1 | #include <stdio.h> |
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2 | #include <string.h> |
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3 | #include <math.h> |
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4 | #include "cv.h" |
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5 | #include "cvaux.h" |
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6 | #include "highgui.h" |
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7 | |
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8 | #define ROTATE(a,i,j,k,l) g=a[i*n + j];h=a[k*n + l];a[i*n + j]=g-s*(h+g*tau);\ |
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9 | a[k*n + l]=h+s*(g-h*tau); |
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10 | |
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11 | /* |
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12 | Computes all eigenvalues and eigenvectors of a real symmetric matrix a[1..n][1..n]. On |
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13 | output, elements of a above the diagonal are destroyed. d[1..n] returns the eigenvalues of a. |
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14 | v[1..n][1..n] is a matrix whose columns contain, on output, the normalized eigenvectors of |
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15 | a. nrot returns the number of Jacobi rotations that were required. |
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16 | */ |
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17 | void jacobi(float *a, int n, float d[], float *v, int *nrot) |
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18 | { |
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19 | int j,iq,ip,i; |
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20 | float tresh,theta,tau,t,sm,s,h,g,c,*b,*z; |
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21 | |
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22 | b = (float *) malloc(n * sizeof(float)); |
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23 | z = (float *) malloc(n * sizeof(float)); |
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24 | |
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25 | for (ip=0;ip<n;ip++) { // Initialize to the identity matrix. |
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26 | for (iq=0;iq<n;iq++) v[ip*n + iq]=0.0; |
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27 | v[ip*n + ip]=1.0; |
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28 | } |
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29 | for (ip=0;ip<n;ip++) { // Initialize b and d to the diagonal of a. |
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30 | b[ip]=d[ip]=a[ip*n + ip]; |
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31 | z[ip]=0.0; // This vector will accumulate terms of the form t*a[pq] as in equation (11.1.14). |
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32 | } |
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33 | |
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34 | *nrot=0; |
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35 | for (i=1;i<=50;i++) { |
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36 | sm=0.0; |
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37 | for (ip=0;ip<n-1;ip++) { // Sum off-diagonal elements. |
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38 | for (iq=ip+1;iq<n;iq++) |
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39 | sm += fabs(a[ip*n + iq]); |
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40 | } |
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41 | if (sm == 0.0) { // The normal return, which relies on quadratic convergence to machine underflow. |
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42 | free(z); |
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43 | free(b); |
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44 | return; |
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45 | } |
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46 | if (i < 4) |
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47 | tresh=0.2*sm/(n*n); // ...on the first three sweeps. |
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48 | else |
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49 | tresh=0.0; // ...thereafter. |
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50 | for (ip=0;ip<n-1;ip++) { |
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51 | for (iq=ip+1;iq<n;iq++) { |
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52 | g=100.0*fabs(a[ip*n + iq]); |
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53 | if (i > 4 && (float)(fabs(d[ip])+g) == (float)fabs(d[ip]) // After four sweeps, skip the rotation if the off-diagonal element is small. |
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54 | && (float)(fabs(d[iq])+g) == (float)fabs(d[iq])) |
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55 | a[ip*n + iq]=0.0; |
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56 | else if (fabs(a[ip*n + iq]) > tresh) { |
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57 | h=d[iq]-d[ip]; |
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58 | if ((float)(fabs(h)+g) == (float)fabs(h)) |
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59 | t=(a[ip*n + iq])/h; // t = 1/(2*theta) |
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60 | else { |
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61 | theta=0.5*h/(a[ip*n + iq]); // Equation (11.1.10). |
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62 | t=1.0/(fabs(theta)+sqrt(1.0+theta*theta)); |
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63 | if (theta < 0.0) t = -t; |
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64 | } |
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65 | |
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66 | c=1.0/sqrt(1+t*t); |
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67 | s=t*c; |
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68 | tau=s/(1.0+c); |
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69 | h=t*a[ip*n + iq]; |
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70 | z[ip] -= h; |
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71 | z[iq] += h; |
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72 | d[ip] -= h; |
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73 | d[iq] += h; |
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74 | a[ip*n + iq]=0.0; |
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75 | |
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76 | for (j=0;j<=ip-1;j++) { // Case of rotations 1 <= j < p. |
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77 | ROTATE(a,j,ip,j,iq) |
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78 | } |
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79 | for (j=ip+1;j<=iq-1;j++) { // Case of rotations p < j < q. |
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80 | ROTATE(a,ip,j,j,iq) |
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81 | } |
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82 | for (j=iq+1;j<n;j++) { // Case of rotations q < j <= n. |
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83 | ROTATE(a,ip,j,iq,j) |
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84 | } |
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85 | for (j=0;j<n;j++) { |
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86 | ROTATE(v,j,ip,j,iq) |
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87 | } |
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88 | |
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89 | ++(*nrot); |
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90 | } |
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91 | } |
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92 | } |
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93 | |
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94 | for (ip=0;ip<n;ip++) { |
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95 | b[ip] += z[ip]; |
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96 | d[ip]=b[ip]; // Updte d with the sum of t*a[pq], |
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97 | z[ip]=0.0; // and reinitialize z. |
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98 | } |
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99 | } |
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100 | |
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101 | printf("Too many iterations in routine jacobi\n"); |
