OpenCV中图像旋转(warpAffine)算法的实现过程

在OpenCV中，目前并没有现成的函数直接用来实现图像旋转，它是用仿射变换函数cv::warpAffine来实现的，此函数目前支持4种插值算法，最近邻、双线性、双三次、兰索斯插值，如果传进去的参数为基于像素区域关系插值算法(INTER_AREA)，则按双线性插值。

通常使用2*3矩阵来表示仿射变换：

其中，T相当于变换前的原始图像，x,y为变换后的图像坐标。

对于cv::getRotationMatrix2D函数的实现公式为：

其中scale为缩放因子(x、y方向保持一致)，angle为旋转角度(弧长)，centerx，centery为旋转中心。

以lena.jpg图像旋转45度为例：

采用最近邻插值算法的实现代码为：

	cv::Mat matSrc = cv::imread("lena.jpg", 2 | 4);

	if (matSrc.empty()) return;

	const double degree = 45;
	double angle = degree * CV_PI / 180.;
	double alpha = cos(angle);
	double beta = sin(angle);
	int iWidth = matSrc.cols;
	int iHeight = matSrc.rows;
	int iNewWidth = cvRound(iWidth * fabs(alpha) + iHeight * fabs(beta));
	int iNewHeight = cvRound(iHeight * fabs(alpha) + iWidth * fabs(beta));

	double m[6];
	m[0] = alpha;
	m[1] = beta;
	m[2] = (1 - alpha) * iWidth / 2. - beta * iHeight / 2.;
	m[3] = -m[1];
	m[4] = m[0];
	m[5] = beta * iWidth / 2. + (1 - alpha) * iHeight / 2.;

	cv::Mat M = cv::Mat(2, 3, CV_64F, m);
	cv::Mat matDst1 = cv::Mat(cv::Size(iNewWidth, iNewHeight), matSrc.type(), cv::Scalar::all(0));

	double D = m[0]*m[4] - m[1]*m[3];
	D = D != 0 ? 1./D : 0;
	double A11 = m[4]*D, A22 = m[0]*D;
	m[0] = A11; m[1] *= -D;
	m[3] *= -D; m[4] = A22;
	double b1 = -m[0]*m[2] - m[1]*m[5];
	double b2 = -m[3]*m[2] - m[4]*m[5];
	m[2] = b1; m[5] = b2;

	int round_delta = 512;//nearest
	for (int y=0; y<iNewHeight; ++y)
	{
		for (int x=0; x<iNewWidth; ++x)
		{
			//int tmpx = cvFloor(m[0] * x + m[1] * y + m[2]);
			//int tmpy = cvFloor(m[3] * x + m[4] * y + m[5]);
			int adelta = cv::saturate_cast<int>(m[0] * x * 1024);
			int bdelta = cv::saturate_cast<int>(m[3] * x * 1024);
			int X0 = cv::saturate_cast<int>((m[1] * y + m[2]) * 1024) + round_delta;
			int Y0 = cv::saturate_cast<int>((m[4] * y + m[5]) * 1024) + round_delta;
			int X = (X0 + adelta) >> 10;
			int Y = (Y0 + bdelta) >> 10;

			if ((unsigned)X < iWidth && (unsigned)Y < iHeight)
			{
				matDst1.at<cv::Vec3b>(y, x) = matSrc.at<cv::Vec3b>(Y, X);
			}
		}
	}
	cv::imwrite("rotate_nearest_1.jpg", matDst1);

	M = cv::getRotationMatrix2D(cv::Point2f(iWidth / 2., iHeight / 2.), degree, 1);

	cv::Mat matDst2;
	cv::warpAffine(matSrc, matDst2, M, cv::Size(iNewWidth, iNewHeight), 0, 0, 0);
	cv::imwrite("rotate_nearest_2.jpg", matDst2);

