Question

我正在尝试计算2张图像的基本矩阵（同一相机拍摄的静态场景的不同照片）。

我使用 findFundamentalMat 计算它，我使用结果计算其他矩阵（Essential，Rotation，...）。结果显然是错误的。所以，我试图确定计算出的基本矩阵的准确性。

使用极线约束方程，计算基本矩阵误差。错误非常高（如几百）。我不知道我的代码有什么问题。我非常感谢任何帮助。特别是：在基本矩阵计算中是否有任何遗漏的东西？是我计算错误的方式吗？

另外，我运行的代码数量非常不同。通常有很多异常值。例如，在超过80场比赛的情况下，只有10个内线。

Mat img_1 = imread( "imgl.jpg", CV_LOAD_IMAGE_GRAYSCALE );
Mat img_2 = imread( "imgr.jpg", CV_LOAD_IMAGE_GRAYSCALE );
if( !img_1.data || !img_2.data )
{ return -1; }

//-- Step 1: Detect the keypoints using SURF Detector

int minHessian = 1000;
SurfFeatureDetector detector( minHessian );
std::vector<KeyPoint> keypoints_1, keypoints_2;

detector.detect( img_1, keypoints_1 );
detector.detect( img_2, keypoints_2 );

//-- Step 2: Calculate descriptors (feature vectors)

SurfDescriptorExtractor extractor;
Mat descriptors_1, descriptors_2;
extractor.compute( img_1, keypoints_1, descriptors_1 );
extractor.compute( img_2, keypoints_2, descriptors_2 );

//-- Step 3: Matching descriptor vectors with a brute force matcher

BFMatcher matcher(NORM_L1, true);
std::vector< DMatch > matches;
matcher.match( descriptors_1, descriptors_2, matches );

vector<Point2f>imgpts1,imgpts2;
for( unsigned int i = 0; i<matches.size(); i++ )
{
    // queryIdx is the "left" image
    imgpts1.push_back(keypoints_1[matches[i].queryIdx].pt);
    // trainIdx is the "right" image
    imgpts2.push_back(keypoints_2[matches[i].trainIdx].pt);
}

//-- Step 4: Calculate Fundamental matrix

Mat f_mask;
Mat F =  findFundamentalMat  (imgpts1, imgpts2, FM_RANSAC, 0.5, 0.99, f_mask);

//-- Step 5: Calculate Fundamental matrix error

//Camera intrinsics
double data[] = {1189.46 , 0.0, 805.49,
                0.0, 1191.78, 597.44,
                0.0, 0.0, 1.0};
Mat K(3, 3, CV_64F, data);
//Camera distortion parameters
double dist[] = { -0.03432, 0.05332, -0.00347, 0.00106, 0.00000};
Mat D(1, 5, CV_64F, dist);

//working with undistorted points
vector<Point2f> undistorted_1,undistorted_2;
vector<Point3f> line_1, line_2;
undistortPoints(imgpts1,undistorted_1,K,D);
undistortPoints(imgpts2,undistorted_2,K,D);
computeCorrespondEpilines(undistorted_1,1,F,line_1);
computeCorrespondEpilines(undistorted_2,2,F,line_2);

double f_err=0.0;
double fx,fy,cx,cy;
fx=K.at<double>(0,0);fy=K.at<double>(1,1);cx=K.at<double>(0,2);cy=K.at<double>(1,2);
Point2f pt1, pt2;
int inliers=0;
//calculation of fundamental matrix error for inliers
for (int i=0; i<f_mask.size().height; i++)
    if (f_mask.at<char>(i)==1)
    {
        inliers++;
        //calculate non-normalized values
        pt1.x = undistorted_1[i].x * fx + cx;
        pt1.y = undistorted_1[i].y * fy + cy;
        pt2.x = undistorted_2[i].x * fx + cx;
        pt2.y = undistorted_2[i].y * fy + cy;
        f_err += = fabs(pt1.x*line_2[i].x +
                pt1.y*line_2[i].y + line_2[i].z)
                + fabs(pt2.x*line_1[i].x +
                pt2.y*line_1[i].y + line_1[i].z);
    }

double AvrErr = f_err/inliers;

Answer 1

我认为问题是因为你只计算了基于强力匹配器的基本矩阵，你应该对这些对应点做一些更优化，比如定量测试和对称测试。我建议你准备好第233页，来自Book＆＃34; OpenCV2计算机视觉应用程序设计手册＆＃34;第9章。它解释得很好！

Answer 2

在计算基本矩阵之前，似乎没有对点进行标准化。可能是openCV的findFundamentalMat没有使用标准化的8点算法而只使用没有标准化的算法。如果是这种情况，那么由于缺少规范化，您的结果将会出错。

Answer 3

鉴于我们提供了内在矩阵K和失真矩阵D，我们应该在将它提供给findFundamentalMat之前对图像点进行无失真处理，并且应该在今后的未失真图像协调上工作（即用于计算误差）。我发现这个简单的改变将任何图像点对的最大误差从176.0f减少到0.2，并且内部数量从18增加到77.

