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- あゆみ あかさか
- 5 years ago
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Transcription
1 G01P038-0
2 ( ) ( )
3 (V = 1, θ = 0) (T = 0.1, θ = 0) ( ) (V = 1, θ = 0) (T = 0.1, θ = 0) PSNR PSNR(Peak Signal to Noise Ratio)
4 A 40 A A.1.1 pgm.h A.1.2 pgm.c A A.2.1 FFT1.h A.2.2 FFT1.c A.2.3 FFT2.h A.2.4 FFT2.c A A.3.1 convertdata.h A.3.2 convertdata.c A A.4.1 blur.c A A.5.1 inverse.c A.5.2 inverse A.5.3 wiener.c A.5.4 inverse2 2.c
5 1 1.1 (PSF) ( ) PSF ( ) ( ) PSF PSF 2 ( ) C 4
6 1.3 2 ( ) 3 PSF ( )
7 2 2.1 ( ) 2.2 ( ) g(x, y) g(x, y) = h(x, y, α, β, γ)f(α, β)dαdβ (2.1) f(α, β) h(,,, ) (PSF) (2.1) 2 g(x, y) = h(x α, y β)f(α, β)dαdβ (2.2) g(x, y) = f(x, y) h(x, y) (2.3) (2.3) 2 G(µ, ν) = F{g(x, y) = F{f(x, y) h(x, y) = H(µ, ν)f (µ, ν) (2.4) 6
8 µ, ν x, y H(µ, ν) (OTF) n(x, y) N(µ, ν) (2.2) (2.4) g(x, y) = h(x α, y β)f(α, β)dαdβ + n(x, y) (2.5) G(µ, ν) = H(µ, ν)f (µ, ν) + N(µ, ν) (2.6) (2.2) f g g = [H]f + n (2.7) n 2.3 ˆf g [B] b(x, y) B(µ, ν) ˆf(x, y) ˆF (µ, ν) ˆf(x, y) = b(x α, y β)g(α, β)dαdβ (2.8) ˆF (µ, ν) = [H(µ, ν)f (µ, ν) + N(µ, ν)]b(µ, ν) (2.9) (2.8) (2.5) (deconvolution) B(µ, ν) B(µ, ν) = 1 H(µ, ν) (2.10) 7
9 ˆF (µ, ν) ˆF (µ, ν) = F (µ, ν) + N(µ, ν) H(µ, ν) (2.11) (2.10) H(µ, ν) (inverse filter) F (µ, ν) H(µ, ν) (2.11) 2 (2.7) [H] [H] 1 ˆf ˆf = f + [H] 1 (2.12) [H] 1 (2.12) 2 (ill-conditioned problem) (ill-posed problem) (reguralization) ( ) 2 E ɛ 2 = E[{f(x, y) ˆf(x, y) 2 ] (2.13) E[ ] 2 2 (least square filter) (Wiener filter) 8
10 2 B(µ, ν) = H (µ, ν) H(µ, ν) 2 + S n (µ, ν)/s f (µ, ν) (2.14) S f (µ, ν) S n (µ, ν) R f (x, y) R n (x, y) S f (µ, ν) = S n (µ, ν) = R f (x, y) exp{ j2π(µx + νy)dxdy (2.15) R n (x, y) exp{ j2π(µx + νy)dxdy (2.16) (2.14) B(µ, ν) H (µ, ν) H(µ, ν) 2 + Γ (2.17) Γ (2.7) 2 [B] ˆf ˆf = [B]g (2.18) ɛ 2 2 [B] min E[ɛɛ T ] = min E[(f ˆf)(f ˆf) T ] (2.19) [B] (2.7),(2.18) E[(f [B]g)(f [B]g) T ] = E[{ff T [B]([H]ff T + nf T ) (ff T [H] + fn T )[B] +[B]([H]ff T [H] T + nf[h] T + [H]fn T + nn T )[B] T ] (2.20) E[fn T ] = E[n T f] = 0 (2.21) 9
11 f n E[ff T ] = [R ff ], E[nn T ] = [R nn ] (2.22) (2.20) E[ɛɛ T ] = [R ff ] 2[B][H][R ff ] + [B][H][R ff ][H][B] T + [B][R nn ][B] T E[ɛɛ T ] [B] (2.23) = 0 (2.24) [B] = [R ff ][H] T ([H][R ff ][H] T + [R nn ]) 1 (2.25) 2 f 2 f [R ff ] = R 00 R R 0(M 1) R 10 R R (M 1) R (M 1)(M 1) (2.26) (2.26) R ij N N R ij = E[f i f T j ] (2.27) f i f j i j R ij = R ji (2.26) (2.14) (2.25) 2 (2.13) (2.19) (2.14) H(µ, ν) = 0 B(µ, ν) 10
12 2.4 ( ) PSF ( ) 11
13 3 3.1 PSF ( ) 3.2 f(x, y) x y α(t) β(t) T g(x, y) g(x, y) = T 2 T 2 f(x α(t), y β(t))dt (3.1) = = G(µ, ν) ( T ) 2 f(x α(t), y β(t))dt exp{ j2π(µx + νy)dxdy T 2 T 2 T 2 dt f(x α(t), y β(t)) exp{ j2π(µx + νy)dxdy (3.2) u = x α(t), v = y β(t) (3.3) G(µ, ν) = T 2 T 2 dt f(u, v) exp{ j2π(µ(u + α(t)) + ν(v + β(t))dudv 12
14 = = T 2 T 2 T 2 T 2 dt f(u, v) exp{ j2π(µu + νv) exp{ j2π(µα(t) + νβ(t))dudv exp{ j2π(α(t)µ + β(t)ν)dt F (µ, ν) (3.4) H(µ, ν) = T 2 T 2 exp{ j2π(α(t)µ + β(t)ν)dt (3.5) G(µ, ν) = H(µ, ν)f (µ, ν) (3.6) (3.5) V θ H(µ, ν) = α(t) = V cos θ t, β(t) = V sin θ t (3.7) T 2 T 2 exp{ j2π(v cos θ tµ + V sin θ tνdt = sin πv (µ cos θ + ν sin θ)t πv (µ cos θ + ν sin θ) = T sin c{πv (µ cos θ + ν sin θ)t (3.8) 3.3 (2.10) (3.8) B(µ, ν) B(µ, ν) = = 1 H(µ, ν) 1 T sin c{πv (µ cos θ + ν sin θ)t ˆF (µ, ν) ˆF (µ, ν) = G(µ, ν)b(µ, ν) (3.9) 13
15 = G(µ, ν) T sin c{πv (µ cos θ + ν sin θ)t (3.10) ˆf (3.8) H(µ, ν) = 0 (2.11) r B(µ, ν) = 1 H(µ,ν) µ 2 + ν 2 r 2 1 µ 2 + ν 2 > r 2 (3.11) H(µ, ν) ɛ B(µ, ν) = 1 H(µ,ν) H(µ, ν) > ɛ 0 H(µ, ν) ɛ (3.12) 3.4 ( ) (2.14) (3.8) B(µ, ν) B(µ, ν) = = H (µ, ν) H(µ, ν) 2 + S n (µ, ν)/s f (µ, ν) T sin c{πv (µ cos θ + ν sin θ)t T sin c{πv (µ cos θ + ν sin θ)t 2 + S n (µ, ν)/s f (µ, ν) T sin c{πv (µ cos θ + ν sin θ)t (3.13) T sin c{πv (µ cos θ + ν sin θ)t 2 + Γ 14
16 ˆF (µ, ν) ˆF (µ, ν) = G(µ, ν)b(µ, ν) = G(µ, ν)t sin c{πv (µ cos θ + ν sin θ)t T sin c{πv (µ cos θ + ν sin θ)t 2 + S n (µ, ν)/s f (µ, ν) G(µ, ν)t sin c{πv (µ cos θ + ν sin θ)t T sin c{πv (µ cos θ + ν sin θ)t 2 + Γ (3.14) ˆf 3.5 PSF ( ) 15
17 4 4.1 (, ) (2.5) (2.11) 4.2 g(x, y) g(x, y) = F 1 {F{f(x, y)h(µ, ν) (4.1) g(x, y) g(x, y) = g(x, y) = g(x, y) + n(x, y) (4.2) n(x, y) or 0 g(x, y) g(x, y) g(x, y) + 1 ( ) F 1 {F{g(x, y)b(µ, ν) F 1 {F{ g(x, y)b(µ, ν) F 1 {F{g(x, y) + 1B(µ, ν) F 1 {F{g(x, y)b(µ, ν) F 1 {F{ g(x, y)b(µ, ν) F 1 {F{g(x, y) + 1B(µ, ν) F 1 {F{g(x, y)b(µ, ν) f(x, y) 16
18 F 1 {F{g(x, y) + 1B(µ, ν) or F 1 {F{g(x, y)b(µ, ν) f(x, y) F 1 {F{g(x, y) + 1B(µ, ν) (4.3) ˆf(x, y) = F 1 {F{g(x, y)b(µ, ν) + F 1 {F{g(x, y) + 1B(µ, ν) 2 (4.4) ˆf(x, y)
19 5 5.1 PSNR(Peak Signal to Noise Ratio) 5.2 CPU : Celeron 2.00GHz Memory : 768MB OS : Windows XP 18
20 5.3 pgm(portable graymap) ( ) : 19
21 5.5 (3.8) T, V, θ (4.1) PSF 5.2: T = 0.1, V = 1, θ = 0 5.3: T = 0.1, V = 1, θ = 0 5.4: T = 0.1, V = 1, θ = π/2 5.5: T = 0.1, V = 1, θ = π/2 20
22 5.5.1 (V = 1, θ = 0) 5.6: T = 0.01, V = 1, θ = 0 5.7: T = 0.01, V = 1, θ = 0 5.8: T = 0.1, V = 1, θ = 0 5.9: T = 0.1, V = 1, θ = 0 21
23 5.10: T = 1, V = 1, θ = : T = 1, V = 1, θ = (T = 0.1, θ = 0) 5.12: T = 0.1, V = 0.1, θ = : T = 0.1, V = 0.1, θ = 0 22
24 5.14: T = 0.1, V = 1, θ = : T = 0.1, V = 1, θ = : T = 0.1, V = 10, θ = : T = 0.1, V = 10, θ = 0 23
25 5.6 (3.8) T = 0.1, V = 1, θ = : (r = 5) 5.19: PSF(r = 5) 5.20: (r = 9) 5.21: PSF(r = 9) 24
26 5.22: (r = 10) 5.23: PSF(r = 10) 5.24: ( ) 5.25: PSF( ) 25
27 5.6.2 ɛ = : (ɛ = 0.010) 5.27: PSF(ɛ = 0.010) 5.28: (ɛ = 0.004) 5.29: PSF(ɛ = 0.004) 26
28 5.30: (ɛ = 0.001) 5.31: PSF(ɛ = 0.001) 5.32: ( ) 5.33: PSF( ) 27
29 5.6.3 ( ) Γ = : (Γ = ) 5.35: PSF(Γ = ) 5.36: (Γ = ) 5.37: PSF(Γ = ) 28
30 5.38: (Γ = ) 5.39: PSF(Γ = ) 5.40: (Γ = ) 5.41: PSF(Γ = ) 29
31 5.42: (Γ = ) 5.43: PSF(Γ = ) 30
32 : (ɛ = 0.010) 5.45: PSF(ɛ = 0.010) 5.46: (ɛ = 0.005) 5.47: PSF(ɛ = 0.005) 31
33 5.48: (ɛ = 0.004) 5.49: PSF(ɛ = 0.004) 5.50: (ɛ = 0.001) 5.51: PSF(ɛ = 0.001) 32
34 (V = 1, θ = 0) 5.52: (T = 0.05) 5.53: (T = 0.05) 5.54: (T = 0.25) 5.55: (T = 0.25) 33
35 5.7.2 (T = 0.1, θ = 0) 5.56: (V = 0.5) 5.57: (V = 0.5) 5.58: (V = 2.5) 5.59: (V = 2.5) 34
36 5.8 PSNR PSNR(Peak Signal to Noise Ratio) PSNR(Peak Signal to Noise Ratio) ( ( ) 2 ) P SNR = 10 log 10 sqrt({f(x, y) ˆf(x, (db) (5.1) y) 2 ) PSNR inverse2 inverse2 2 ɛ inverse2 inverse : PSNR(dB) 35
37 5.8.3 PSNR inverse2 inverse2 2 T inverse2 inverse : PSNR(dB)(V = 1, θ = 0) V inverse2 inverse : PSNR(dB)(T = 0.1, θ = 0) 36
