OpenCV3入門（九）圖像幾何變換

時間 2020-02-19

標籤 opencv3 opencv 入門圖像幾何變換简体版

原文原文鏈接

1、圖像縮放

假設圖像x軸的縮放因子Sx， y軸方向的縮放因子Sy，相應的變換表達式爲：html

函數原型爲：編程

CV_EXPORTS_W void resize( InputArray src, OutputArray dst,
                          Size dsize, double fx = 0, double fy = 0,
                          int interpolation = INTER_LINEAR );

示例程序以下。app

img = imread("D:\\WORK\\5.OpenCV\\LeanOpenCV\\pic_src\\pic9.bmp");
imshow("原圖", img);
resize(img, img2, Size(), 0.5, 0.5);
imshow("縮放圖1", img2);
resize(img, img3, Size(), 0.8, 0.5);
imshow("縮放圖2", img3);

運行效果以下圖。函數

resize(img, img2, Size(), 1.2, 1.2);學習

2、圖像平移

假設圖像x軸的平移量Tx， y軸方向的平移量Ty，相應的變換表達式爲：測試

仿射變換的原理爲：spa

dst(x,y)=src(M11x+M12y+M13,M21x+M22y+M23)3d

平移操做可使用OpenCV的仿射變換函數來實現，使用的變換矩陣爲：code

函數原型爲：htm

CV_EXPORTS_W void warpAffine( InputArray src, OutputArray dst,
                              InputArray M, Size dsize,
                              int flags = INTER_LINEAR,
                              int borderMode = BORDER_CONSTANT,
                              const Scalar& borderValue = Scalar());

圖像平移示例。

img = imread("D:\\WORK\\5.OpenCV\\LeanOpenCV\\pic_src\\pic9.bmp", IMREAD_GRAYSCALE);
imshow("原圖", img);

// x軸平移20，y軸平移10, 2 * 3矩陣
Mat M = Mat::zeros(2, 3, CV_32FC1);
M.at<float>(0, 0) = 1;
M.at<float>(0, 2) = 20;
M.at<float>(1, 1) = 1;
M.at<float>(1, 2) = 10;
warpAffine(img, img2, M, img.size());
imshow("平移圖", img2);

3、圖像旋轉

假設點P0(x0,y0)，角度爲a，令L=|OP|=sqrt(x*x + y*y).

P0選擇b度到P1(x1,y1)，則

x1=L*cos(a+b)=L* cos(a)*cos(b) – L*sin(a)*sin(b) = x0*cos(b) - y0*sin(b)

y1=L*sin(a+b)=L* sin(a)*cos(b) + L*cos(a)*sin(b) = y0*cos(b) + x0*sin(b)

OpenCV內置仿射變換的旋轉函數，支持任意點爲中心的圖像旋轉，函數原型爲：

CV_EXPORTS_W Mat getRotationMatrix2D( Point2f center, double angle, double scale );

示例代碼以下。

img = imread("D:\\WORK\\5.OpenCV\\LeanOpenCV\\pic_src\\pic9.bmp");
imshow("原圖", img);

Point center = Point(img.cols / 2, img.rows / 2);
Mat m1= getRotationMatrix2D(center, 30, 1.0);
Mat m2 = getRotationMatrix2D(center, 30, 0.7);
Mat m3 = getRotationMatrix2D(center, 30, 1.2);
warpAffine(img, img1, m1, img.size());
warpAffine(img, img2, m2, img.size());
warpAffine(img, img3, m3, img.size());
imshow("img1", img1);
imshow("img2", img2);
imshow("img3", img3);

修改旋轉角度效果以下圖。

Mat m1= getRotationMatrix2D(center, 180, 1.0);

Mat m2 = getRotationMatrix2D(center, 270, 0.7);

若是旋轉點的座標原點不在圖片中心，則圖片繞着指定點旋轉。

Point center = Point(0, 0);

Mat m1= getRotationMatrix2D(center, 30, 1.0);

Mat m2 = getRotationMatrix2D(center,-45, 1.0);

對應的矩陣爲：

m1=

[0.8660254037844387, 0.4999999999999999, 0;