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102 | } |
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103 | |
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104 | /* |
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105 | Given the eigenvalues d[1..n] and eigenvectors v[1..n][1..n] as output from jacobi |
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106 | (x11.1) or tqli (x11.3), this routine sorts the eigenvalues into descending order, and rearranges |
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107 | the columns of v correspondingly. The method is straight insertion. |
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108 | */ |
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109 | void eigsrt(float d[], float *v, int n) |
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110 | { |
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111 | int k,j,i; |
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112 | float p; |
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113 | for (i=0;i<n-1;i++) { |
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114 | p=d[k=i]; |
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115 | for (j=i+1;j<n;j++) |
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116 | if (d[j] >= p) p=d[k=j]; |
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117 | if (k != i) { |
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118 | d[k]=d[i]; |
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119 | d[i]=p; |
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120 | for (j=0;j<n;j++) { |
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121 | p=v[j*n + i]; |
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122 | v[j*n + i]=v[j*n + k]; |
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123 | v[j*n + k]=p; |
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124 | } |
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125 | } |
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126 | } |
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127 | } |
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128 | |
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129 | void calcMeanImage(int nFaces, uchar** faceArr, int faceStep, |
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130 | CvSize size, float* avg, int avgStep) |
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131 | { |
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132 | int i,j,k; |
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133 | float m = 1.0f / (float) nFaces; |
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134 | float* bf = avg; |
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135 | |
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136 | for( i = 0; i < size.height; i++, bf += avgStep) |
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137 | for( j = 0; j < size.width; j++ ) |
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138 | bf[j] = 0.f; |
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139 | |
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140 | for( i = 0; i < nFaces; i++ ) |
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141 | { |
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142 | uchar* bu = faceArr[i]; |
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143 | bf = avg; |
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144 | for( k = 0; k < size.height; k++, bf += avgStep, bu += faceStep ) |
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145 | for( j = 0; j < size.width; j++ ) |
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146 | bf[j] += bu[j]; |
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147 | } |
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148 | |
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149 | bf = avg; |
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150 | for( i = 0; i < size.height; i++, bf += avgStep) |
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151 | for( j = 0; j < size.width; j++ ) { |
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152 | bf[j] *= m; |
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153 | } |
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154 | } |
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155 | |
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156 | void calcCovarMatrix(int nFaces, uchar** faceArr, int faceStep, CvSize size, |
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157 | float* avg, int avgStep, float *covarMatrix) |
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158 | { |
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159 | int i, j; |
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160 | |
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161 | for( i = 0; i < nFaces; i++ ) |
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162 | { |
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163 | uchar *bu = faceArr[i]; |
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164 | |
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165 | for( j = i; j < nFaces; j++ ) |
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166 | { |
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167 | int k, l; |
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168 | float w = 0.f; |
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169 | float *a = avg; |
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170 | uchar *bu1 = bu; |
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171 | uchar *bu2 = faceArr[j]; |
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172 | |
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173 | for( k = 0; k < size.height; |
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174 | k++, bu1 += faceStep, bu2 += faceStep, a += avgStep ) |
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175 | { |
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176 | for( l = 0; l < size.width - 3; l += 4 ) |
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177 | { |
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178 | float f = a[l]; |
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179 | uchar u1 = bu1[l]; |
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180 | uchar u2 = bu2[l]; |
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181 | |
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182 | w += (u1 - f) * (u2 - f); |
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183 | f = a[l + 1]; |
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184 | u1 = bu1[l + 1]; |
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185 | u2 = bu2[l + 1]; |
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186 | w += (u1 - f) * (u2 - f); |
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187 | f = a[l + 2]; |
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188 | u1 = bu1[l + 2]; |
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189 | u2 = bu2[l + 2]; |
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190 | w += (u1 - f) * (u2 - f); |
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191 | f = a[l + 3]; |
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192 | u1 = bu1[l + 3]; |
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193 | u2 = bu2[l + 3]; |
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194 | w += (u1 - f) * (u2 - f); |
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195 | } |
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196 | for( ; l < size.width; l++ ) |
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197 | { |
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198 | float f = a[l]; |
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199 | uchar u1 = bu1[l]; |
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200 | uchar u2 = bu2[l]; |
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201 | |
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202 | w += (u1 - f) * (u2 - f); |
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203 | } |
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204 | } |
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205 | |
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206 | covarMatrix[i * nFaces + j] = covarMatrix[j * nFaces + i] = w; |
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207 | } |
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208 | } |
