η η η η GAR = 1 F RR η F RR F AR F AR F RR η F RR F AR

µ µ µ µ µ µ

Γ R N=mxn W T X x mean X W T x g W P x = W T (x g x mean )

X = X x mean P x = W T X d P x P i, i = 1, 2..., G

M s t t << s S T S T = 1 M M (x i µ)(x i µ) T n=1 µ x i W pca t t t s M t t < s S w

S b S w = 1 N S b = 1 N N c j (x j i µ j)(x j i µ j) T j=1 i=1 c N j (µ j µ)(µ j µ) T j=1 x j i i j µ j j c N j j N µ det S b det S w S w W S 1 w S b c 1 f c 1 t + c S w t g f

U = W X

X[k, l] = 2 N c a 1 kc l c k, c l = m=0 n=0 b 1 x[m, n] [ { ( 1 2 ) 1 2, k = 0, l = 0 (2m + 1)kπ ] [ 2N 1, k = 1, 2,..., a 1, l = 1, 2,..., b 1 (2n + 1)lπ ] 2N m n k l

m j [y 1j, y 2j,..., y mj ] j k [w 1jk, w 2jk,..., w mjk ] w ijk y ij f [v 1f, v 2f,..., v mf ] v if y ij f j k j = 1, 2,..., p k = 1, 2,..., q D NNfjk = m w ijk v if i=1 f j D NNfjk D NNfgh, j g, k h

ψ µ,υ (x) = k2 kµ,υ µ,υ 2 x 2 σ 2 e 2σ 2 [e ikµ,υx e σ2 2 ] µ = 0,..., L 1 u = 0,..., M 1 L M k µ,υ = k max λ υ eiµ π L k max f(x) x 0 x 0 j µ,υ (x 0 ) = f(x) ψ µ,υ (x x 0 ) j(x 0 ) = [j 0,0 (x 0 ), j 1,0 (x 0 ),..., j L 1,M 1 (x 0 )] T

x l j(x) j(x l ) = [f 1 (x l ),..., f M (x l )] T f i (x l ) f i M C f (j(x l t), j(x l r)) = j(x l r) j(x l t) 3 3 3 3 2 8 = 256 (P, R) P R LBP P,R (x c, y c ) = P 1 p=0 s(g p g c )2 p

s = { 1, x 0 0, x < 0 (x c, y c ) (g p, g c )

I( x, t) = (c( x, t) I( x, t)) t ( x, t) x t c( x, t) I t+1 (x, y) = I t + 1 4 [c N,t(x, y) I N,t (x, y) + c S,t (x, y) I S,t (x, y) +c E,t (x, y) I E,t (x, y) + c W,t (x, y) I W,t (x, y)] (x, y) I N,t 2 (x,y) c N,t (x, y) = e k 2 I N,t = I t (x, y + 1) I t (x, y) I open = (I S) S I top = I I open I open I top S

Ψ(x, y) (x, y) ( 0, N 1,..., N 7 ) (x, y) ( 7 i=0 N i) > 2) M(x, y, Ψ) N

M(x n, y n, Ψ n ), n = 1,..., N M(x, y, Ψ) L M = {{d 1, ϕ 1, θ 1 }, {d 2, ϕ 2, θ 2 },..., {d N, ϕ N, θ N }, Ψ} d n = (x n x) 2 + (y n y) 2 ϕ n = diff(ψ n, Ψ) θ n = diff( y n y x n x, Ψ) n = 1, 2,..., N d n M(x, y, Ψ) (0 2π) I t M M

{δd min, δϕ min, δθ min, δ ψ } {T d, T ϕ, T θ, T ψ } Score = NUM match max{num test, NUM database } NUM match NUM test NUM database

1536 2048 240 320

(x min, y min, x max, y max ) x min y min x max y max

left = x min top = y min width = x max x min + 1 height = y max y min + 1

c I 1, I 2,..., I M n m I Γ n m I = x 11 x 12.. x 1m............ x n1 x n2.. x nm Γ = x 11 x 12... x nm n m d = n m 2048 1536

n m K K < (n m) P i = W T Γ i i = 1, 2,.., M W S W J(W ) = tr(s W ) S W = E(P EP )(P EP ) T = E[W T Γ E(W T Γ)][W T Γ E(W T Γ)] T = E[W T (Γ EΓ)][W T (Γ EΓ)] T tr(s W ) = W T [E(Γ EΓ)(Γ EΓ) T ]W C = E(Γ EΓ)(Γ EΓ) T

C = 1 M M (Γ i Γ)(Γ i Γ) T i=1 J(W ) = W T CW C (n m) (n m) n m n m W pca W C K W pca = W T CW = W = [w 1, w 2,..., w K ] {w i i = 1, 2,..., K} n m K I i Γ i Γ Γ = 1 M M i=1 Γ i Φ i = Γ i Γ

