【机器视觉学习笔记】双线性插值实现图片任意角度旋转（C++）

平台：Windows 10 20H2
Visual Studio 2015
OpenCV 4.5.3

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原理

如图所示，我们需要求P点的像素值。我们已知了Q11、Q21、Q12、Q22、P的坐标。也知道Q11、Q21、Q12、Q22的像素值。所以先用关于X的单线性插值去分别计算R1、R2的像素值

再使用关于y方向的单线性插值计算P点的像素值。

由以上思路可化简得到如下式子。$I_x$为该点上的像素值或灰度值

源码

RotateImage_BilinearInterpolation

Mat RotateImage_BilinearInterpolation(Mat src, double angle)
{
	int x0, y0, x1, y1;
	angle = angle * 3.1415926535897932384626433832795 / 180;
	int dx = abs((int)src.cols*cos(angle)) + abs((int)src.rows*sin(angle));
	int dy = abs((int)src.cols*sin(angle)) + abs((int)src.rows*cos(angle));
	Mat dst(dy, dx, CV_8UC3, Scalar(0));  //创建新图像
	for (x1 = 0; x1 < dst.cols; x1++)
	{
		for (y1 = 0; y1 < dst.rows; y1++)
		{
			double fx0, fy0;
			double fx1, fy1;
			double R;
			double sita, sita0, sita1;
			int x01, y01;
			int x02, y02;
			int x03, y03;
			int x04, y04;
			double p, q;

			//将图片中点设为坐标原点
			fx1 = x1 - dst.cols / 2;
			fy1 = y1 - dst.rows / 2;
			R = sqrt(fx1 * fx1 + fy1 * fy1);	//极径
			sita = angle;
			sita1 = atan2(fy1, fx1);			//新点极角
			sita0 = sita1 + sita;				//旧点极角
												//旧点直角坐标(中点为坐标原点)
			fx0 = R * cos(sita0);
			fy0 = R * sin(sita0);
			//旧点直角坐标(坐标原点在角上)
			x0 = fx0 + src.cols / 2 + 0.5;
			y0 = fy0 + src.rows / 2 + 0.5;

			x01 = (int)(fx0 + src.cols / 2);
			y01 = (int)(fy0 + src.rows / 2);
			x02 = x01 + 1;
			y02 = y01;
			x03 = x01 + 1;
			y03 = y01 + 1;
			x04 = x01;
			y04 = y01 + 1;
			p = (fx0 + src.cols / 2) - x01;
			q = (fy0 + src.rows / 2) - y01;

			if (x01 >= 0 && x03 < src.cols && y01 >= 0 && y03 < src.rows)
			{
				for (int i = 0; i < 3; ++i)
					dst.at<Vec3b>(Point(x1, y1))[i] = src.at<Vec3b>(Point(x01, y01))[i] * (1 - p) * (1 - q) + src.at<Vec3b>(Point(x02, y02))[i] * p * (1 - q) + src.at<Vec3b>(Point(x03, y03))[i] * p * q + src.at<Vec3b>(Point(x04, y04))[i] * (1 - p) * q;
			}
			else if (x0 >= 0 && x0 < src.cols && y0 >= 0 && y0 < src.rows)
				dst.at<Vec3b>(Point(x1, y1)) = src.at<Vec3b>(Point(x0, y0));
			else
				dst.at<Vec3b>(Point(x1, y1)) = 0;
		}
	}
	return dst;
}

主函数

int main(int argc, char * argv[])
{
	Mat src;
	
	src = imread("D:\\Work\\OpenCV\\Workplace\\Test_1\\4.jpg");
	imshow("原图", src);
	imshow("输出", RotateImage_BilinearInterpolation(src, 45));
	
	waitKey(0);
	return 0;
}

效果

与最近邻插值比较

原图

最近邻插值效果（局部）

双线性插值效果（局部）

完整源码

#include 
#include 

using namespace cv;
using namespace std;

Mat RotateImage_BilinearInterpolation(Mat src, double angle)
{
	int x0, y0, x1, y1;
	angle = angle * 3.1415926535897932384626433832795 / 180;
	int dx = abs((int)src.cols*cos(angle)) + abs((int)src.rows*sin(angle));
	int dy = abs((int)src.cols*sin(angle)) + abs((int)src.rows*cos(angle));
	Mat dst(dy, dx, CV_8UC3, Scalar(0));  //创建新图像
	for (x1 = 0; x1 < dst.cols; x1++)
	{
		for (y1 = 0; y1 < dst.rows; y1++)
		{
			double fx0, fy0;
			double fx1, fy1;
			double R;
			double sita, sita0, sita1;
			int x01, y01;
			int x02, y02;
			int x03, y03;
			int x04, y04;
			double p, q;

			//将图片中点设为坐标原点
			fx1 = x1 - dst.cols / 2;
			fy1 = y1 - dst.rows / 2;
			R = sqrt(fx1 * fx1 + fy1 * fy1);	//极径
			sita = angle;
			sita1 = atan2(fy1, fx1);			//新点极角
			sita0 = sita1 + sita;				//旧点极角
												//旧点直角坐标(中点为坐标原点)
			fx0 = R * cos(sita0);
			fy0 = R * sin(sita0);
			//旧点直角坐标(坐标原点在角上)
			x0 = fx0 + src.cols / 2 + 0.5;
			y0 = fy0 + src.rows / 2 + 0.5;

			x01 = (int)(fx0 + src.cols / 2);
			y01 = (int)(fy0 + src.rows / 2);
			x02 = x01 + 1;
			y02 = y01;
			x03 = x01 + 1;
			y03 = y01 + 1;
			x04 = x01;
			y04 = y01 + 1;
			p = (fx0 + src.cols / 2) - x01;
			q = (fy0 + src.rows / 2) - y01;

			if (x01 >= 0 && x03 < src.cols && y01 >= 0 && y03 < src.rows)
			{
				for (int i = 0; i < 3; ++i)
					dst.at<Vec3b>(Point(x1, y1))[i] = src.at<Vec3b>(Point(x01, y01))[i] * (1 - p) * (1 - q) + src.at<Vec3b>(Point(x02, y02))[i] * p * (1 - q) + src.at<Vec3b>(Point(x03, y03))[i] * p * q + src.at<Vec3b>(Point(x04, y04))[i] * (1 - p) * q;
			}
			else if (x0 >= 0 && x0 < src.cols && y0 >= 0 && y0 < src.rows)
				dst.at<Vec3b>(Point(x1, y1)) = src.at<Vec3b>(Point(x0, y0));
			else
				dst.at<Vec3b>(Point(x1, y1)) = 0;
		}
	}
	return dst;
}

int main(int argc, char * argv[])
{
	Mat src;

	src = imread("D:\\Work\\OpenCV\\Workplace\\Test_1\\4.jpg");
	imshow("原图", src);
	imshow("输出", RotateImage_BilinearInterpolation(src, 45));

	waitKey(0);
	return 0;
}