openCV光平面标定——空间平面拟合

最新推荐文章于 2025-05-23 18:38:53 发布

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本文详细介绍了一种基于SVD的三维点云平面拟合算法，通过计算几何质心、减去质心、评估协方差矩阵的SVD来估计平面参数。文中提供了具体的C++代码实现，并解释了如何调用函数进行点云拟合。

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//Ax+by+cz=D
void cvFitPlane(const CvMat* points, float* plane){
// Estimate geometric centroid.
int nrows = points->rows;
int ncols = points->cols;
int type = points->type;
CvMat* centroid = cvCreateMat(1, ncols, type);
cvSet(centroid, cvScalar(0));
for (int c = 0; c<ncols; c++){ //用地址的形式才能实现先列后行的操作，如果用Mat型只能先行后列
for (int r = 0; r < nrows; r++)
{
centroid->data.fl[c] += points->data.fl[ncolsr + c];
}
centroid->data.fl[c] /= nrows;
}
// Subtract geometric centroid from each point.
CvMat points2 = cvCreateMat(nrows, ncols, type);
for (int r = 0; r<nrows; r++)
for (int c = 0; c<ncols; c++)
points2->data.fl[ncolsr + c] = points->data.fl[ncolsr + c] - centroid->data.fl[c];
// Evaluate SVD of covariance matrix.
CvMat* A = cvCreateMat(ncols, ncols, type);
CvMat* W = cvCreateMat(ncols, ncols, type);
CvMat* V = cvCreateMat(ncols, ncols, type);
cvGEMM(points2, points, 1, NULL, 0, A, CV_GEMM_A_T); //points也要为CVMat型
cvSVD(A, W, NULL, V, CV_SVD_V_T);
// Assign plane coefficients by singular vector corresponding to smallest singular value.
plane[ncols] = 0;
for (int c = 0; c<ncols; c++){
plane[c] = V->data.fl[ncols*(ncols - 1) + c];
plane[ncols] += plane[c] * centroid->data.fl[c];
}
// Release allocated resources.
cvReleaseMat(¢roid);
cvReleaseMat(&points2);
cvReleaseMat(&A);
cvReleaseMat(&W);
cvReleaseMat(&V);
}

调用的方式：
[cpp] view plain copy

CvMatpoints_mat = cvCreateMat(X_vector.size(), 3, CV_32FC1);//定义用来存储需要拟合点的矩阵
for (int i=0;i < X_vector.size(); ++i)
{
points_mat->data.fl[i3+0] = X_vector[i];//矩阵的值进行初始化 X的坐标值
points_mat->data.fl[i * 3 + 1] = Y_vector[i];// Y的坐标值
points_mat->data.fl[i * 3 + 2] = Z_vector[i];// Z的坐标值

    }  
    float plane12[4] = { 0 };//定义用来储存平面参数的数组   
    cvFitPlane(points_mat, plane12);//调用方程

我们拟合出来的方程：Ax+By+Cz=D
其中 A=plane12[0], B=plane12[1], C=plane12[2], D=plane12[3],

这是要注意的方程的表示