清太郎, 金谷 健一, 菅谷 保之, ハノ アッカーマン, 未校正因子分解法による 3 次元復元 比較実験, 情報処理学会研究報告, 25-VIM-5-2 (25-), ) R I Hartley, In deense o the eight-point algorithm, IEEE Trans Patt Anal Mach Intell, 9-6 (997-6), ) R Hartley and A Zisserman, Multiple View Geometry in omputer Vision, 2nd ed, ambridge University Press, ambridge, UK, 24 5) 金出武雄, コンラッド ポールマン, 森田俊彦, 因子分解法による物体形状とカメラ運 動の復元 電子情報通信学会論文誌 D-II, J74-D-II-8 (993-8), ) K Kanatani, Group-Theoretical Methods in Image Understanding, Springer, erlin, Germany, 99 7) K Kanatani, Statistical Optimization or Geometric omputation: Theory and Practice Elsevier, Amsterdam, the Netherlands, 996; reprinted, Dover, York, NY, USA, 25 8) 金谷健一, 形状 AD と図形の数学, 共立出版, 998 図 2 (a) 用いた 36 画像中の一つ (b) 点を抜き出した場合のヘッセ係数行列の非零パタン (c) 反復回数に対する再投影誤差 e のグラフ (d) 反復回数に対する再投影誤差 e の値 (e) 3 次元 復元 赤 初期位置 緑 収束位置 最小二乗法による初期復元の再投影誤差は e = 画素であったが バンドル調整の 結果 e = 画素に低下した 反復回数による e の変化を図 2(c) に その具体的な数 値を図 2(d) に示す 反復回数は 49 回であり 実行時間は 2 分 5 秒であった ただし ++言語を用い PU には Intel ore2duo E675, 266GHz 主メモリ 4G OS には Windows Vista を用いた 図 2(e) は復元した各点の 3 次元位置をある方向から眺めたもの である 赤は最小二乗法による初期位置であり 緑が最終的な復元位置である 7 2 Inormation Processing Society o Japan
8 9),,, 25 ) ( ),, 2,, 29, pp ),,,,,, 25-VIM-5-6 (25-9), ),,,, PRMU23-8 (23-), ),, FNS,, 27-VIM-58-4, (27-3), ) K Kanatani and Y Sugaya, ompact undamental matrix computation, IPSJ Trans omput Vis Appl 2 (2-3), ) M I A Lourakis and A A Argyros, Is Levenberg-Marquardt the most eicient optimization algorithm or implementing bundle adjustment?, Proc th Int on omput Vis, Vol 2, October 25, eijing, hina, pp ) M I A Lourakis and A A Argyros, SA: A sotware package or generic sparse bundle adjustment, AM Trans Math Sotware, 36- (29-3), 2: 3 7),,, 3,, 44- (23-), ),,, :,, 27-VIM-57-5 (27-), 9 6 9),,,,, 4-SIG3 (24-2), ),,, 29-VIM (29-6), 6 2) Triggs, P F McLauchlan, R I Hartley, and A Fitzgibbon, undle adjustment A modern synthesis, in Triggs, A Zisserman, and R Szeliski, (eds), Vision Algorithms: Theory and Practice, Springer, erlin, 2, pp ),,,, 3,, 29-VIM-68-5 (29-9), 8 A ( P = Q ) q P 3 3 Q 4 q () P det Q < Q q Q = ckr, q = ckr t (34) c t t = Q q (35) R R R = I (34) QQ = c 2 KR RK = c 2 KK (36) (QQ ) = c 2 (K ) (K ) (37) (QQ ) (QQ ) = (38) (37), (38) = c K = ck (39) (34) (39) Q = R (4) R R = (Q) (4) K (39) (3,3) A2 3 (3) xp 3 X + xp 32 Y + xp 33 Z + xp 34 = P X + P 2 Y + P 3 Z + P 4 yp 3 X + yp 32 Y + yp 33 Z + yp 34 = P 2 X + P 22 Y + P 23 Z + P 24 (42) p α n α (= I = α) p α 3 X α 2n α x α P 3 P x α P 32 P 2 x α P 33 y α P 3 P 2 y α P 32 P 22 y α P 33 P 23 P 3 X α Y α Z α x α P 34 P 4 = y α P 34 P 24 9) Vol2-VIM-75 No9 2//2 (43) 8 c 2 Inormation Processing Society o Japan
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
, ( 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
![, ( 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](/thumbs/80/81723780.jpg ", ( 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")
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
(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,
[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 [email protected]
