OpenCV每日函数几何图像变换模块 (3) getPerspectiveTransform函数

一、概述

透视变换(Perspective Transformation)是将成像投影到一个新的视平面(Viewing Plane)，也称作投影映射(Projective Mapping)。

getPerspectiveTransform函数从四对对应点计算透视变换。该函数计算透视变换的 3×3 矩阵，使得：

其中 $dst(i)=({x}'_i,{y}′_i),src(i)=(x_i,y_i),i=0,1,2,3$ 。

二、getPerspectiveTransform函数

1、函数原型

cv::getPerspectiveTransform (InputArray src, InputArray dst, int solveMethod=DECOMP_LU)
cv::getPerspectiveTransform (const Point2f src[], const Point2f dst[], int solveMethod=DECOMP_LU)

2、参数详解

src	源图像中四边形顶点的坐标。
dst	目标图像中相应四边形顶点的坐标。
solveMethod	传递给 cv::solve (DecompTypes) 的方法

三、OpenCV源码

1、源码路径

opencv\modules\imgproc\src\imgwarp.cpp

2、源码代码

cv::Mat cv::getPerspectiveTransform(InputArray _src, InputArray _dst, int solveMethod)
{
    Mat src = _src.getMat(), dst = _dst.getMat();
    CV_Assert(src.checkVector(2, CV_32F) == 4 && dst.checkVector(2, CV_32F) == 4);
    return getPerspectiveTransform((const Point2f*)src.data, (const Point2f*)dst.data, solveMethod);
}

/* Calculates coefficients of perspective transformation
 * which maps (xi,yi) to (ui,vi), (i=1,2,3,4):
 *
 *      c00*xi + c01*yi + c02
 * ui = ---------------------
 *      c20*xi + c21*yi + c22
 *
 *      c10*xi + c11*yi + c12
 * vi = ---------------------
 *      c20*xi + c21*yi + c22
 *
 * Coefficients are calculated by solving linear system:
 * / 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/
 *
 * where:
 *   cij - matrix coefficients, c22 = 1
 */
cv::Mat cv::getPerspectiveTransform(const Point2f src[], const Point2f dst[], int solveMethod)
{
    CV_INSTRUMENT_REGION();

    Mat M(3, 3, CV_64F), X(8, 1, CV_64F, M.ptr());
    double a[8][8], b[8];
    Mat A(8, 8, CV_64F, a), B(8, 1, CV_64F, b);

    for( int i = 0; i < 4; ++i )
    {
        a[i][0] = a[i+4][3] = src[i].x;
        a[i][1] = a[i+4][4] = src[i].y;
        a[i][2] = a[i+4][5] = 1;
        a[i][3] = a[i][4] = a[i][5] =
        a[i+4][0] = a[i+4][1] = a[i+4][2] = 0;
        a[i][6] = -src[i].x*dst[i].x;
        a[i][7] = -src[i].y*dst[i].x;
        a[i+4][6] = -src[i].x*dst[i].y;
        a[i+4][7] = -src[i].y*dst[i].y;
        b[i] = dst[i].x;
        b[i+4] = dst[i].y;
    }

    solve(A, B, X, solveMethod);
    M.ptr<double>()[8] = 1.;

    return M;
}

四、简单使用示例

根据两组分别是四个点的坐标，进行的透视变换得到的3*3的矩阵。

观察数据的倍数变化以及矩阵数值的变化。

OpenCV每日函数 几何图像变换模块 (3) getPerspectiveTransform函数