利用C++ OpenCV 实现从投影图像恢复仿射特性

l = x1 × x2

x = l1 × l2

H = （（1，0，0），（0，1，0），（l1，l2，l3））

x = Hx'

int main()
{
	Mat src = imread("distortion.jpg", IMREAD_GRAYSCALE);
	IplImage *src1 = cvLoadImage("distortion.jpg");
	//第一步，通过鼠标获取图片中某个点的坐标，运行第一步时注释掉Rectify(points_3d, src, src1);，将获取到的八个点写入
	//points_3d[8]坐标数组中，因为是齐次坐标，x3 = 1
	GetMouse(src1);
	//输入畸变图上的8个关键点
	Point3d points_3d[8] = { Point3d(99, 147, 1), Point3d(210, 93, 1), Point3d(144, 184, 1), Point3d(261, 122, 1),
						Point3d(144, 184, 1), Point3d(99, 147, 1), Point3d(261, 122, 1), Point3d(210, 93, 1) };
	//第二步，校正图像，运行此步骤时注释掉GetMouse(src1);，解除注释Rectify(points_3d, src, src1);
	//Rectify(points_3d, src, src1);
	imshow("yuantu", src);
	waitKey(0);	
}

void on_mouse(int event, int x, int y, int flags, void* ustc)
{
    CvFont font;
    cvInitFont(&font, CV_FONT_HERSHEY_SIMPLEX, 0.5, 0.5, 0, 1, CV_AA);

    if (event == CV_EVENT_LBUTTONDOWN)
    {
        CvPoint pt = cvPoint(x, y);
        char temp[16];
        sprintf(temp, "(%d,%d)", pt.x, pt.y);
        cvPutText(src, temp, pt, &font, cvScalar(255, 255, 255, 0));
        cvCircle(src, pt, 2, cvScalar(255, 0, 0, 0), CV_FILLED, CV_AA, 0);
        cvShowImage("src", src);
    }
}

void GetMouse(IplImage *img)
{
    src = img;
    cvNamedWindow("src", 1);
    cvSetMouseCallback("src", on_mouse, 0);

    cvShowImage("src", src);
    waitKey(0);
}

ab // cd		  ac // bd

int main()
{
	Mat src = imread("distortion.jpg", IMREAD_GRAYSCALE);
	IplImage *src1 = cvLoadImage("distortion.jpg");
	//第一步，通过鼠标获取图片中某个点的坐标，运行第一步时注释掉Rectify(points_3d, src, src1);，将获取到的八个点写入
	//points_3d[8]矩阵中，因为是齐次坐标，x3 = 1
	//GetMouse(src1);
	//输入畸变图上的8个关键点
	Point3d points_3d[8] = { Point3d(99, 147, 1), Point3d(210, 93, 1), Point3d(144, 184, 1), Point3d(261, 122, 1),
						Point3d(144, 184, 1), Point3d(99, 147, 1), Point3d(261, 122, 1), Point3d(210, 93, 1) };
	//第二步，校正图像，运行此步骤时注释掉GetMouse(src1);，解除注释Rectify(points_3d, src, src1);
	Rectify(points_3d, src, src1);
	imshow("yuantu", src);
	waitKey(0);	
}

void Rectify(Point3d* points, Mat src, IplImage* img)
{
    //通过输入的8个点得到4条连线
    vector<vector<float>> lines;
    int num_lines = 4;
    for(int i = 0; i < num_lines; i++)
    {
        //获取两点连线
        GetLineFromPoints(points[2 * i], points[2 * i + 1], lines);
    }
    //分别求取两个交点
    vector<Point3f> intersect_points;
    int num_intersect_points = 2;
    for (int i = 0; i < num_intersect_points; i++)
    {
        //计算交点
        GetIntersectPoint(lines[2 * i], lines[2 * i + 1], intersect_points);
    }
    //通过两个交点连线求消失线
    vector<vector<float>> vanishing_line;
    GetLineFromPoints(intersect_points[0], intersect_points[1], vanishing_line);
    //恢复矩阵
    float H[3][3] = {{1, 0, 0},
                     {0, 1, 0},
                     {vanishing_line[0][0], vanishing_line[0][1], vanishing_line[0][2]}};
    Mat image = Mat::zeros(src.rows, src.cols, CV_8UC1);
    GetRectifingImage(vanishing_line[0], src, image);
    int i = 0;
}

void GetLineFromPoints(Point3d point1, Point3d point2, vector<vector<float>> &lines)
{
    vector<float> line;
    //定义直线的三个齐次坐标
    float l1 = 0;
    float l2 = 0;
    float l3 = 0;
    l1 = (point1.y * point2.z - point1.z * point2.y);
    l2 = (point1.z * point2.x - point1.x * point2.z);
    l3 = (point1.x * point2.y - point1.y * point2.x);
    //归一化
    l1 = l1 / l3;
    l2 = l2 / l3;
    l3 = 1;
    line.push_back(l1);
    line.push_back(l2);
    line.push_back(l3); 
    lines.push_back(line);
}

void GetIntersectPoint(vector<float> line1, vector<float> line2, vector<Point3f> &intersect_points)
{
    Point3f intersect_point;
    //定义交点的三个齐次坐标
    float x1 = 0;
    float x2 = 0;
    float x3 = 0;
    x1 = (line1[1] * line2[2] - line1[2] * line2[1]);
    x2 = (line1[2] * line2[0] - line1[0] * line2[2]);
    x3 = (line1[0] * line2[1] - line1[1] * line2[0]);
    //归一化
    x1 = x1 / x3;
    x2 = x2 / x3;
    x3 = 1;
    intersect_point.x = x1;
    intersect_point.y = x2;
    intersect_point.z = x3;
    intersect_points.push_back(intersect_point);
}

int Round(float x)
{
    return (x > 0.0) ? floor(x + 0.5) : ceil(x - 0.5);
}

void GetRectifingImage(vector<float> line, Mat src, Mat dst)
{
    Size size_src = src.size();
    for (int i = 0; i < size_src.height; i++)
    {
        for (int j = 0; j < size_src.width; j++)
        {
            float x3 = line[0] * j + line[1] * i + line[2] * 1;
            int x1 = Round(j / x3);
            int x2 = Round(i / x3);
            if (x1 < size_src.width && x1 >= 0 && x2 < size_src.height && x2 >= 0)
            {
                dst.at<uint8_t>(x2, x1) = src.at<uint8_t>(i, j);
            }
        }
    }
    imshow("src", src);
    imshow("dst", dst);
    waitKey(0);
}