Microsoft PowerPoint - CV10.ppt [互換モード]
![Microsoft PowerPoint - CV10.ppt [互換モード]](/thumbs/83/88335853.jpg "Microsoft PowerPoint - CV10.ppt [互換モード]")
カメラキャリブレーション 呉海元 @ 和歌山大学 2010 年 6 月 21 日 カメラキャリブレーション ( 校正 ) 実世界のカメラとカメラモデルとの対応付け 2 カメラキャリブレーション項目 幾何学的キャリブレーション - 外部パラメータ : 6 世界座標系におけるレンズの中心座標 (t) レンズ光軸の方向 (R) - 内部パラメータ : 5 焦点距離 画像中心 画像像 ( 画素 ) サイズ
(3.6 ) (4.6 ) 2. [3], [6], [12] [7] [2], [5], [11] [14] [9] [8] [10] (1) Voodoo 3 : 3 Voodoo[1] 3 ( 3D ) (2) : Voodoo 3D (3) : 3D (Welc
![(3.6 ) (4.6 ) 2. [3], [6], [12] [7] [2], [5], [11] [14] [9] [8] [10] (1) Voodoo 3 : 3 Voodoo[1] 3 ( 3D ) (2) : Voodoo 3D (3) : 3D (Welc](/thumbs/65/54056306.jpg "(3.6 ) (4.6 ) 2. [3], [6], [12] [7] [2], [5], [11] [14] [9] [8] [10] (1) Voodoo 3 : 3 Voodoo[1] 3 ( 3D ) (2) : Voodoo 3D (3) : 3D (Welc")
1,a) 1,b) Obstacle Detection from Monocular On-Vehicle Camera in units of Delaunay Triangles Abstract: An algorithm to detect obstacles by using a monocular on-vehicle video camera is developed. Since
情報処理学会研究報告 IPSJ SIG Technical Report Vol.2014-GN-90 No.6 Vol.2014-CDS-9 No.6 Vol.2014-DCC-6 No /1/23 Bullet Time 1,a) 1 Bullet Time Bullet Time
Bullet Time 1,a) 1 Bullet Time Bullet Time Generation Technique and Eveluation on High-Resolution Bullet-Time Camera Work Ryuuki Sakamoto 1,a) Ding Chen 1 Abstract: The multi-camera environment have been
258 5) GPS 1 GPS 6) GPS DP 7) 8) 10) GPS GPS 2 3 4 5 2. 2.1 3 1) GPS Global Positioning System
Vol. 52 No. 1 257 268 (Jan. 2011) 1 2, 1 1 measurement. In this paper, a dynamic road map making system is proposed. The proposition system uses probe-cars which has an in-vehicle camera and a GPS receiver.
& 3 3 ' ' (., (Pixel), (Light Intensity) (Random Variable). (Joint Probability). V., V = {,,, V }. i x i x = (x, x,, x V ) T. x i i (State Variable),
.... Deeping and Expansion of Large-Scale Random Fields and Probabilistic Image Processing Kazuyuki Tanaka The mathematical frameworks of probabilistic image processing are formulated by means of Markov
Input image Initialize variables Loop for period of oscillation Update height map Make shade image Change property of image Output image Change time L
1,a) 1,b) 1/f β Generation Method of Animation from Pictures with Natural Flicker Abstract: Some methods to create animation automatically from one picture have been proposed. There is a method that gives
1214_KiyotaCalib_matsusita_fixed2.pdf
1 1 3 2 3 Efficient Projector Calibration Method using Plane with Checkerboard Pattern Shota Kiyota, 1 Hiroshi Kawasaki, 1 Ryo Furukawa 3 and Ryusuke Sagawa 2 In recent years, development on 3D measurement
xx/xx Vol. Jxx A No. xx 1 Fig. 1 PAL(Panoramic Annular Lens) PAL(Panoramic Annular Lens) PAL (2) PAL PAL 2 PAL 3 2 PAL 1 PAL 3 PAL PAL 2. 1 PAL
PAL On the Precision of 3D Measurement by Stereo PAL Images Hiroyuki HASE,HirofumiKAWAI,FrankEKPAR, Masaaki YONEDA,andJien KATO PAL 3 PAL Panoramic Annular Lens 1985 Greguss PAL 1 PAL PAL 2 3 2 PAL DP
φ 4 Minimal subtraction scheme 2-loop ε 2008 (University of Tokyo) (Atsuo Kuniba) version 21/Apr/ Formulas Γ( n + ɛ) = ( 1)n (1 n! ɛ + ψ(n + 1)
