opencv 中，使用cvSolve函数，求解线性方程组，或者最小二乘法问题

求解线性系统或者最小二乘法问题

int cvSolve( const CvArr* src1, const CvArr* src2, CvArr* dst, int method=CV_LU );

src1

输入矩阵

src2

线性系统的右部

dst

输出解答

method

解决方法(矩阵求逆) :

CV_LU - 最佳主元选取的高斯消除法

CV_SVD - 奇异值分解法 (SVD)

CV_SVD_SYM - 对正定对称矩阵的 SVD 方法

函数 cvSolve 解决线性系统或者最小二乘法问题 (后者用 SVD 方法可以解决):

dst = argmin |src1*X -src2|

如果使用 CV_LU 方法。 如果 src1 是非奇异的，该函数则返回 1 ，否则返回 0 ，在后一种情况下 dst 是无效的。

如：

u=(A*x+B*y+C)/(G*x+H*y+1);

v=(D*x+E*y+F)/(G*x+H*y+1);

见下关系：

* / x0 y0 1 0 0 0 -x0*u0 -y0*u0 \ /c00\ /u0\

* | x1 y1 1 0 0 0 -x1*u1 -y1*u1 | |c01| |u1|

* | x2 y2 1 0 0 0 -x2*u2 -y2*u2 | |c02| |u2|

* | x3 y3 1 0 0 0 -x3*u3 -y3*u3 |.|c10|=|u3|,

* | 0 0 0 x0 y0 1 -x0*v0 -y0*v0 | |c11| |v0|

* | 0 0 0 x1 y1 1 -x1*v1 -y1*v1 | |c12| |v1|

* | 0 0 0 x2 y2 1 -x2*v2 -y2*v2 | |c20| |v2|

* \ 0 0 0 x3 y3 1 -x3*v3 -y3*v3 / \c21/ \v3/

int numPoints=10;

double **a=new double *[2*numPoints];

for(int i = 0; i <2*numPoints;i++)

a[i] = new double[8];

double *b =new double[2*numPoints];

CvMat A = cvMat (2*numPoints,8, CV_64F, a);

CvMat B = cvMat (2*numPoints,1, CV_64F, b);

CvMat *X = cvCreateMat (8, 1, CV_64F);

for( int i = 0; i <numPoints; ++i )

{

a[i][0] = a[i+numPoints][3] =points1[i].x;

a[i][1] = a[i+numPoints][4] =points1[i].y;

a[i][2] = a[i+numPoints][5] = 1;

a[i][3] = a[i][4] = a[i][5] =0;

a[i+numPoints][0] = a[i+numPoints][1] = a[i+numPoints][2] = 0;

a[i][6] = -points1[i].x*points2[i].x;

a[i][7] = -points1[i].y*points2[i].x;

a[i+numPoints][6] = -points1[i].x*points2[i].y;

a[i+numPoints][7] = -points1[i].y*points2[i].y;

b[i] =points2[i].x;

b[i+numPoints] =points2[i].y;

}

cvSolve(&A,&B,X,CV_SVD);

for(int i=0;i<8;i++)

cvmSet(H_Mat2,i/3,i%3,cvmGet(X,i,0));

cvmSet(H_Mat2,2,2,1.0);

for(int i = 0; i<2*numPoints;i++)

{

delete [8]a[i];

a[i]=NULL;

}

delete [2*numPoints]a;

delete [2*numPoints]b;

a=NULL;

b=NULL;