-0.4999999999999999, 0.8660254037844387, 0]

m2=

[0.7071067811865476, -0.7071067811865476, 0;

0.7071067811865476, 0.7071067811865476, 0]

輸出效果以下圖。

4、圖像重映射

重映射就是把一個圖像中一個爲之的像素放置到另外一個圖片指定位置過程。因爲映射後的圖像在原圖中可能沒有對應的整數座標點像素，因此爲了完成重映射須要作一些插值做爲非整數像素座標。咱們經過重映射來表達每一個像素的位置(x, y)：g(x, y)=f(h(x,y))

OpenCV使用remap函數完成重映射功能，函數原型爲：

CV_EXPORTS_W void remap( InputArray src, OutputArray dst,
                         InputArray map1, InputArray map2,
                         int interpolation, int borderMode = BORDER_CONSTANT,
                         const Scalar& borderValue = Scalar());

測試代碼以下。

void update_map(int ind, Mat &map_x, Mat &map_y)
{
    for (int i = 0; i < map_x.rows; i++)
    {
        for (int j = 0; j < map_x.cols; j++)
        {
            switch (ind)
            {
            case 0:
                if (j > map_x.cols*0.25 && j < map_x.cols*0.75 && i > map_x.rows*0.25 && i < map_x.rows*0.75)
                {
                    map_x.at<float>(i, j) = 2 * (j - map_x.cols*0.25f) + 0.5f;
                    map_y.at<float>(i, j) = 2 * (i - map_x.rows*0.25f) + 0.5f;
                }
                else
                {
                    map_x.at<float>(i, j) = 0;
                    map_y.at<float>(i, j) = 0;
                }
                break;
            case 1:
                map_x.at<float>(i, j) = (float)j;
                map_y.at<float>(i, j) = (float)(map_x.rows - i);
                break;
            case 2:
                map_x.at<float>(i, j) = (float)(map_x.cols - j);
                map_y.at<float>(i, j) = (float)i;
                break;
            case 3:
                map_x.at<float>(i, j) = (float)(map_x.cols - j);
                map_y.at<float>(i, j) = (float)(map_x.rows - i);
                break;
            default:
                break;
            } // end of switch
        }
    }
}

int main() {
    Mat src = imread("D:\\WORK\\5.OpenCV\\LeanOpenCV\\pic_src\\pic9.bmp");
    imshow("原圖", src);

    Mat dst(src.size(), src.type());
    Mat map_x(src.size(), CV_32FC1);
    Mat map_y(src.size(), CV_32FC1);

    update_map(0, map_x, map_y);
    remap(src, img1, map_x, map_y, INTER_LINEAR, BORDER_CONSTANT, Scalar(0, 0, 0));
    imshow("img1", img1);

    update_map(1, map_x, map_y);
    remap(src, img2, map_x, map_y, INTER_LINEAR, BORDER_CONSTANT, Scalar(0, 0, 0));
    imshow("img2", img2);

    update_map(2, map_x, map_y);
    remap(src, img3, map_x, map_y, INTER_LINEAR, BORDER_CONSTANT, Scalar(0, 0, 0));
    imshow("img3", img3);

    update_map(3, map_x, map_y);
    remap(src, img4, map_x, map_y, INTER_LINEAR, BORDER_CONSTANT, Scalar(0, 0, 0));
    imshow("img4", img4);

    waitKey();
}

輸入圖像：

代碼實現四種remap效果。

remap後的圖像：

例子2：x軸不壓縮，y軸按照一元二次曲線進行壓縮，對稱抽爲src.rows / 2。當y= src.rows / 2，對應變換前的圖座標src.rows，因此圖像被壓縮。當y=[ src.rows / 2，src.rows]時，y軸被反轉。

for (int i = 0; i < src.rows; i++)
{
    for (int j = 0; j < src.cols; j++)
    {
        map_x.at<float>(i, j) = j;
        map_y.at<float>(i, j) = (float)((-1 * pow(i- src.rows / 2, 2) / pow(src.rows / 2, 2)) + 1) * src.rows;
    }
}