38 5.9 PSNR 37
39 ( ) PSNR 2 ( ) 3 PSF ( ) sin ( ) 38
40 PSNR(dB) 6.3 ( ) ( ) 39
41
42 1. N.Mastronardi, P.Lemmerling, and S.Van Huffel Fast structured total least squares algorithm for solving the basic deconvolution problem,siam Journal on Matrix Analysis and Applications,22(2): ,(2000)
43 A A.1 A.1.1 pgm.h /********************************************************* /* pgm.h /* pgm.c /********************************************************* /* #define MAX_IMAGESIZE #define MAX_BRIGHTNESS #define GRAYLEVEL #define MAX_FILENAME #define MAX_BUFFERSIZE 1024 /* 255 /* 256 /* (= +1) 256 /* 256 /* /* /* unsigned char image1[max_imagesize][max_imagesize], image2[max_imagesize][max_imagesize]; int x_size1, y_size1, /* image1 x_size2, y_size2; /* image2 /* void load_image_data( ); /* void save_image_data( ); /* A.1.2 pgm.c /************************************************************** /* pgm.c /* pgm /************************************************************** #include <stdio.h> #include <stdlib.h> 42
44 #include "pgm.h" /************************************************************** /* pgm /* image1[ ][ ] x_size1 y_size1 /************************************************************** void load_image_data( ) { char file_name[max_filename]; /* char buffer[max_buffersize]; /* FILE *fp; /* int max_gray; /* int x, y; /* /* printf(" \n"); printf(" \n"); printf(" \n"); printf(" pgm, \n"); printf(" (*.pgm) : "); scanf("%s",file_name); fp = fopen( file_name, "rb" ); if ( NULL == fp ){ printf(" \n"); exit(1); /* (=P5) fgets( buffer, MAX_BUFFERSIZE, fp ); if ( buffer[0]!= P buffer[1]!= 5 ){ printf(" P5 \n"); exit(1); /* x_size1, y_size1 # x_size1 = 0; y_size1 = 0; while ( x_size1 == 0 y_size1 == 0 ){ fgets( buffer, MAX_BUFFERSIZE, fp ); if ( buffer[0]!= # ){ sscanf( buffer, "%d %d", &x_size1, &y_size1 ); /* max_gray # max_gray = 0; while ( max_gray == 0 ){ fgets( buffer, MAX_BUFFERSIZE, fp ); if ( buffer[0]!= # ){ sscanf( buffer, "%d", &max_gray ); 43
45 /* printf(" = %d, = %d\n", x_size1, y_size1 ); printf(" = %d\n",max_gray); if ( x_size1 > MAX_IMAGESIZE y_size1 > MAX_IMAGESIZE ){ printf(" %d x %d \n", MAX_IMAGESIZE, MAX_IMAGESIZE); printf(" \n"); exit(1); if ( max_gray!= MAX_BRIGHTNESS ){ printf(" \n"); exit(1); /* for ( y = 0; y < y_size1; y ++ ){ for ( x = 0; x < x_size1; x ++ ){ image1[y][x] = (unsigned char)fgetc( fp ); printf(" \n"); printf(" \n"); fclose(fp); /**************************************************************** /* image2[ ][ ], x_size2, y_size2 /* pgm /**************************************************************** void save_image_data( ) { char file_name[max_filename]; /* FILE *fp; /* int x, y; /* /* printf(" \n"); printf(" pgm \n"); printf(" \n"); printf(" (*.pgm) : "); scanf("%s",file_name); fp = fopen(file_name, "wb"); /* "P5" fputs( "P5\n", fp ); /* # fputs( "# Created by Image Processing\n", fp ); /* fprintf( fp, "%d %d\n", x_size2, y_size2 ); /* fprintf( fp, "%d\n", MAX_BRIGHTNESS ); 44