C (n m) (n m) C = 1 M Φ i Φ T i = AA T M i=1 A (n m) M A = [Φ 1 Φ 2...Φ M ] u i C C n m n m A T A M M y i µ i A T A A T Ay i = µ i y i AA T Ay i = µ i Ay i CAy i = µ i Ay i Cu i = µ i u i u i = Ay i AA T A T A A T A y i A T A AA T n m M c M c W (n m) M c

M c 25 90 90

W P i M c 1 Φ i P i w i 1 P i = w2 i..., i = 1, 2,..., M. wm c i Γ Φ = Γ Γ P = W T Φ P = w 1 w 2... w M c

P i P e r = min i P P i e r

reconstruct = W y T i, i = 1, 2,..., M c yi T M c A T A

X n I n m X Y = IX m Y I X J(X) = tr(s X ) S X S x = E(Y EY )(Y EY ) T = E[IX E(IX)][IX E(IX)] T C = E[(I EI)X][(I EI)X] T tr(s x ) = X T [E(I EI) T (I EI)]X C = E[(I EI) T (I EI)] C = 1 M M (I j I) T (I j I) j=1 n m J(X) = X T CX X 2DP CA C X 1,..., X K J(X) { X 1,..., X K = argmaxj(x) Xi T X j = 0 i j i, j = 1,..., K

I = 1 M M i=1 I i C C m m C m m 1 30 90

X 1,..., X c+1 C c + 1 c + 1 X m c + 1 X = X 1 X 2 X c+1 I i i = 1,..., M Y n 1 Y i = I X i, i = 1, 2,..., c + 1 B i = [Y i 1, Y i 2,..., Y i c+1], i = 1, 2,..., M n c + 1

B 1... B i... Y1 i Y2 i... Y i c+1... B M... Y1 M Y2 M... Y M c+1... Y1 1 Y2 1... Y 1 c+1... I Φ = I I Φ B Φ B i = [Y1 i, Y 2 i,..., Y c+1 i ] B Φ = [Y1 Φ, Y 2 Φ,..., Y c+1 Φ ] c+1 d(b i, B Φ ) = Yk i Y k Φ k=1 i = 1, 2,..., M Φ e r = min i d(b i, B Φ ) e r

reconstruct = B i X T

S w S b S w = 1 M M c j (Γ j i Γ j)(γ j i Γ j) T j=1 i=1 S b = 1 M c M j (Γ j Γ)(Γ j Γ) T j=1 Γ j i i j Γ j j M j j Γ j = 1 M j Γ c j Γ S w W W T S b W W T S w W = [w 1 w 2...w k ] w i i = 1, 2,..., k S b S w k {λ i i = 1, 2,..., m} S b w i = λ i S w w i, i = 1, 2,..., m c 1 k c 1 c S w n n M c S w M c c 1 W T opt = W T lda W T pca

W pca = W T CW W W lda = W W T W T pcas b W pca W W T W T pcas W W pca W W P CA M c P w 1 w 2 P i =, i = 1, 2,..., M P = P 1 P 2 P M w M c P S w S b Γ Γ = 1 M M i=1 P i j Γ j Γ j = 1 M j M j P i c j P i P Γ j Γ M c M c S b S w M c M c c 1 c 1 W LDA M c c 1 80 100

V = W T LDAP V c 1 M

V i c 1 1 V i = k i 1 k i 2... k i c 1, i = 1, 2,..., M Γ Φ = Γ Γ V = W T LDA W T pca Φ V = k 1 k 2... k c 1 V i V e r = min i V V i e r

C r i,j j i i = 1,..., C j = 1,..., N R j j

R j = C i=1 r i,j ϵ R j = C r i,j + ϵ j i=1 C i=1 ϵ j = r i,j K j ϵ j K j = 1 r 1,1 = 1 r 2,1 = 2 j = 2 r 1,2 = 3 r 2,2 = 1 R 1 = 1 R 2 = 1 K = 100 R 1 = 1 + 3 100 R 2 = 1 + 4 100 R 1 R j = C i=1 r i,j j = 1 R 1 = 109 j = 2 R 2 = 60 R 1 C i=1 r i,j = 0

R 1 = 9 R 2 = 45 R 1 f M V M T M F = 0.5M v + 0.5M T s s I s = [s min, s max ] I d = [s min, s max] s I s I s s = s min + s s min s max s min (s max s min)

I f (x, y) = I 1(x, y) + I 2 (x, y) 2 I 1 (x, y) I 2 (x, y) ϕ ω 1 I(x, y) I(x, y) = ω 1 (ϕ(ω(i 1 (x, y)), ω(i 2 (x, y)))) ϕ

Z (n m) 2 C Z D V V D 2 2 V V m P 2 1 P = V m Vm I f (x, y) = P (1)I 1 (x, y) + P (2)I 2 (x, y)

80 90 80 80 90 100 90 70