φ 4 Minimal subtraction scheme 2-loop ε 28 University of Tokyo Atsuo Kuniba version 2/Apr/28 Formulas Γ n + ɛ = n n! ɛ + ψn + + Oɛ n =,, 2, ψn + = + 2 + + γ, 2 n ψ = γ =.5772... Euler const, log + ax x
( ) [1] [4] ( ) 2. [5] [6] Piano Tutor[7] [1], [2], [8], [9] Radiobaton[10] Two Finger Piano[11] Coloring-in Piano[12] ism[13] MIDI MIDI 1 Fig. 1 Syst
![( ) [1] [4] ( ) 2. [5] [6] Piano Tutor[7] [1], [2], [8], [9] Radiobaton[10] Two Finger Piano[11] Coloring-in Piano[12] ism[13] MIDI MIDI 1 Fig. 1 Syst](/thumbs/91/107597950.jpg "( ) [1] [4] ( ) 2. [5] [6] Piano Tutor[7] [1], [2], [8], [9] Radiobaton[10] Two Finger Piano[11] Coloring-in Piano[12] ism[13] MIDI MIDI 1 Fig. 1 Syst")
情報処理学会インタラクション 2015 IPSJ Interaction 2015 15INT014 2015/3/7 1,a) 1,b) 1,c) Design and Implementation of a Piano Learning Support System Considering Motivation Fukuya Yuto 1,a) Takegawa Yoshinari 1,b) Yanagi
ActionScript Flash Player 8 ActionScript3.0 ActionScript Flash Video ActionScript.swf swf FlashPlayer AVM(Actionscript Virtual Machine) Windows
ActionScript3.0 1 1 YouTube Flash ActionScript3.0 Face detection and hiding using ActionScript3.0 for streaming video on the Internet Ryouta Tanaka 1 and Masanao Koeda 1 Recently, video streaming and video
waseda2010a-jukaiki1-main.dvi
November, 2 Contents 6 2 8 3 3 3 32 32 33 5 34 34 6 35 35 7 4 R 2 7 4 4 9 42 42 2 43 44 2 5 : 2 5 5 23 52 52 23 53 53 23 54 24 6 24 6 6 26 62 62 26 63 t 27 7 27 7 7 28 72 72 28 73 36) 29 8 29 8 29 82 3
カメラレディ原稿
IS2-A2 カメラを回転させた時の特徴点軌跡を用いた魚眼カメラの内部パラメータ推定 - モデルと評価関数の変更による改良 - 田中祐輝, 増山岳人, 梅田和昇 Yuki TANAKA, Gakuto MASUYAMA, Kazunori UMEDA : 中央大学大学院理工学研究科,[email protected] 中央大学理工学部,{masuyama, umeda}@mech.chuo-u.ac.jp
23 Fig. 2: hwmodulev2 3. Reconfigurable HPC 3.1 hw/sw hw/sw hw/sw FPGA PC FPGA PC FPGA HPC FPGA FPGA hw/sw hw/sw hw- Module FPGA hwmodule hw/sw FPGA h
23 FPGA CUDA Performance Comparison of FPGA Array with CUDA on Poisson Equation ([email protected]), ([email protected]), ([email protected]), ([email protected]),
1 Fig. 1 Extraction of motion,.,,, 4,,, 3., 1, 2. 2.,. CHLAC,. 2.1,. (256 ).,., CHLAC. CHLAC, HLAC. 2.3 (HLAC ) r,.,. HLAC. N. 2 HLAC Fig. 2
CHLAC 1 2 3 3,. (CHLAC), 1).,.,, CHLAC,.,. Suspicious Behavior Detection based on CHLAC Method Hideaki Imanishi, 1 Toyohiro Hayashi, 2 Shuichi Enokida 3 and Toshiaki Ejima 3 We have proposed a method for
第5章 偏微分方程式の境界値問題
October 5, 2018 1 / 113 4 ( ) 2 / 113 Poisson 5.1 Poisson ( A.7.1) Poisson Poisson 1 (A.6 ) Γ p p N u D Γ D b 5.1.1: = Γ D Γ N 3 / 113 Poisson 5.1.1 d {2, 3} Lipschitz (A.5 ) Γ D Γ N = \ Γ D Γ p Γ N Γ
28 Horizontal angle correction using straight line detection in an equirectangular image
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
& Vol.5 No (Oct. 2015) TV 1,2,a) , Augmented TV TV AR Augmented Reality 3DCG TV Estimation of TV Screen Position and Ro
TV 1,2,a) 1 2 2015 1 26, 2015 5 21 Augmented TV TV AR Augmented Reality 3DCG TV Estimation of TV Screen Position and Rotation Using Mobile Device Hiroyuki Kawakita 1,2,a) Toshio Nakagawa 1 Makoto Sato
THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE.
THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE. E-mail: {ytamura,takai,tkato,tm}@vision.kuee.kyoto-u.ac.jp Abstract Current Wave Pattern Analysis for Anomaly
(Basic of Proability Theory). (Probability Spacees ad Radom Variables , (Expectatios, Meas) (Weak Law
I (Radom Walks ad Percolatios) 3 4 7 ( -2 ) (Preface),.,,,...,,.,,,,.,.,,.,,. (,.) (Basic of Proability Theory). (Probability Spacees ad Radom Variables...............2, (Expectatios, Meas).............................
24 21 21115025 i 1 1 2 5 2.1.................................. 6 2.1.1........................... 6 2.1.2........................... 7 2.2...................................... 8 2.3............................
88 th Annual Meeting of the Zoological Society of Japan Abstracts 88 th Annual Meeting of the Zoological Society of Japan Abstracts 88 th Annual Meeting of the Zoological Society of Japan Abstracts 88
untitled
K-Means 1 5 2 K-Means 7 2.1 K-Means.............................. 7 2.2 K-Means.......................... 8 2.3................... 9 3 K-Means 11 3.1.................................. 11 3.2..................................
,, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising
![,, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising](/thumbs/94/118770363.jpg ",, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising")
,, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising Model 1 Ising 1 Ising Model N Ising (σ i = ±1) (Free
2 Part A B C A > B > C (0) 90, 69, 61, 68, 6, 77, 75, 20, 41, 34 (1) 8, 56, 16, 50, 43, 66, 44, 77, 55, 48 (2) 92, 74, 56, 81, 84, 86, 1, 27,
/ (1) (2) (3) [email protected] (4) (0) (10) 11 (10) (a) (b) (c) (5) - - 11160939-11160939- - 1 2 Part 1. 1. 1. A B C A > B > C (0) 90, 69, 61, 68, 6, 77, 75, 20, 41, 34 (1) 8, 56, 16, 50, 43, 66, 44,
1: A/B/C/D Fig. 1 Modeling Based on Difference in Agitation Method artisoc[7] A D 2017 Information Processing
![1: A/B/C/D Fig. 1 Modeling Based on Difference in Agitation Method artisoc[7] A D 2017 Information Processing](/thumbs/88/115893223.jpg "1: A/B/C/D Fig. 1 Modeling Based on Difference in Agitation Method artisoc[7] A D 2017 Information Processing")
1,a) 2,b) 3 Modeling of Agitation Method in Automatic Mahjong Table using Multi-Agent Simulation Hiroyasu Ide 1,a) Takashi Okuda 2,b) Abstract: Automatic mahjong table refers to mahjong table which automatically
スケーリング理論とはなにか? - --尺度を変えて見えること--
? URL: http://maildbs.c.u-tokyo.ac.jp/ fukushima mailto:[email protected] DEX-SMI @ 2006 12 17 ( ) What is scaling theory? DEX-SMI 1 / 40 Outline Outline 1 2 3 4 ( ) What is scaling theory?
