python - cv2.estimateRigidTransform 最小点数？

Question

cv2.estimateRigidTransform 所需的最小点数是多少？

据我所知，fullAffine=False 它有 4 个自由度，所以 2 个点就足够了。

但是:

使用 2 个 numpy 数组作为输入:

src_pts_subset.shape (2, 2)
tgt_pts_subset.shape (2, 2)
type(src_pts_subset) <class 'numpy.ndarray'>
type(tgt_pts_subset) <class 'numpy.ndarray'>
src_pts_subset.dtype int64
tgt_pts_subset.dtype int64

到

m = cv2.estimateRigidTransform(src_pts, tgt_pts, fullAffine=False)

给我 None。

Answer 1

理论上，非完全仿射设置只需要 2 个对点，详见 ngia ho。 .但是查看openCV的源码发现，函数要返回RANSAC计算出的值，至少需要3对点。

我在下面包含了相应的功能供您引用。它位于 openCV 源文件中的 lkpyramid.cpp 文件中。

cv::Mat cv::estimateRigidTransform( InputArray src1, InputArray src2, bool fullAffine )
{
    return estimateRigidTransform(src1, src2, fullAffine, 500, 0.5, 3);
}

cv::Mat cv::estimateRigidTransform( InputArray src1, InputArray src2, bool fullAffine, int ransacMaxIters, double ransacGoodRatio,
                                    const int ransacSize0)
{
    CV_INSTRUMENT_REGION()

    Mat M(2, 3, CV_64F), A = src1.getMat(), B = src2.getMat();

    const int COUNT = 15;
    const int WIDTH = 160, HEIGHT = 120;

    std::vector<Point2f> pA, pB;
    std::vector<int> good_idx;
    std::vector<uchar> status;

    double scale = 1.;
    int i, j, k, k1;

    RNG rng((uint64)-1);
    int good_count = 0;

    if( ransacSize0 < 3 )
        CV_Error( Error::StsBadArg, "ransacSize0 should have value bigger than 2.");

    if( ransacGoodRatio > 1 || ransacGoodRatio < 0)
        CV_Error( Error::StsBadArg, "ransacGoodRatio should have value between 0 and 1");

    if( A.size() != B.size() )
        CV_Error( Error::StsUnmatchedSizes, "Both input images must have the same size" );

    if( A.type() != B.type() )
        CV_Error( Error::StsUnmatchedFormats, "Both input images must have the same data type" );

    int count = A.checkVector(2);

    if( count > 0 )
    {
        A.reshape(2, count).convertTo(pA, CV_32F);
        B.reshape(2, count).convertTo(pB, CV_32F);
    }
    else if( A.depth() == CV_8U )
    {
        int cn = A.channels();
        CV_Assert( cn == 1 || cn == 3 || cn == 4 );
        Size sz0 = A.size();
        Size sz1(WIDTH, HEIGHT);

        scale = std::max(1., std::max( (double)sz1.width/sz0.width, (double)sz1.height/sz0.height ));

        sz1.width = cvRound( sz0.width * scale );
        sz1.height = cvRound( sz0.height * scale );

        bool equalSizes = sz1.width == sz0.width && sz1.height == sz0.height;

        if( !equalSizes || cn != 1 )
        {
            Mat sA, sB;

            if( cn != 1 )
            {
                Mat gray;
                cvtColor(A, gray, COLOR_BGR2GRAY);
                resize(gray, sA, sz1, 0., 0., INTER_AREA);
                cvtColor(B, gray, COLOR_BGR2GRAY);
                resize(gray, sB, sz1, 0., 0., INTER_AREA);
            }
            else
            {
                resize(A, sA, sz1, 0., 0., INTER_AREA);
                resize(B, sB, sz1, 0., 0., INTER_AREA);
            }

            A = sA;
            B = sB;
        }

        int count_y = COUNT;
        int count_x = cvRound((double)COUNT*sz1.width/sz1.height);
        count = count_x * count_y;

        pA.resize(count);
        pB.resize(count);
        status.resize(count);

        for( i = 0, k = 0; i < count_y; i++ )
            for( j = 0; j < count_x; j++, k++ )
            {
                pA[k].x = (j+0.5f)*sz1.width/count_x;
                pA[k].y = (i+0.5f)*sz1.height/count_y;
            }

