-周波数分解- - Riken

1 1 II 2 6218 - - DCT Shin Yoshizawa: 1..2. Discrete Cosine Transform (DCT, ) . p(^^)q Shin Yoshizawa: wavelet KL CG-ARTS Shin Yoshizawa: CG-ARTS Shin Yoshizawa: (Frequency) wikipedia (1/ ). (Period) . Amplitude : . Shin Yoshizawa: wikipedia LxbLxbLxbLxaLxaLxaaxf 3sin2sinsin 3cos2coscos23213210 ( ) .. :sin, cos :a, b 2 Shin Yoshizawa.

2 ( ) ..( ))(xf aaa 21 vvv 21 ),(vuf aaaaaaaaaa 212222111211 vvvvvvvvva 212222111211 Shin Yoshizawa: : . 103213210sincos23sin2sinsin 3cos2coscos2nnnLxnbLxnaaLxbLxbLxbLxaLxaL xaaxf LLnLLndxLxnxfLbdxLxnxfLa sin1cos1 . H. Suzuki, U. Tokyo nxLninecxf sincosiei wikipediaShin Yoshizawa: : .. : dkekFxfdxexfkFikxikx 2121 21.

3 KaFxafkGkFxgxf , CG-ARTS H. Suzuki, U. Tokyo sincosiei Shin Yoshizawa: : .. : .. 1024 1024 2x1024 1024 :102( )( ) exp()(0,1,..,1)NijikFkf sNkN (cos) (sin) + log(1+F) ..- (FFT): . 2 512 1,024 (N ).Shin Yoshizawa: 1010)exp(),(),(NiMjjifvuF Shin Yoshizawa: : . 222),(Im),(Re),(vuFvuFvuF 41231234 1 3, 2 4, 3 1, 4 2.

4 ( ) (cos) (sin) 3 Shin Yoshizawa: 2 )cos(),(vyuxAyxf CG-ARTS Shin Yoshizawa: CG-ARTS Shin Yoshizawa: (DCT) 10101010),()2)1(2cos()2)1(2cos()()(4,),( )2)1(2cos()2)1(2cos()()(,NiMjNiMjjiFNyiM xjjCiCMNyxfjifNviMujvCuCvuF (cos) :- y DCT .- . )0(1)0(21)(xxxC wikipedia Shin Yoshizawa: (DCT) DCT Shin Yoshizawa: (DCT) FFT ( ) : DCT : DCTShin Yoshizawa: H.

5 - .- .. CG-ARTS H. Suzuki, U. Tokyo),(),(),(vuHvuFvuG 4 Shin Yoshizawa: CG-ARTS Shin Yoshizawa: -u0 u0 .. CG-ARTS Shin Yoshizawa: 2 CG-ARTS (u,v)=(0,0) 1 (u,v)=(0,0) .Shin Yoshizawa: CG-ARTS -u0 u0 .),(1),(vuHvuHlowhigh .Shin Yoshizawa: .),(1),(vukHvuHhighemphh CG-ARTS Shin Yoshizawa: Overshooting.

6 MathWorld wikipedia5 Shin Yoshizawa: Overshooting MathWorldShin Yoshizawa: .-KL(Karhunen-Loeve) ..- : ( ).-Zernike etc. (PCA) PCA: Principal Component Analysis MathWorld- :- Hyperplane ( ).-Covariance matrix( = ) Best fit ellipsoid . wavelet : . - ..- (Multiresolution Analysis) .Shin Yoshizawa: Shin Yoshizawa: CG-ARTS Shin Yoshizawa: : (BMP PPM ) or or Shin Yoshizawa: Ex08 : : Image *DCT(Image *in,int X,intY): in X Y DCT.

7 - : . void InverseDCT(Image *dct,Image *out, intX,intY):DCT() dct X Y out .6 Shin Yoshizawa: Ex08 : . make . 1. BMP .2. ( .bmp ).3. (int).4. (int): ../testDCT BMP (.bmp ) (int) (int) 3 bmp : Yoshizawa: 16x16 1,2,3,4,8 .. Shin Yoshizawa: 32x32 : Shin Yoshizawa: 32x32 : Ex08.

8 Shin Yoshizawa: 1. : .2. : .3. : .4. : .- ( ) DCT DCT . p(^^)q )2exp(),(222 yxyxg Shin Yoshizawa: FFT . 10/5.