| 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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