opencv C++ 旋转任意角度图片

摘要：opencv里面似乎没有直接的旋转图片的接口，这里实现一个旋转任意角度的方法，在旋转的时候调用opencv里面的仿射变换函数实现。有两种旋转模式：一种按图片中心旋转，尺寸与原图一致；另外一种模式是扩充图片尺寸以包含所有像素点。

1. 示例：

2. 原理

旋转平移的坐标变换

设有任意一点$p，在平面直角坐标中其坐标为(x,y),在平面极坐标系中其坐标为(\rho ,\theta )$，则根据坐标系转换公式有
$$\{\begin{array}{l}x=\rho \ast cos\theta \\ y=\rho \ast sin\theta \end{array}$$
在这里$x,y\in [-\infty ,\infty ],\rho \in [0,\infty ],\theta \in [0,2\pi )$. 假设对$p$点对应的极径$\overline{op}逆时针旋转\alpha 弧度$得到$\overline{o{p}^{\prime }}$，则$p^{\prime }$点的坐标为
$$\{\begin{array}{ll}{x}^{\prime }& =\rho \ast cos(\theta +\alpha )\\ & =\rho \ast cos\theta \ast cos\alpha -\rho \ast sin\theta \ast \sin \alpha \\ & =x\ast cos\alpha -y\ast sin\alpha \\ & \\ y^{\prime }& =\rho \ast sin(\theta +\alpha )\\ & =\rho \ast sin\theta \ast cos\alpha +\rho \ast cos\theta \ast \sin \alpha \\ & =y\ast cos\alpha +x\ast sin\alpha \end{array}$$
再在直角坐标系中按向量$(Tx,Ty)$平移$p^{\prime }$到$p^{\prime \prime }$，则$p^{\prime \prime }$的坐标为
$$\{\begin{array}{ll}{x}^{\prime \prime }& =x^{\prime }+Tx\\ & =x\ast cos\alpha -y\ast sin\alpha +Tx\\ & \\ y^{\prime \prime }& =y^{\prime }+Ty\\ & =y\ast cos\alpha +x\ast sin\alpha +Ty\end{array}$$
转为矩阵形式为
$$\left[\begin{array}{c}{x}^{\prime \prime }\\ y^{\prime \prime }\end{array}\right]=\left[\begin{array}{ccc}\cos \alpha & -sin\alpha & Tx\\ sin\alpha & \cos \alpha & Ty\end{array}\right]\cdot \left[\begin{array}{c}x\\ y\\ 1\end{array}\right]$$
也就是说只要知道仿射变换矩阵，那么每一个像素点(x,y)都可以用上面的公式直接计算了。

3. 两种方式

• 方式一
  从仿射变换矩阵$\left[\begin{array}{ccc}\cos \alpha & -sin\alpha & Tx\\ sin\alpha & \cos \alpha & Ty\end{array}\right]$看，参数有3个：$\alpha ,Tx,Ty$，如果有把它们都看成未知数，那么只要有三个独立的方程就可以解出仿射变换矩阵,对应实际的情况就是不共线的三个点。而opencv中提供了一个函数cv::getAffineTransform，只需要输入三个对应点对就可以得到仿射变换矩阵，然后用cv::warpAffine进行变换。这种方式主要是因为矩形的角点很容易计算，只需要计算三个点就可以得到变换矩阵。
• 方式二
  直接构造仿射变换矩阵，角度已知，只需要求平移量，而平移量就是“最负”的点的坐标值，因为负数坐标的地方不显示，加上一点偏移使得所有坐标为负的点都变为正的。

4. 源码

#include 
#include
#include "opencv.hpp"

int rotateImage(const cv::Mat &src, cv::Mat &dst, const double angle, const int mode)
{
	//mode = 0 ,Keep the original image size unchanged
	//mode = 1, Change the original image size to fit the rotated scale, padding with zero

	if (src.empty())
	{
		std::cout << "Damn, the input image is empty!\n";
		return -1;
	}

	if (mode == 0)
	{
		cv::Point2f center((src.cols - 1) / 2.0, (src.rows - 1) / 2.0);
		cv::Mat rot = cv::getRotationMatrix2D(center, angle, 1.0);
		cv::warpAffine(src, dst, rot, src.size());//the original size
	}
	else {

		double alpha = -angle * CV_PI / 180.0;//convert angle to radian format 

		cv::Point2f srcP[3];
		cv::Point2f dstP[3];
		srcP[0] = cv::Point2f(0, src.rows);
		srcP[1] = cv::Point2f(src.cols, 0);
		srcP[2] = cv::Point2f(src.cols, src.rows);
		