46 /* for ( y = 0; y < y_size2; y ++ ){ for ( x = 0; x < x_size2; x ++ ){ fputc( image2[y][x], fp ); printf(" \n"); printf(" \n"); fclose(fp); A.2 A.2.1 FFT1.h /********************************* /* FFT1.h /* FFT1.c /********************************* #define FFT_MAX 1024 #define PI /* int calc_power_of_two( int number ); void make_initial_data( double *re_part, double *im_part, int num_of_data, int power ); void FFT1( double *re_part, double *im_part, int num_of_data, int flag ); A.2.2 FFT1.c /************************************** /* FFT1.c /* 1 FFT /************************************** #include "FFT1.h" /************************************** /* number /* 8 --> 3, 16 --> 4, 32 --> 5,... /************************************** int calc_power_of_two( int number ) { int power; power = 0; 45
47 while ( number!= 1 ){ power ++; number = number >> 1; return power; /* /******************************************************************** /* FFT /* double *re_part, /* *im_part; ( ) /* int num_of_data; /* int power; num_of_data power /******************************************************************** void make_initial_data( double *re_part, double *im_part, int num_of_data, int power ) { int i, j; /* int ptr, offset; /* int new_ptr; /* int dft; /* DFT ( i double re_buf[fft_max], im_buf[fft_max]; /* dft = num_of_data; for ( i = 1; i < power; i ++ ){ /* i new_ptr = 0; offset = 0; while( new_ptr < num_of_data ){ ptr = 0; while( ptr < dft ){ re_buf[new_ptr] = *( re_part + offset + ptr ); im_buf[new_ptr] = *( im_part + offset + ptr ); new_ptr ++; ptr = ptr + 2; if ( ptr == dft ) ptr = 1; offset = offset + dft; /* for ( j = 0; j < num_of_data; j ++ ){ *( re_part + j ) = re_buf[j]; *( im_part + j ) = im_buf[j]; dft = dft / 2; /******************************************************************** 46
48 /* FFT (flag = 1), FFT (flag = -1) /* double *re_part, /* *im_part; ( ) /* int num_of_data, flag; FFT /******************************************************************** void FFT1( double *re_part, double *im_part, int num_of_data, int flag ) { int i,j,k,power; /* double unit_angle,step_angle; /* int dft,half,num_of_dft; /* DFT DFT int num_out,num_in1,num_in2; /* DFT double re_buf,im_buf,angle; /* /* static double re_part_new[fft_max],im_part_new[fft_max]; /* FFT ( flg = -1 ) num_of_data /* if ( flag == -1){ for ( i = 0; i < num_of_data; i ++ ){ *( re_part + i ) = *( re_part + i ) / num_of_data; *( im_part + i ) = - *( im_part + i ) / num_of_data; /* num_of_data (power) power = calc_power_of_two( num_of_data ); /* make_initial_data( re_part, im_part, num_of_data, power ); /* 2 DFT, 4 DFT, 8 DFT,... unit_angle = 2.0 * PI / num_of_data; dft = 2; /* = DFT for ( i = 0; i < power; i ++ ){ /* DFT DFT /* i=0 -> 2, i=1 -> 4, i=2 -> 8,... num_of_dft = num_of_data / dft; /* DFT step_angle = unit_angle * num_of_dft; half = dft / 2; for ( j = 0; j < num_of_dft; j ++ ){ angle = 0.0; for ( k = 0; k < dft; k ++ ){ /* No.num_in1 No.num_in2 No.num_out /* No.num_in1 num_out = j * dft + k; if ( k < half ){ num_in1 = num_out; num_in2 = num_in1 + half; else { num_in2 = num_out; num_in1 = num_out - half; 47