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209 | } |
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210 | |
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211 | void calcEigenFaces(int nFaces, IplImage** facesArr, IplImage** eigArr, int iter, |
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212 | IplImage *avg, float *eigVals) |
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213 | { |
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214 | int i,j,k,l, p; |
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215 | float *covarMat, *ev; |
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216 | |
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217 | float *avg_data; |
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218 | int avg_step = 0, eig_step = 0; |
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219 | CvSize size; |
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220 | |
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221 | cvGetImageRawData( avg, (uchar **) & avg_data, &avg_step, &size ); |
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222 | |
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223 | avg_step = avg_step/4; |
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224 | uchar **faces = (uchar **) cvAlloc( sizeof( uchar * ) * nFaces ); |
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225 | float **eigs = (float **) cvAlloc( sizeof( float * ) * iter ); |
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226 | int face_step = 0; |
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227 | |
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228 | for( i = 0; i < nFaces; i++ ) |
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229 | { |
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230 | IplImage *face = facesArr[i]; |
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231 | uchar *face_data; |
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232 | |
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233 | cvGetImageRawData( face, (uchar **) &face_data, &face_step, NULL); |
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234 | faces[i] = face_data; |
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235 | } |
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236 | |
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237 | |
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238 | for( i = 0; i < iter; i++ ) |
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239 | { |
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240 | IplImage *eig = eigArr[i]; |
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241 | float *eig_data; |
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242 | |
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243 | cvGetImageRawData( eig, (uchar **) & eig_data, NULL, NULL); |
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244 | eigs[i] = eig_data; |
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245 | } |
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246 | |
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247 | calcMeanImage( nFaces, |
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248 | faces, |
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249 | face_step, |
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250 | size, |
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251 | avg_data, |
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252 | avg_step ); |
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253 | |
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254 | covarMat = (float *) cvAlloc( sizeof( float ) * nFaces * nFaces ); |
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255 | |
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256 | //~ calcCovarMatrix( nFaces, |
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257 | //~ faces, |
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258 | //~ avg_step, |
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259 | //~ size, |
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260 | //~ avg_data, |
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261 | //~ avg_step, |
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262 | //~ covarMat ); |
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263 | |
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264 | //~ for ( i = 0; i < nFaces; i++ ) |
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265 | //~ { |
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266 | //~ for ( j = 0; j < nFaces; j++ ) |
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267 | //~ { |
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268 | //~ printf("%f ", covarMat[i*nFaces+j]); |
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269 | //~ } |
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270 | //~ printf("\n"); |
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271 | //~ } |
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272 | |
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273 | cvCalcCovarMatrixEx( nFaces, facesArr, 0, 0, NULL, NULL, avg, covarMat ); |
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274 | |
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275 | printf("\n"); |
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276 | for ( i = 0; i < nFaces; i++ ) |
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277 | { |
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278 | for ( j = 0; j < nFaces; j++ ) |
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279 | { |
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280 | printf("%f ", covarMat[i*nFaces+j]); |
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281 | } |
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282 | printf("\n"); |
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283 | } |
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284 | printf("\n"); |
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285 | |
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286 | ev = (float *) cvAlloc( sizeof( float ) * nFaces * nFaces ); |
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287 | |
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288 | int nrot=0; |
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289 | jacobi(covarMat, nFaces, eigVals, ev, &nrot); |
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290 | eigsrt(eigVals, ev, nFaces); |
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291 | //JacobiEigens_32f(covarMat, ev, eigVals, nFaces, 0); |
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292 | |
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293 | for ( j = 0; j < nFaces; j++ ) |
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294 | { |
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295 | printf("%f ", eigVals[j]); |
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296 | } |
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297 | printf("\n\n"); |
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298 | |
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299 | for ( i = 0; i < nFaces; i++ ) |
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300 | { |
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301 | for ( j = 0; j < nFaces; j++ ) |
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302 | { |
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303 | printf("%f ", ev[i*nFaces+j]); |
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304 | } |
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305 | printf("\n"); |
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306 | } |
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307 | |
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308 | for( i = 0; i < iter; i++ ) |
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309 | eigVals[i] = (float) (1.0 / sqrt( (double)eigVals[i] )); |
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310 | |
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311 | for( i = 0; i < iter; i++ ) |
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312 | { |
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313 | float *be = eigs[i]; |
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314 | |
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315 | for( k = 0; k < size.height; k++, be += avg_step ) |
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316 | for( l = 0; l < size.width; l++ ) |