液晶の物理１：連続体理論（弾性，粘性）
The Physics of Liquid Crystals P. G. de Gennes and J. Prost (Oxford University Press, 1993) Liquid crystals are beautiful and mysterious; I am fond of them for both reasons. My hope is that some readers
.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T
NHK 204 2 0 203 2 24 ( ) 7 00 7 50 203 2 25 ( ) 7 00 7 50 203 2 26 ( ) 7 00 7 50 203 2 27 ( ) 7 00 7 50 I. ( ν R n 2 ) m 2 n m, R = e 2 8πε 0 hca B =.09737 0 7 m ( ν = ) λ a B = 4πε 0ħ 2 m e e 2 = 5.2977
量子力学 問題
3 : 203 : 0. H = 0 0 2 6 0 () = 6, 2 = 2, 3 = 3 3 H 6 2 3 ϵ,2,3 (2) ψ = (, 2, 3 ) ψ Hψ H (3) P i = i i P P 2 = P 2 P 3 = P 3 P = O, P 2 i = P i (4) P + P 2 + P 3 = E 3 (5) i ϵ ip i H 0 0 (6) R = 0 0 [H,
図 : CGC 回転面. 左の図は 正の場合の平行曲面として得られる平均曲率 一定回転面 ダラネーアンデュロイド 上 とノドイド 下, 中の図は その平行正 CGC 回転面 右の図は負 CGC 回転面 ミンディング曲面と呼 ばれる 図 2: 回転面でない位相的な円柱面 螺旋対称性を持つ. ダラネー
[email protected] (K ) Nick Schmitt (Tübingen ) [6] R 3 K CGC [], R 3 CGC, R 3 CGC CGC CGC CGC 2, [2]. CGC CGC [6] C 3 CGC [4] CGC. 図 : CGC 回転面. 左の図は 正の場合の平行曲面として得られる平均曲率 一定回転面 ダラネーアンデュロイド 上
1 Edward Waring Lagrange n {(x i, y i )} n i=1 x i p i p i (x j ) = δ ij P (x) = p i p i (x) = n y i p i (x) (1) i=1 n j=1 j i x x j x i x j (2) Runge
Edwrd Wring Lgrnge n {(x i, y i )} n x i p i p i (x j ) = δ ij P (x) = p i p i (x) = n y i p i (x) () n j= x x j x i x j (2) Runge [] [2] = ξ 0 < ξ < ξ n = b [, b] [ξ i, ξ i ] y = /( + 25x 2 ) 5 2,, 0,,
( ) ) AGD 2) 7) 1
( 9 5 6 ) ) AGD ) 7) S. ψ (r, t) ψ(r, t) (r, t) Ĥ ψ(r, t) = e iĥt/ħ ψ(r, )e iĥt/ħ ˆn(r, t) = ψ (r, t)ψ(r, t) () : ψ(r, t)ψ (r, t) ψ (r, t)ψ(r, t) = δ(r r ) () ψ(r, t)ψ(r, t) ψ(r, t)ψ(r, t) = (3) ψ (r,
II (Percolation) ( 3-4 ) 1. [ ],,,,,,,. 2. [ ],.. 3. [ ],. 4. [ ] [ ] G. Grimmett Percolation Springer-Verlag New-York [ ] 3
![II (Percolation) ( 3-4 ) 1. [ ],,,,,,,. 2. [ ],.. 3. [ ],. 4. [ ] [ ] G. Grimmett Percolation Springer-Verlag New-York [ ] 3](/thumbs/94/121840826.jpg "II (Percolation) ( 3-4 ) 1. [ ],,,,,,,. 2. [ ],.. 3. [ ],. 4. [ ] [ ] G. Grimmett Percolation Springer-Verlag New-York [ ] 3")
II (Percolation) 12 9 27 ( 3-4 ) 1 [ ] 2 [ ] 3 [ ] 4 [ ] 1992 5 [ ] G Grimmett Percolation Springer-Verlag New-York 1989 6 [ ] 3 1 3 p H 2 3 2 FKG BK Russo 2 p H = p T (=: p c ) 3 2 Kesten p c =1/2 ( )
http://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................