49 /* (re_) (im_) re_buf = *( re_part + num_in2 ); im_buf = *( im_part + num_in2 ); re_part_new[num_out] = *( re_part + num_in1 ) + re_buf * cos(angle) + im_buf * sin(angle); im_part_new[num_out] = *( im_part + num_in1 ) + im_buf * cos(angle) - re_buf * sin(angle); /* angle = angle + step_angle; /* for ( j = 0; j < num_of_data; j ++ ){ *( re_part + j ) = re_part_new[j]; *( im_part + j ) = im_part_new[j]; dft = dft * 2; /* DFT /* FFT ( flg = -1 ) if ( flag == -1 ){ for ( j = 0; j < num_of_data; j ++ ){ *( im_part + j ) = - *( im_part + j ); A.2.3 FFT2.h /************************************* /* FFT2.h /* FFT2.c /************************************* /* double data[fft_max][fft_max]; /* double jdata[fft_max][fft_max]; /* int num_of_data; /* /* void FFT2( int flag ); A.2.4 FFT2.c /*************************** /* FFT2.c 48
50 /* 2 FFT /*************************** #include "FFT1.h" #include "FFT2.h" /********************************************************* /* data, jdata, num_of_data /* flag = 1 : FFT, flag = -1 : FFT /********************************************************* void FFT2( int flag ) { int i, j; /* static double re[fft_max], im[fft_max]; /* for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ re[j] = data[i][j]; im[j] = jdata[i][j]; FFT1( re, im, num_of_data, flag ); for ( j = 0; j < num_of_data; j ++ ){ data[i][j] = re[j]; jdata[i][j] = im[j]; for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ re[j] = data[j][i]; im[j] = jdata[j][i]; FFT1( re, im, num_of_data, flag ); for ( j = 0; j < num_of_data; j ++ ){ data[j][i] = re[j]; jdata[j][i] = im[j]; A.3 A.3.1 convertdata.h /******************************** /* convertdata.h /* convertdata.c 49
51 /******************************** /* void make_original_data( ); /* FFT void make_output_image( ); /* FFT A.3.2 convertdata.c /***************************************** /* convertdata.c /* <--> FFT /***************************************** #include <stdio.h> #include <stdlib.h> #include "pgm.h" #include "FFT1.h" #include "FFT2.h" /************************************************************* /* image1[y][x] data[y][x], jdata[y][x] /************************************************************* void make_original_data( ) { int i, j; /* if ( x_size1!= y_size1 ){ printf(" \n"); exit(-1); else { printf("\n \n"); num_of_data = x_size1; for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ data[i][j] = (double)image1[i][j]; jdata[i][j] = 0.0; /**************************************************************** /* data[y][x], jdata[y][x] image2[y][x] /*, [0,255] /**************************************************************** void make_output_image( ) 50
52 { int x, y; /* double max, min; /*, max = 0.0; min = MAX_BRIGHTNESS; printf("\n FFT \n"); x_size2 = num_of_data; y_size2 = num_of_data; for ( y = 0; y < y_size2; y ++ ){ for ( x = 0; x < x_size2; x ++ ){ if ( data[y][x] < 0 ) data[y][x] = 0; if ( data[y][x] < min ) min = data[y][x]; if ( data[y][x] > max ) max = data[y][x]; for ( y = 0; y < y_size2; y ++ ){ for ( x = 0; x < x_size2; x ++ ){ data[y][x] = MAX_BRIGHTNESS/(max-min)*(data[y][x]-min); image2[y][x] = (unsigned char)data[y][x]; A.4 A.4.1 blur.c /******************************************************************** /* blur.c /* /******************************************************************** #include <stdio.h> #include <stdlib.h> #include <math.h> #include "pgm.h" #include "FFT1.h" #include "FFT2.h" #include "convertdata.h" /*********************** /* sinc /*********************** double sinc(double x){ double n; if ( x == 0 ) n = 1; 51