        // find the corresponding points in B
        calcOpticalFlowPyrLK(A, B, pA, pB, status, noArray(), Size(21, 21), 3,
                             TermCriteria(TermCriteria::MAX_ITER,40,0.1));

        // repack the remained points
        for( i = 0, k = 0; i < count; i++ )
            if( status[i] )
            {
                if( i > k )
                {
                    pA[k] = pA[i];
                    pB[k] = pB[i];
                }
                k++;
            }
        count = k;
        pA.resize(count);
        pB.resize(count);
    }
    else
        CV_Error( Error::StsUnsupportedFormat, "Both input images must have either 8uC1 or 8uC3 type" );

    good_idx.resize(count);

    if( count < ransacSize0 )
        return Mat();

    Rect brect = boundingRect(pB);

    std::vector<Point2f> a(ransacSize0);
    std::vector<Point2f> b(ransacSize0);

    // RANSAC stuff:
    // 1. find the consensus
    for( k = 0; k < ransacMaxIters; k++ )
    {
        std::vector<int> idx(ransacSize0);
        // choose random 3 non-complanar points from A & B
        for( i = 0; i < ransacSize0; i++ )
        {
            for( k1 = 0; k1 < ransacMaxIters; k1++ )
            {
                idx[i] = rng.uniform(0, count);

                for( j = 0; j < i; j++ )
                {
                    if( idx[j] == idx[i] )
                        break;
                    // check that the points are not very close one each other
                    if( fabs(pA[idx[i]].x - pA[idx[j]].x) +
                        fabs(pA[idx[i]].y - pA[idx[j]].y) < FLT_EPSILON )
                        break;
                    if( fabs(pB[idx[i]].x - pB[idx[j]].x) +
                        fabs(pB[idx[i]].y - pB[idx[j]].y) < FLT_EPSILON )
                        break;
                }

                if( j < i )
                    continue;

                if( i+1 == ransacSize0 )
                {
                    // additional check for non-complanar vectors
                    a[0] = pA[idx[0]];
                    a[1] = pA[idx[1]];
                    a[2] = pA[idx[2]];

                    b[0] = pB[idx[0]];
                    b[1] = pB[idx[1]];
                    b[2] = pB[idx[2]];

                    double dax1 = a[1].x - a[0].x, day1 = a[1].y - a[0].y;
                    double dax2 = a[2].x - a[0].x, day2 = a[2].y - a[0].y;
                    double dbx1 = b[1].x - b[0].x, dby1 = b[1].y - b[0].y;
                    double dbx2 = b[2].x - b[0].x, dby2 = b[2].y - b[0].y;
                    const double eps = 0.01;

                    if( fabs(dax1*day2 - day1*dax2) < eps*std::sqrt(dax1*dax1+day1*day1)*std::sqrt(dax2*dax2+day2*day2) ||
                        fabs(dbx1*dby2 - dby1*dbx2) < eps*std::sqrt(dbx1*dbx1+dby1*dby1)*std::sqrt(dbx2*dbx2+dby2*dby2) )
                        continue;
                }
                break;
            }

            if( k1 >= ransacMaxIters )
                break;
        }

        if( i < ransacSize0 )
            continue;

        // estimate the transformation using 3 points
        getRTMatrix( a, b, 3, M, fullAffine );

        const double* m = M.ptr<double>();
        for( i = 0, good_count = 0; i < count; i++ )
        {
            if( std::abs( m[0]*pA[i].x + m[1]*pA[i].y + m[2] - pB[i].x ) +
                std::abs( m[3]*pA[i].x + m[4]*pA[i].y + m[5] - pB[i].y ) < std::max(brect.width,brect.height)*0.05 )
                good_idx[good_count++] = i;
        }

        if( good_count >= count*ransacGoodRatio )
            break;
    }

    if( k >= ransacMaxIters )
        return Mat();

    if( good_count < count )
    {
        for( i = 0; i < good_count; i++ )
        {
            j = good_idx[i];
            pA[i] = pA[j];
            pB[i] = pB[j];
        }
    }

    getRTMatrix( pA, pB, good_count, M, fullAffine );
    M.at<double>(0, 2) /= scale;
    M.at<double>(1, 2) /= scale;

    return M;
}