a L = Ψ éiγ c pa qaa mc ù êë ( - )- úû Ψ 1 Ψ 4 γ a a 0, 1,, 3 {γ a, γ b } η ab æi O ö æo ö β, σ = ço I α = è - ø çèσ O ø γ 0 x iβ γ i x iβα i
解説 4 matsuo.mamoru jaea.go.jp 4 eizi imr.tohoku.ac.jp 4 maekawa.sadamichi jaea.go.jp i ii iii i Gd Tb Dy g khz Pt ii iii Keywords vierbein 3 dreibein 4 vielbein torsion JST-ERATO 1 017 1. 1..1 a L = Ψ
13 0 1 1 4 11 4 12 5 13 6 2 10 21 10 22 14 3 20 31 20 32 25 33 28 4 31 41 32 42 34 43 38 5 41 51 41 52 43 53 54 6 57 61 57 62 60 70 0 Gauss a, b, c x, y f(x, y) = ax 2 + bxy + cy 2 = x y a b/2 b/2 c x
1 3DCG [2] 3DCG CG 3DCG [3] 3DCG 3 3 API 2 3DCG 3 (1) Saito [4] (a) 1920x1080 (b) 1280x720 (c) 640x360 (d) 320x G-Buffer Decaudin[5] G-Buffer D
![1 3DCG [2] 3DCG CG 3DCG [3] 3DCG 3 3 API 2 3DCG 3 (1) Saito [4] (a) 1920x1080 (b) 1280x720 (c) 640x360 (d) 320x G-Buffer Decaudin[5] G-Buffer D](/thumbs/91/105248386.jpg "1 3DCG [2] 3DCG CG 3DCG [3] 3DCG 3 3 API 2 3DCG 3 (1) Saito [4] (a) 1920x1080 (b) 1280x720 (c) 640x360 (d) 320x G-Buffer Decaudin[5] G-Buffer D")
3DCG 1) ( ) 2) 2) 1) 2) Real-Time Line Drawing Using Image Processing and Deforming Process Together in 3DCG Takeshi Okuya 1) Katsuaki Tanaka 2) Shigekazu Sakai 2) 1) Department of Intermedia Art and Science,
v v = v 1 v 2 v 3 (1) R = (R ij ) (2) R (R 1 ) ij = R ji (3) 3 R ij R ik = δ jk (4) i=1 δ ij Kronecker δ ij = { 1 (i = j) 0 (i
1. 1 1.1 1.1.1 1.1.1.1 v v = v 1 v 2 v 3 (1) R = (R ij ) (2) R (R 1 ) ij = R ji (3) R ij R ik = δ jk (4) δ ij Kronecker δ ij = { 1 (i = j) 0 (i j) (5) 1 1.1. v1.1 2011/04/10 1. 1 2 v i = R ij v j (6) [
4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.
A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c
IPSJ SIG Technical Report Vol.2016-MUS-111 No /5/21 1, 1 2,a) HMM A study on an implementation of semiautomatic composition of music which matc
1, 1 2,a) HMM A study on an implementation of semiautomatic composition of music which matches impressions of color still image Sae NEMOTO 1, 1 Yasuyuki SAITO 2,a) Abstract: This paper shows a creation
1 Web [2] Web [3] [4] [5], [6] [7] [8] S.W. [9] 3. MeetingShelf Web MeetingShelf MeetingShelf (1) (2) (3) (4) (5) Web MeetingShelf
![1 Web [2] Web [3] [4] [5], [6] [7] [8] S.W. [9] 3. MeetingShelf Web MeetingShelf MeetingShelf (1) (2) (3) (4) (5) Web MeetingShelf](/thumbs/79/80104027.jpg "1 Web [2] Web [3] [4] [5], [6] [7] [8] S.W. [9] 3. MeetingShelf Web MeetingShelf MeetingShelf (1) (2) (3) (4) (5) Web MeetingShelf")
1,a) 2,b) 4,c) 3,d) 4,e) Web A Review Supporting System for Whiteboard Logging Movies Based on Notes Timeline Taniguchi Yoshihide 1,a) Horiguchi Satoshi 2,b) Inoue Akifumi 4,c) Igaki Hiroshi 3,d) Hoshi
2. CABAC CABAC CABAC 1 1 CABAC Figure 1 Overview of CABAC 2 DCT 2 0/ /1 CABAC [3] 3. 2 値化部 コンテキスト計算部 2 値算術符号化部 CABAC CABAC
![2. CABAC CABAC CABAC 1 1 CABAC Figure 1 Overview of CABAC 2 DCT 2 0/ /1 CABAC [3] 3. 2 値化部 コンテキスト計算部 2 値算術符号化部 CABAC CABAC](/thumbs/92/108208872.jpg "2. CABAC CABAC CABAC 1 1 CABAC Figure 1 Overview of CABAC 2 DCT 2 0/ /1 CABAC [3] 3. 2 値化部 コンテキスト計算部 2 値算術符号化部 CABAC CABAC")
H.264 CABAC 1 1 1 1 1 2, CABAC(Context-based Adaptive Binary Arithmetic Coding) H.264, CABAC, A Parallelization Technology of H.264 CABAC For Real Time Encoder of Moving Picture YUSUKE YATABE 1 HIRONORI