透视变换MATLAB仿真，OpenCV验证

问题：

Matlab仿真

思路

将原图像的四个顶点分别左乘变换矩阵，并对其归一化。然后使用一个矩形将这个四边形框在内，矩形的选取规则为：左下顶点为所有xy的最小值，右上顶点为所有xy的最大值。

代码

% 原图像F的四个顶点坐标
x0y0 = [0;0;1];
xnyn = [640;480;1];
x0yn = [0;480;1];
xny0 = [640;0;1];
% 变换矩阵
A = [6.01 -1.65 537;0.188 2.88 554;0.000584 -0.000620 1];
% 计算透视变换后图像的四个顶点坐标
toushi_x0y0 = (A * x0y0) / (A(3,1) * x0y0(1,1) + A(3,2) * x0y0(2,1) + 1);
toushi_xnyn = (A * xnyn) / (A(3,1) * xnyn(1,1) + A(3,2) * xnyn(2,1) + 1);
toushi_x0yn = (A * x0yn) / (A(3,1) * x0yn(1,1) + A(3,2) * x0yn(2,1) + 1);
toushi_xny0 = (A * xny0) / (A(3,1) * xny0(1,1) + A(3,2) * xny0(2,1) + 1);

% 画图
figure(1);
% 原图像（黑色）
plot(x0y0(1,1),x0y0(2,1),'k*');hold on;
plot(x0yn(1,1),x0yn(2,1),'k*');hold on;
plot(xnyn(1,1),xnyn(2,1),'k*');hold on;
plot(xny0(1,1),xny0(2,1),'k*');hold on;
line([x0y0(1,1),x0yn(1,1)],[x0y0(2,1),x0yn(2,1)],'color','k');hold on;
line([x0yn(1,1),xnyn(1,1)],[x0yn(2,1),xnyn(2,1)],'color','k');hold on;
line([xnyn(1,1),xny0(1,1)],[xnyn(2,1),xny0(2,1)],'color','k');hold on;
line([xny0(1,1),x0y0(1,1)],[xny0(2,1),x0y0(2,1)],'color','k');hold on;

% 变换后图像（蓝色）
plot(toushi_x0y0(1,1),toushi_x0y0(2,1),'b*');hold on;
plot(toushi_x0yn(1,1),toushi_x0yn(2,1),'b*');hold on;
plot(toushi_xnyn(1,1),toushi_xnyn(2,1),'b*');hold on;
plot(toushi_xny0(1,1),toushi_xny0(2,1),'b*');hold on;
line([toushi_x0y0(1,1),toushi_x0yn(1,1)],[toushi_x0y0(2,1),toushi_x0yn(2,1)],'color','b');hold on;
line([toushi_x0yn(1,1),toushi_xnyn(1,1)],[toushi_x0yn(2,1),toushi_xnyn(2,1)],'color','b');hold on;
line([toushi_xnyn(1,1),toushi_xny0(1,1)],[toushi_xnyn(2,1),toushi_xny0(2,1)],'color','b');hold on;
line([toushi_xny0(1,1),toushi_x0y0(1,1)],[toushi_xny0(2,1),toushi_x0y0(2,1)],'color','b');hold on;

% 用一个矩形框起来（绿色）
all_x = [toushi_x0y0(1,1),toushi_x0yn(1,1),toushi_xny0(1,1),toushi_xnyn(1,1)];
all_y = [toushi_x0y0(2,1),toushi_x0yn(2,1),toushi_xny0(2,1),toushi_xnyn(2,1)];
new_x0y0 = [min(all_x);min(all_y)]
new_x0yn = [min(all_x);max(all_y)];
new_xnyn = [max(all_x);max(all_y)]
new_xny0 = [max(all_x);min(all_y)];
plot(new_x0y0(1,1),new_x0y0(2,1),'g*');hold on;
plot(new_x0yn(1,1),new_x0yn(2,1),'g*');hold on;
plot(new_xnyn(1,1),new_xnyn(2,1),'g*');hold on;
plot(new_xny0(1,1),new_xny0(2,1),'g*');hold on;
line([new_x0y0(1,1),new_x0yn(1,1)],[new_x0y0(2,1),new_x0yn(2,1)],'color','g');hold on;
line([new_x0yn(1,1),new_xnyn(1,1)],[new_x0yn(2,1),new_xnyn(2,1)],'color','g');hold on;
line([new_xnyn(1,1),new_xny0(1,1)],[new_xnyn(2,1),new_xny0(2,1)],'color','g');hold on;
line([new_xny0(1,1),new_x0y0(1,1)],[new_xny0(2,1),new_x0y0(2,1)],'color','g');hold on;

%输出G的尺寸
delta_x = max(all_x) - min(all_x)
delta_y = max(all_y) - min(all_y)

结果

运行代码，输出图像，下图中黑色矩形为原图像F，蓝色矩形为透视变换后的图像，绿色矩形是用矩形框起来的最终图像G：

同时MATLAB控制台输出delta_x = 3.7003e+03，delta_y = 2.2660e+03

也就是说经过透视变换后的图像G的尺寸为3700.3*2266

OpenCV验证

思路

随便选取一张图片，将其拉伸到640*480，再对其进行上述变换矩阵指定的透视变换，最后输出图片。

代码

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

using namespace cv;
using namespace std;

int main()
{
	string path = "res/test_image.jpg";
	Mat img = imread(path);

	// 伸缩图片至640*480
	Mat imgResize;
	resize(img, imgResize, Size(640,480));

	// 变换前与变换后的顶点坐标
	Point2f src[4] = { {0,0},{640,480},{0,480},{640,0} };
	Point2f dst[4] = { {537.0f,554.0f},{3337.2f,1911.2f},{-363.0f,2756.8},{3190.8,490.9} };

	//创建变换矩阵
	Mat matrix = getPerspectiveTransform(src, dst);

	// 透视变换
	Mat imgWarp;
	warpPerspective(imgResize, imgWarp, matrix, Size(4000, 3000));

	// 标记原始图像位置
	rectangle(imgWarp, Point(0, 0), Point(640, 480), Scalar(255, 255, 255), FILLED);
	putText(imgWarp, "Origin Image", Point(100, 200), FONT_HERSHEY_COMPLEX, 2, Scalar(0, 69, 255),2);

	// 输出变换后图像
	imwrite("res/output.jpg", imgWarp);

	waitKey(0);
}