我还玩弄了将未失真的图像点归一化到它之前找到基本原理，这会将任何图像点对的最大误差减少到几乎为零，但它不会进一步增加内点的数量。

const float kEpsilon = 1.0e-6f;

float sampsonError(const Mat &dblFMat, const Point2f &pt1, const Point2f &pt2)
{


    Mat m_pt1(3, 1 , CV_64FC1 );//m_pt1(pt1);
    Mat m_pt2(3, 1 , CV_64FC1 );
    m_pt1.at<double>(0,0) = pt1.x; m_pt1.at<double>(1,0) = pt1.y; m_pt1.at<double>(2,0) = 1.0f;
    m_pt2.at<double>(0,0) = pt2.x; m_pt2.at<double>(1,0) = pt2.y; m_pt2.at<double>(2,0) = 1.0f;

    assert(dblFMat.rows==3 && dblFMat.cols==3);
    assert(m_pt1.rows==3 && m_pt1.cols==1);
    assert(m_pt2.rows==3 && m_pt2.cols==1);
    Mat dblFMatT(dblFMat.t());
    Mat dblFMatp1=(dblFMat * m_pt1);
    Mat dblFMatTp2=(dblFMatT * m_pt2);
    assert(dblFMatp1.rows==3 && dblFMatp1.cols==1);
    assert(dblFMatTp2.rows==3 && dblFMatTp2.cols==1);

    Mat numerMat=m_pt2.t() * dblFMatp1;
    double numer=numerMat.at<double>(0,0);
    if (numer < kEpsilon)
    {
        return 0;

    } else {
        double denom=dblFMatp1.at<double>(0,0) + dblFMatp1.at<double>(1,0) +  dblFMatTp2.at<double>(0,0) + dblFMatTp2.at<double>(1,0);
        double ret=(numer*numer)/denom;
        return (numer*numer)/denom;
    }
}

#define UNDISTORT_IMG_PTS 1
#define NORMALIZE_IMG_PTS 1

int filter_imgpts_pairs_with_epipolar_constraint(
    const vector<Point2f> &raw_imgpts_1,
    const vector<Point2f> &raw_imgpts_2,
    int imgW,
    int imgH
)
{

#if UNDISTORT_IMG_PTS
    //Camera intrinsics
    double data[] = {1189.46 , 0.0, 805.49,
                    0.0, 1191.78, 597.44,
                    0.0, 0.0, 1.0};
    Mat K(3, 3, CV_64F, data);
    //Camera distortion parameters
    double dist[] = { -0.03432, 0.05332, -0.00347, 0.00106, 0.00000};
    Mat D(1, 5, CV_64F, dist);


    //working with undistorted points
    vector<Point2f> unnormalized_imgpts_1,unnormalized_imgpts_2;
    undistortPoints(raw_imgpts_1,unnormalized_imgpts_1,K,D);
    undistortPoints(raw_imgpts_2,unnormalized_imgpts_2,K,D);

#else
    vector<Point2f> unnormalized_imgpts_1(raw_imgpts_1);
    vector<Point2f> unnormalized_imgpts_2(raw_imgpts_2);
#endif



#if NORMALIZE_IMG_PTS

    float c_col=imgW/2.0f;
    float c_row=imgH/2.0f;
    float multiply_factor= 2.0f/(imgW+imgH);

    vector<Point2f> final_imgpts_1(unnormalized_imgpts_1);
    vector<Point2f> final_imgpts_2(unnormalized_imgpts_2);

    for( auto iit=final_imgpts_1.begin(); iit != final_imgpts_1.end(); ++ iit)
    {
        Point2f &imgpt(*iit);
        imgpt.x=(imgpt.x - c_col)*multiply_factor;
        imgpt.y=(imgpt.y - c_row)*multiply_factor;
    }
    for( auto iit=final_imgpts_2.begin(); iit != final_imgpts_2.end(); ++ iit)
    {
        Point2f &imgpt(*iit);
        imgpt.x=(imgpt.x - c_col)*multiply_factor;
        imgpt.y=(imgpt.y - c_row)*multiply_factor;
    }

#else

    vector<Point2f> final_imgpts_1(unnormalized_imgpts_1);
    vector<Point2f> final_imgpts_2(unnormalized_imgpts_2);
#endif

    int algorithm=FM_RANSAC;
    //int algorithm=FM_LMEDS;


    vector<uchar>status;

    Mat F =  findFundamentalMat  (final_imgpts_1, final_imgpts_2, algorithm, 0.5, 0.99, status);
    int n_inliners=std::accumulate(status.begin(), status.end(), 0);



    assert(final_imgpts_1.size() == final_imgpts_2.size());
    vector<float> serr;
    for( unsigned int i = 0; i< final_imgpts_1.size(); i++ )
    {
        const Point2f &p_1(final_imgpts_1[i]);
        const Point2f &p_2(final_imgpts_2[i]);
        float err= sampsonError(F, p_1, p_2);
        serr.push_back(err);
    }
    float max_serr=*max_element(serr.begin(), serr.end());
    cout << "found " << raw_imgpts_1.size() << "matches " << endl;
    cout << " and " << n_inliners << " inliners" << endl;
    cout << " max sampson err" << max_serr << endl;
    return 0;
}

OpenCV：基本矩阵精度

3 个答案: