平臺：Windows 10 20H2
Visual Studio 2015
OpenCV 4.5.3

本文演算法改進自圖形演算法與實戰：6.影像運動專題（5）影像旋轉-基于近鄰插值的影像旋轉 —— 進擊的CV

原理

將旋轉后影像的像素點映射回原影像，找到它的采樣點，即旋轉的逆變換，映射的結果不會都是整數像素點，那么旋轉后的點的像素值由與采樣點最鄰近的像素值表示，這就是最近鄰插值，

改變尺寸的影像旋轉
這種旋轉是將旋轉后的影像內容完全顯示出來，所以要確定新的影像的尺寸，

原始碼

RotateImage

Mat RotateImage(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));  //創建新影像
	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;

			//將圖片中點設為坐標原點
			fx1 = x1 - dst.cols / 2;
			fy1 = y1 - dst.rows / 2;
			R = sqrt(fx1 * fx1 + fy1 * fy1);	//極徑
			sita = angle;
			sita1 = atan2(fy1, fx1);			//新點極角
			sita0 = sita1 + sita;				//舊點極角
			//舊點直角坐標(中點為坐標原點)
			fx0 = R * cos(sita0);				
			fy0 = R * sin(sita0);
			//舊點直角坐標(坐標原點在角上)
			x0 = fx0 + src.cols / 2 + 0.5;
			y0 = fy0 + src.rows / 2 + 0.5;

			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;
}

主函式

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

	src = imread("D:\\Work\\OpenCV\\Workplace\\Test_1\\4.jpg");
	imshow("原圖", src);

	for (short i = -360; i <= 360; ++i)
	{
		imshow("輸出", RotateImage(src, i));
		waitKey(1);
	}
	waitKey(0);

	return 0;
}

效果

完整原始碼

#include <opencv2\opencv.hpp>
#include <iostream>

using namespace cv;
using namespace std;

Mat RotateImage(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));  //創建新影像
	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;

			//將圖片中點設為坐標原點
			fx1 = x1 - dst.cols / 2;
			fy1 = y1 - dst.rows / 2;
			R = sqrt(fx1 * fx1 + fy1 * fy1);	//極徑
			sita = angle;
			sita1 = atan2(fy1, fx1);			//新點極角
			sita0 = sita1 + sita;				//舊點極角
												//舊點直角坐標(中點為坐標原點)
			fx0 = R * cos(sita0);
			fy0 = R * sin(sita0);
			//舊點直角坐標(坐標原點在角上)
			x0 = fx0 + src.cols / 2 + 0.5;
			y0 = fy0 + src.rows / 2 + 0.5;

			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("原圖", src);

	for (short i = -360; i <= 360; ++i)
	{
		imshow("輸出", RotateImage(src, i));
		waitKey(1);
	}
	waitKey(0);

	return 0;
}

速度優化

原始碼

Mat RotateImage(Mat src, float angle)
{
	int x0, y0, x1, y1;
	angle = angle * 3.1415926535897932384626433832795 / 180;
	float sin_sita = sin(angle), cos_sita = cos(angle);
	Mat dst(abs((int)src.cols*sin_sita) + abs((int)src.rows*cos_sita), abs((int)src.cols*cos_sita) + abs((int)src.rows*sin_sita), CV_8UC3, Scalar(0));  //創建新影像
	for (x1 = 0; x1 < dst.cols; ++x1)
	{
		for (y1 = 0; y1 < dst.rows; ++y1)
		{
			float fx1, fy1;

			//將圖片中點設為坐標原點
			fx1 = x1 - dst.cols / 2;
			fy1 = y1 - dst.rows / 2;

			//舊點直角坐標(坐標原點在角上)
			x0 = fx1*cos_sita - fy1*sin_sita + src.cols / 2 + 0.5;
			y0 = fx1*sin_sita + fy1*cos_sita + src.rows / 2 + 0.5;

			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;
}

優化效果

旋轉一幅1200×562的影像


用時幾乎是原來的1/2