53 else n = sin(x)/x; return n; /*************************************** /* /*************************************** void blur( ) { int i, j; /* double T; /* double V; /* double x; /* double h[num_of_data][num_of_data]; /* printf(" T :"); scanf("%lf",&t); printf(" V :"); scanf("%lf",&v); printf(" :"); scanf("%lf",&x); for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ /* h[i][j] = T*sinc(PI*V*T*(j*cos(x)+i*sin(x))); printf("\nfft \n"); for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ data[i][j] *= h[i][j]; jdata[i][j] *= h[i][j]; /*********************** /* /*********************** main( ) { load_image_data( ); /* make_original_data( ); /* FFT2( 1 ); /* FFT blur( ); /* FFT2( -1 ); /* FFT make_output_image( ); /* 52
54 save_image_data( ); /* return 0; A.5 A.5.1 inverse.c /*********************************************************** /* inverse.c /* /* /*********************************************************** #include <stdio.h> #include <stdlib.h> #include <math.h> #include "pgm.h" #include "FFT1.h" #include "FFT2.h" #include "convertdata.h" /*********************** /* sinc /*********************** double sinc(double x){ double n; if ( x == 0 ) n = 1; else n = sin(x)/x; return n; /************************************************************** /* /* 1 /************************************************************** void inverse( ) { int i, j; /* double T; /* double V; /* double x; /* double r; /* double b[num_of_data][num_of_data]; /* 53
55 printf(" T :"); scanf("%lf",&t); printf(" V :"); scanf("%lf",&v); printf(" :"); scanf("%lf",&x); printf(" r :"); scanf("%lf",&r); /* for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ if ( i*i+j*j <= r*r ) b[i][j] = 1/(T*sinc(PI*V*T*(j*cos(x)+i*sin(x)))); else b[i][j] = 1; printf("\nfft \n"); for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ data[i][j] *= b[i][j]; jdata[i][j] *= b[i][j]; /*********************** /* /*********************** main( ) { load_image_data( ); /* make_original_data( ); /* FFT2( 1 ); /* FFT inverse( ); /* FFT2( -1 ); /* FFT make_output_image( ); /* save_image_data( ); /* return 0; A.5.2 inverse2 /********************************************************* /* inverse2.c /* 54
56 /* /********************************************************* #include <stdio.h> #include <stdlib.h> #include <math.h> #include "pgm.h" #include "FFT1.h" #include "FFT2.h" #include "convertdata.h" /*********************** /* sinc /*********************** double sinc(double x){ double n; if ( x == 0 ) n = 1; else n = sin(x)/x; return n; /****************************************************************** /* /* 0 /****************************************************************** void inverse2( ) { int i, j; /* double T; /* double V; /* double x; /* double n; /* double b[num_of_data][num_of_data]; /* printf(" T :"); scanf("%lf",&t); printf(" V :"); scanf("%lf",&v); printf(" :"); scanf("%lf",&x); printf(" n :"); scanf("%lf",&n); /* for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ b[i][j] = T*sinc(PI*V*T*(j*cos(x)+i*sin(x))); if ( b[i][j] <= n && b[i][j] >= -n ) b[i][j] = 0; else b[i][j] = 1/b[i][j]; 55