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317 | be[l] = 0.0f; |
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318 | } |
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319 | |
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320 | for( k = 0; k < nFaces; k++ ) |
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321 | { |
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322 | uchar *bv = faces[k]; |
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323 | |
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324 | for( i = 0; i < iter; i++ ) |
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325 | { |
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326 | float v = eigVals[i] * ev[k * nFaces + i]; |
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327 | // float v = ev[i * nFaces + k]; |
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328 | float *be = eigs[i]; |
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329 | uchar *bu = bv; |
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330 | |
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331 | float *bf = avg_data; |
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332 | |
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333 | for( p = 0; p < size.height; p++, bu += face_step, |
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334 | bf += avg_step, be += avg_step ) |
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335 | { |
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336 | for( l = 0; l < size.width - 3; l += 4 ) |
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337 | { |
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338 | float f = bf[l]; |
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339 | uchar u = bu[l]; |
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340 | |
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341 | be[l] += v * (u - f); |
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342 | f = bf[l + 1]; |
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343 | u = bu[l + 1]; |
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344 | be[l + 1] += v * (u - f); |
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345 | f = bf[l + 2]; |
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346 | u = bu[l + 2]; |
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347 | be[l + 2] += v * (u - f); |
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348 | f = bf[l + 3]; |
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349 | u = bu[l + 3]; |
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350 | be[l + 3] += v * (u - f); |
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351 | } |
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352 | for( ; l < size.width; l++ ) |
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353 | be[l] += v * (bu[l] - bf[l]); |
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354 | } |
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355 | } |
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356 | } |
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357 | |
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358 | for( i = 0; i < iter; i++ ) |
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359 | eigVals[i] = 1.f / (eigVals[i] * eigVals[i]); |
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360 | } |
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361 | |
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362 | void calcDecomp( IplImage* face, int nEigens, IplImage** eigArr, IplImage *avg, float* coeffs ) |
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363 | { |
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364 | int i, j, k; |
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365 | float w = 0.0f; |
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366 | |
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367 | float *avg_data; |
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368 | uchar *face_data; |
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369 | int avg_step = 0, face_step = 0; |
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370 | CvSize size; |
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371 | |
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372 | cvGetImageRawData( avg, (uchar **) & avg_data, &avg_step, &size ); |
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373 | cvGetImageRawData( face, &face_data, &face_step, NULL); |
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374 | avg_step = avg_step/4; |
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375 | |
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376 | float **eigs = (float **) cvAlloc( sizeof( float * ) * nEigens ); |
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377 | for( i = 0; i < nEigens; i++ ) |
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378 | { |
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379 | IplImage *eig = eigArr[i]; |
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380 | float *eig_data; |
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381 | |
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382 | cvGetImageRawData( eig, (uchar **) & eig_data, NULL, NULL ); |
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383 | eigs[i] = eig_data; |
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384 | } |
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385 | |
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386 | for( k = 0; k < nEigens; k++ ) |
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387 | { |
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388 | float *be = eigs[k]; |
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389 | uchar *bu = face_data; |
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390 | float *bf = avg_data; |
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391 | |
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392 | for( i = 0; i < size.height; i++, bu+= face_step, |
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393 | be += avg_step, bf += avg_step ) |
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394 | { |
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395 | for( j = 0; j < size.width - 4; j += 4 ) |
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396 | { |
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397 | float o = (float) bu[j]; |
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398 | float e = be[j]; |
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399 | float a = bf[j]; |
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400 | |
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401 | w += e * (o - a); |
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402 | o = (float) bu[j + 1]; |
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403 | e = be[j + 1]; |
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404 | a = bf[j + 1]; |
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405 | w += e * (o - a); |
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406 | o = (float) bu[j + 2]; |
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407 | e = be[j + 2]; |
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408 | a = bf[j + 2]; |
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409 | w += e * (o - a); |
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410 | o = (float) bu[j + 3]; |
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411 | e = be[j + 3]; |
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412 | a = bf[j + 3]; |
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413 | w += e * (o - a); |
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414 | } |
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415 | for( ; j < size.width; j++ ) |
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416 | w += be[j] * ((float) bu[j] - bf[j]); |
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417 | } |
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418 | |
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419 | //~ if( w < -1.0e29f ) |
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420 | //~ return CV_NOTDEFINED_ERR; |
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421 | coeffs[i] = w; |
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422 | } |
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423 | } |
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