采用双线性插值算法的实现代码为：

	cv::Mat matSrc = cv::imread("lena.jpg", 2 | 4);

	if (matSrc.empty()) return;

	const double degree = 45;
	double angle = degree * CV_PI / 180.;
	double alpha = cos(angle);
	double beta = sin(angle);
	int iWidth = matSrc.cols;
	int iHeight = matSrc.rows;
	int iNewWidth = cvRound(iWidth * fabs(alpha) + iHeight * fabs(beta));
	int iNewHeight = cvRound(iHeight * fabs(alpha) + iWidth * fabs(beta));

	double m[6];
	m[0] = alpha;
	m[1] = beta;
	m[2] = (1 - alpha) * iWidth / 2. - beta * iHeight / 2.;
	m[3] = -m[1];
	m[4] = m[0];
	m[5] = beta * iWidth / 2. + (1 - alpha) * iHeight / 2.;

	cv::Mat M = cv::Mat(2, 3, CV_64F, m);
	cv::Mat matDst1 = cv::Mat(cv::Size(iNewWidth, iNewHeight), matSrc.type(), cv::Scalar::all(0));

	double D = m[0]*m[4] - m[1]*m[3];
	D = D != 0 ? 1./D : 0;
	double A11 = m[4]*D, A22 = m[0]*D;
	m[0] = A11; m[1] *= -D;
	m[3] *= -D; m[4] = A22;
	double b1 = -m[0]*m[2] - m[1]*m[5];
	double b2 = -m[3]*m[2] - m[4]*m[5];
	m[2] = b1; m[5] = b2;

	for (int y=0; y<iNewHeight; ++y)
	{
		for (int x=0; x<iNewWidth; ++x)
		{
			//int tmpx = cvFloor(m[0] * x + m[1] * y + m[2]);
			//int tmpy = cvFloor(m[3] * x + m[4] * y + m[5]);
			float fx = m[0] * x + m[1] * y + m[2];
			float fy = m[3] * x + m[4] * y + m[5];

			int sy  = cvFloor(fy);
			fy -= sy;
			//sy = std::min(sy, iHeight-2);
			//sy = std::max(0, sy);
			if (sy < 0 || sy >= iHeight) continue;

			short cbufy[2];
			cbufy[0] = cv::saturate_cast<short>((1.f - fy) * 2048);
			cbufy[1] = 2048 - cbufy[0];

			int sx = cvFloor(fx);
			fx -= sx;
			//if (sx < 0) {
			//	fx = 0, sx = 0;
			//}
			//if (sx >= iWidth - 1) {
			//	fx = 0, sx = iWidth - 2;
			//}
			if (sx < 0 || sx >= iWidth) continue;

			short cbufx[2];
			cbufx[0] = cv::saturate_cast<short>((1.f - fx) * 2048);
			cbufx[1] = 2048 - cbufx[0];

			for (int k=0; k<matSrc.channels(); ++k)
			{
				if (sy == iHeight - 1 || sx == iWidth - 1) {
					continue;
				} else {
					matDst1.at<cv::Vec3b>(y, x)[k] = (matSrc.at<cv::Vec3b>(sy, sx)[k] * cbufx[0] * cbufy[0] +
						matSrc.at<cv::Vec3b>(sy+1, sx)[k] * cbufx[0] * cbufy[1] +
						matSrc.at<cv::Vec3b>(sy, sx+1)[k] * cbufx[1] * cbufy[0] +
						matSrc.at<cv::Vec3b>(sy+1, sx+1)[k] * cbufx[1] * cbufy[1]) >> 22;
				}
			}
		}
	}
	cv::imwrite("rotate_bilinear_1.jpg", matDst1);

	M = cv::getRotationMatrix2D(cv::Point2f(iWidth / 2., iHeight / 2.), degree, 1);

	cv::Mat matDst2;
	cv::warpAffine(matSrc, matDst2, M, cv::Size(iNewWidth, iNewHeight), 1, 0, 0);
	cv::imwrite("rotate_bilinear_2.jpg", matDst2);

其它插值算法的实现代码与双线性类似，可参考http://blog.csdn.net/fengbingchun/article/details/17335477