57 printf("\nfft \n"); for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ data[i][j] *= b[i][j]; jdata[i][j] *= b[i][j]; /*********************** /* /*********************** main( ) { load_image_data( ); /* make_original_data( ); /* FFT2( 1 ); /* FFT inverse2( ); /* FFT2( -1 ); /* FFT make_output_image( ); /* save_image_data( ); /* return 0; A.5.3 wiener.c /************************************************************* /* wiener.c /* /* /************************************************************* #include <stdio.h> #include <stdlib.h> #include <math.h> #include "pgm.h" #include "FFT1.h" #include "FFT2.h" #include "convertdata.h" /*********************** /* sinc /*********************** double sinc(double x){ 56
58 double n; if ( x == 0 ) n = 1; else n = sin(x)/x; return n; /******************************************* /* /******************************************* void wiener( ) { int i, j; /* double T; /* double V; /* double x; /* double n; /* SN double b[num_of_data][num_of_data]; /* printf(" T :"); scanf("%lf",&t); printf(" V :"); scanf("%lf",&v); printf(" :"); scanf("%lf",&x); printf("sn n :"); scanf("%lf",&n); /* for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ b[i][j] = T*sinc(PI*V*T*(j*cos(x)+i*sin(x))) /((T*sinc(PI*V*T*(j*cos(x)+i*sin(x))))*(T*sinc(PI*V*T*(j*cos(x)+i*sin(x))))+n); printf("\nfft \n"); for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ data[i][j] *= b[i][j]; jdata[i][j] *= b[i][j]; /*********************** /* /*********************** main( ) { 57
59 load_image_data( ); /* make_original_data( ); /* FFT2( 1 ); /* FFT wiener( ); /* FFT2( -1 ); /* FFT make_output_image( ); /* save_image_data( ); /* return 0; A.5.4 inverse2 2.c /********************************************************* /* inverse2_2.c /* /* /* /********************************************************* #include <stdio.h> #include <stdlib.h> #include <math.h> #include "pgm.h" #include "FFT1.h" #include "FFT2.h" double data1[1024][1024]; double data2[1024][1024]; /*********************** /* sinc /*********************** double sinc(double x){ double n; if ( x == 0 ) n = 1; else n = sin(x)/x; return n; /************************************************************* /* image1[y][x] data[y][x], jdata[y][x] /************************************************************* void make_original_data2( ) { int i, j; /* if ( x_size1!= y_size1 ){ 58
60 printf(" \n"); exit(-1); else { printf("\n \n"); num_of_data = x_size1; for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ data[i][j] = (double)image1[i][j]; jdata[i][j] = 0.0; /* image1[][] +1 /* if ( image1[i][j]!= MAX_BRIGHTNESS) data1[i][j] = (double)image1[i][j]+1; else data1[i][j] = (double)image1[i][j]; /****************************************************************** /* /* 0 /****************************************************************** void inverse2( ) { int i, j; /* double T; /* double V; /* double x; /* double n; /* double b[num_of_data][num_of_data]; /* printf(" T :"); scanf("%lf",&t); printf(" V :"); scanf("%lf",&v); printf(" :"); scanf("%lf",&x); printf(" n :"); scanf("%lf",&n); /* for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ b[i][j] = T*sinc(PI*V*T*(j*cos(x)+i*sin(x))); if ( b[i][j] <= n && b[i][j] >= -n ) b[i][j] = 0; else b[i][j] = 1/b[i][j]; 59
