OpenCV : 投影变换

投影变换

物体在三维空间发生了旋转,叫做投影变换.由于可能出现阴影或遮挡,所以变换后较难复原.如果物体时平面的,就可以通过投影变换物体三维变换进行模型化,这叫做专用的二维投影变换.

矩阵表示:
$\left[\begin{matrix}\tilde{x} \\ \tilde{y}\\ \tilde{z}\end{matrix}\right] = \left[\begin{matrix}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22}& a_{23}\\ a_{31} & a_{32} & a_{33}\end{matrix}\right] \left[\begin{matrix}x \\ y \\ z\end{matrix}\right]$⎣⎡​x~y~​z~​⎦⎤​=⎣⎡​a11​a21​a31​​a12​a22​a32​​a13​a23​a33​​⎦⎤​⎣⎡​xyz​⎦⎤​

求投影矩阵

• getPerspectiveTransform(src, dst)
  1. src : 原坐标
  2. dst : 变换后的坐标
  3. 返回结果为:3x3的投影矩阵,数据类型为CV_64F

计算投影矩阵

#include<iostream>
#include<opencv2/core.hpp>
#include<opencv2/highgui.hpp>
#include<opencv2/imgproc.hpp>

using namespace cv;
using namespace std;

int main()
{
	//原坐标
	Point2f src[] = { Point2f(0, 0), Point2f(20, 0), Point2f(0, 20), Point2f(20, 20) };
	//投影后的坐标
	Point2f dst[] = { Point2f(10, 20),Point2f(20, 2), Point2f(50, 70), Point2f(25, 7) };
	Mat P =getPerspectiveTransform(src, dst);
	cout << P << endl;
	return 0;
}

#include<iostream>
#include<opencv2/core.hpp>
#include<opencv2/highgui.hpp>
#include<opencv2/imgproc.hpp>

using namespace cv;
using namespace std;

int main()
{
	//原坐标
	Mat src = (Mat_<float>(4, 2) << 0, 0, 20, 0, 0, 20, 20, 20);
	//投影后的坐标
	Mat dst = (Mat_<float>(4, 2) << 10, 2, 20, 2, 5, 7, 25, 7);
	Mat P =getPerspectiveTransform(src, dst);
	cout << P << endl;
	return 0;
}

图像的投影变换

• warpPerspective(Mat src, Mat dst, Mat P, Size dsize)
  1. src : 原图
  2. dst : 输出图片
  3. P : 投影矩阵
  4. dsize : 输出图像大小
• circle(Mat img, Point center, int radius, const Scalar & color, int thickness=1, int lineType=8, int shift=0)
  1. img : 图像矩阵(2d)
  2. center : 圆心坐标
  3. radius : 半径长度
  4. color : 颜色
  5. thickness : 线的粗细
  6. lineType : 线的类型
• OpenCV中其他类似的方法还有:rectangle, ellipse, line(矩形,椭圆,线段)

#include<iostream>
#include<opencv2/core.hpp>
#include<opencv2/highgui.hpp>
#include<opencv2/imgproc.hpp>

using namespace cv;
using namespace std;

int main()
{
	Mat img = imread("./People/5g.jpg", 1);
	Mat src = (Mat_<float>(4, 2)<< 0, 0, 1000, 0, 0, 1000, 1000, 1000);
	Mat dst = (Mat_<float>(4, 2) << 0, 0, 1000, 0, 300, 1000, 600, 1000);
	Mat P = getPerspectiveTransform(src, dst);
	Mat O;
	cout << "rows : " << img.rows << endl;
	cout << "cols : " << img.cols << endl;
	warpPerspective(img, O, P, img.size());
	imshow("PerspectiveTransform", O);
	waitKey(0);
	return 0;
}

原图

投影后

通过鼠标点击事件,进行图像投影

#include<iostream>
#include<opencv2/core.hpp>
#include<opencv2/highgui.hpp>
#include<opencv2/imgproc.hpp>

using namespace cv;
using namespace std;

Mat I_img;    // 输入图片
Mat P_img;  // 投影后的图片
Point2f src_point[4];    // 原坐标
Point2f dst_point[4];    // 投影后的坐标
int i = 0, j = 0;               // 记录点击次数
Point2f point_i, point_p;

// 同鼠标事件获得原图中坐标
void mouse_I(int event, int x, int y, int flags, void* param)
{
	switch (event)
	{
	case CV_EVENT_LBUTTONDOWN:
		point_i = Point2f(x, y);
		break;
	case CV_EVENT_LBUTTONUP:
		src_point[i] = point_i;
		circle(I_img, src_point[i], 7, Scalar(0), 3);   //画出点击的坐标
		i += 1;
		break;
	default:
		break;
	}
}

// 在画布上选择投影后的坐标
void mouse_pI(int event, int x, int y, int flags, void* param)
{
	switch (event)
	{
	case CV_EVENT_LBUTTONDOWN:
		point_p = Point2f(x, y);
		break;
	case CV_EVENT_LBUTTONUP:
		dst_point[j] = point_p;
		circle(P_img, dst_point[j], 7, Scalar(0), 3);
		j += 1;
		break;
	default:
		break;
	}
}

int main()
{
	I_img = imread("./People/5.jpg", CV_LOAD_IMAGE_GRAYSCALE);
	if (!I_img.data)
		return -1;
	P_img = 255 * Mat::ones(I_img.size(), CV_8UC1);
	namedWindow("Original Image");
	setMouseCallback("Original Image", mouse_I, NULL);
	namedWindow("Output Image");
	setMouseCallback("Output Image", mouse_pI, NULL);
	imshow("Original Image", I_img);
	imshow("Output Image", P_img);
	while (!(i == 4 && j == 4))
	{
		imshow("Original Image", I_img);
		imshow("Output Image", P_img);
		if (waitKey(50) == 'q')
			break;
	}
	imshow("Original Image", I_img);
	imshow("Output Image", P_img);
	// 撤销鼠标事件
	setMouseCallback("Original Image", NULL, NULL);
	setMouseCallback("Output Image", NULL, NULL);
	// 计算投影矩阵
	Mat P = getPerspectiveTransform(src_point, dst_point);
	// 投影变换
	Mat R;
	warpPerspective(I_img, R, P, I_img.size());
	imshow("Persepctive Result", R);
	waitKey(0);
	return 0;
}

选择原坐标

选定投影后的坐标

投影后的图片