		//rotate the pixels
		for (int i=0;i<3;i++)
					dstP[i] = cv::Point2f(srcP[i].x*cos(alpha) - srcP[i].y*sin(alpha), srcP[i].y*cos(alpha) + srcP[i].x*sin(alpha));
		double minx, miny, maxx, maxy;
		minx = std::min(std::min(std::min(dstP[0].x, dstP[1].x), dstP[2].x),float(0.0));
		miny  = std::min(std::min(std::min(dstP[0].y, dstP[1].y), dstP[2].y),float(0.0));
		maxx = std::max(std::max(std::max(dstP[0].x, dstP[1].x), dstP[2].x),float(0.0));
		maxy = std::max(std::max(std::max(dstP[0].y, dstP[1].y), dstP[2].y),float(0.0));

		int w = maxx - minx;
		int h = maxy - miny;

		//translation
		for (int i = 0; i < 3; i++)
		{
			if (minx < 0)
				dstP[i].x -= minx;
			if (miny < 0)
				dstP[i].y -= miny;
		}

		cv::Mat warpMat = cv::getAffineTransform(srcP, dstP);
		cv::warpAffine(src, dst, warpMat, cv::Size(w, h));//extend size

	}//end else

	return 0;
}

int rotateImage2(const cv::Mat &src, cv::Mat &dst, const double angle, const int mode)
{
	//mode = 0 ,Keep the original image size unchanged
	//mode = 1, Change the original image size to fit the rotated scale, padding with zero

	if (src.empty())
	{
		std::cout << "Damn, the input image is empty!\n";
		return -1;
	}

	if (mode == 0)
	{
		cv::Point2f center((src.cols - 1) / 2.0, (src.rows - 1) / 2.0);
		cv::Mat rot = cv::getRotationMatrix2D(center, angle, 1.0);
		cv::warpAffine(src, dst, rot, src.size());//the original size
	}
	else {

		double alpha = -angle * CV_PI / 180.0;//convert angle to radian format 

		cv::Point2f srcP[3];
		cv::Point2f dstP[3];
		srcP[0] = cv::Point2f(0, src.rows);
		srcP[1] = cv::Point2f(src.cols, 0);
		srcP[2] = cv::Point2f(src.cols, src.rows);

		//rotate the pixels
		for (int i = 0; i < 3; i++)
			dstP[i] = cv::Point2f(srcP[i].x*cos(alpha) - srcP[i].y*sin(alpha), srcP[i].y*cos(alpha) + srcP[i].x*sin(alpha));
		double minx, miny, maxx, maxy;
		minx = std::min(std::min(std::min(dstP[0].x, dstP[1].x), dstP[2].x), float(0.0));
		miny = std::min(std::min(std::min(dstP[0].y, dstP[1].y), dstP[2].y), float(0.0));
		maxx = std::max(std::max(std::max(dstP[0].x, dstP[1].x), dstP[2].x), float(0.0));
		maxy = std::max(std::max(std::max(dstP[0].y, dstP[1].y), dstP[2].y), float(0.0));

		int w = maxx - minx;
		int h = maxy - miny;

		cv::Mat warpMat =cv::Mat::zeros(cv::Size(3,2),CV_64F);//rows=2,cols=3
		
		std::cout << warpMat.type() << std::endl;
		std::cout << warpMat.size()<<std::endl;
		warpMat.at<double>(0, 0) = cos(alpha);
		warpMat.at<double>(0, 1) = 0- sin(alpha);
		warpMat.at<double>(1, 0) = sin(alpha);
		warpMat.at<double>(1, 1) = cos(alpha);
		warpMat.at<double>(0, 2) =0- minx;
		warpMat.at<double>(1, 2) =0-miny;
		//std::cout << warpMat;
		cv::warpAffine(src, dst, warpMat, cv::Size(w, h));//extend size

	}//end else

	return 0;
}

int main()
{
    std::cout << "Hello World!\n";
	std::string filePath = "K:\\imageData\\lena\\images.png";
	cv::Mat src = cv::imread(filePath);
	cv::Mat dst1,dst2;
	for (double i = -360; i <= 360; i++)
	{
		int flg1 = rotateImage(src, dst1, i, 0);
		int flg2 = rotateImage(src, dst2, i, 1);
		if (flg1 == -1 || flg2 == -1) continue;
		cv::imshow("src", src);
		cv::imshow("dst1", dst1);
		cv::imshow("dst2", dst2);
		cv::waitKey(5);
	}
	cv::waitKey(0);
	cv::destroyAllWindows();

}