61 printf("\nfft \n"); for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ data[i][j] *= b[i][j]; jdata[i][j] *= b[i][j]; /**************************************************************** /* data[y][x], jdata[y][x] image2[y][x] /*, [0,255] /**************************************************************** void make_output_image2( ) { int x, y; /* double max, min; /*, max = 0.0; min = MAX_BRIGHTNESS; printf("\n FFT \n"); x_size2 = num_of_data; y_size2 = num_of_data; for ( y = 0; y < y_size2; y ++ ){ for ( x = 0; x < x_size2; x ++ ){ /* data[y][x] = (data[y][x]+data2[y][x])/2; if ( data[y][x] < 0 ) data[y][x] = 0; if ( data[y][x] < min ) min = data[y][x]; if ( data[y][x] > max ) max = data[y][x]; for ( y = 0; y < y_size2; y ++ ){ for ( x = 0; x < x_size2; x ++ ){ data[y][x] = MAX_BRIGHTNESS/(max-min)*(data[y][x]-min); image2[y][x] = (unsigned char)data[y][x]+0.5; /*********************** /* /*********************** main( ) { int i, j; /* load_image_data( ); /* make_original_data2( ); /* 60
62 FFT2( 1 ); /* FFT inverse2( ); /* FFT2( -1 ); /* FFT /* for ( i = 0; i < num_of_data; i ++ ){ for ( j = 0; j < num_of_data; j ++ ){ data2[i][j] = data[i][j]; data[i][j] = data1[i][j]; jdata[i][j] = 0.0; FFT2( 1 ); /* FFT inverse2( ); /* FFT2( -1 ); /* FFT make_output_image2( ); /* save_image_data( ); /* return 0; 61
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数学の基礎訓練I
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スライド 1
数値解析 平成 29 年度前期第 14 週 [7 月 10 日 ] 静岡大学工学研究科機械工学専攻ロボット 計測情報分野創造科学技術大学院情報科学専攻 三浦憲二郎 期末試験 7 月 31 日 ( 月 ) 9 10 時限 A : 佐鳴会議室 B : 佐鳴ホール 講義アウトライン [7 月 10 日 ] 関数近似と補間 最小 2 乗近似による関数近似 ( 復習 ) ラグランジュ補間 形状処理工学の基礎
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Microsoft PowerPoint - guidance.ppt
例題 1. プログラム実行の体験 Microsoft Visual C++ を使ってみよう コンピュータを役に立つ道具として実 感するために, 次ページのプログラムを使って, Microsoft Visual C++ で のプログラム実行を体験する 例題 1 のプログラムの機能 計算の繰り返し キーボードからのデータ読み込み ファイルへの書き出し #include #include
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02: 変数と標準入出力
C プログラミング入門 基幹 7 ( 水 5) 1 10: ファイル入出力 Linux にログインし 以下の講義ページを開いておくこと http://www-it.sci.waseda.ac.jp/teachers/w48369 2/CPR1/ 2016-06-15 今日の内容 2 標準ライブラリ関数によりファイルの出力を行う画像ファイルの生成を例題として 配列の作成を復習する 文字列の扱いを復習する
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スライド 1
数値解析 平成 24 年度前期第 13 週 [7 月 11 日 ] 静岡大学創造科学技術大学院情報科学専攻工学部機械工学科計測情報講座 三浦憲二郎 講義アウトライン [7 月 11 日 ] 関数近似と補間 最小 2 乗近似による関数近似 ラグランジュ補間 形状処理工学の基礎 点列からの曲線の生成 T.Kanai, U.Tokyo 関数近似 p.116 複雑な関数を簡単な関数で近似する関数近似 閉区間
スライド 1
数値解析 2019 年度前期第 13 週 [7 月 11 日 ] 静岡大学創造科学技術大学院情報科学専攻工学部機械工学科計測情報講座 三浦憲二郎 講義アウトライン [7 月 11 日 ] 関数近似と補間 最小 2 乗近似による関数近似 ラグランジュ補間 T.Kanai, U.Tokyo 関数近似 p.116 複雑な関数を簡単な関数で近似する 関数近似 閉区間 [a,b] で定義された関数 f(x)
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PowerPoint プレゼンテーション
プログラミング初級 第 13 回 2017 年 7 月 10 日 標準ライブラリ関数 1 標準ライブラリ関数とは 関数には (1) 自分で作る関数 (2) はじめから用意されている関数特に C 言語用用意されているもの : 標準ライブラリ関数 文字列の代入文字列の長さを求める文字列の比較文字列の連結 strcpy strlen strcmp strcat 2 文字列の操作 - 具体例を通して (141
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