在 C++ 中的 OpenCV 中旋轉圖像而不裁剪

Question

我想旋轉圖像，但我無法在不裁剪的情況下獲得旋轉的圖像

我的原圖：

現在我使用這個代碼：

#include <opencv2/core/core.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/imgproc/imgproc.hpp>

// Compile with g++ code.cpp -lopencv_core -lopencv_highgui -lopencv_imgproc

int main()
{
    cv::Mat src = cv::imread("im.png", CV_LOAD_IMAGE_UNCHANGED);
    cv::Mat dst;

    cv::Point2f pc(src.cols/2., src.rows/2.);
    cv::Mat r = cv::getRotationMatrix2D(pc, -45, 1.0);

    cv::warpAffine(src, dst, r, src.size()); // what size I should use?

    cv::imwrite("rotated_im.png", dst);

    return 0;
}

並獲得以下圖像：

但我想得到這個：

Answer 1

我的回答受到以下帖子/博客條目的啟發：

• 使用 cv::warpAffine 偏移目標圖像旋轉 cv::Mat
• http://john.freml.in/opencv-rotation

主要觀點：

• 通過向新圖像中心添加平移來調整旋轉矩陣
• 使用cv::RotatedRect盡可能依賴現有的 opencv 功能

使用 opencv 3.4.1 測試的代碼：

#include "opencv2/opencv.hpp"

int main()
{
    cv::Mat src = cv::imread("im.png", CV_LOAD_IMAGE_UNCHANGED);
    double angle = -45;

    // get rotation matrix for rotating the image around its center in pixel coordinates
    cv::Point2f center((src.cols-1)/2.0, (src.rows-1)/2.0);
    cv::Mat rot = cv::getRotationMatrix2D(center, angle, 1.0);
    // determine bounding rectangle, center not relevant
    cv::Rect2f bbox = cv::RotatedRect(cv::Point2f(), src.size(), angle).boundingRect2f();
    // adjust transformation matrix
    rot.at<double>(0,2) += bbox.width/2.0 - src.cols/2.0;
    rot.at<double>(1,2) += bbox.height/2.0 - src.rows/2.0;

    cv::Mat dst;
    cv::warpAffine(src, dst, rot, bbox.size());
    cv::imwrite("rotated_im.png", dst);

    return 0;
}

Answer 2

只需嘗試下面的代碼，想法很簡單：

1. 您需要在以任何角度旋轉時創建一個具有您期望的最大尺寸的空白圖像。 在這里你應該使用上面評論中提到的畢達哥拉斯。

2. 現在將源圖像復制到新創建的圖像並將其傳遞給warpAffine 。 在這里，您應該使用新創建的圖像的中心進行旋轉。

3. 在warpAffine之后，如果您需要為此裁剪精確圖像，請使用此處所述的旋轉矩陣在放大圖像中轉換源圖像的四個角

4. 從上面的結果中找到上角的最小 x 和最小 y，以及下角的最大 x 和最大 y 以裁剪圖像。

這是代碼：

int theta = 0;
Mat src,frame, frameRotated;
src = imread("rotate.png",1);
cout<<endl<<endl<<"Press '+' to rotate anti-clockwise and '-' for clockwise 's' to save" <<endl<<endl;

int diagonal = (int)sqrt(src.cols*src.cols+src.rows*src.rows);
int newWidth = diagonal;
int newHeight =diagonal;

int offsetX = (newWidth - src.cols) / 2;
int offsetY = (newHeight - src.rows) / 2;
Mat targetMat(newWidth, newHeight, src.type());
Point2f src_center(targetMat.cols/2.0F, targetMat.rows/2.0F);


while(1){
src.copyTo(frame);
double radians = theta * M_PI / 180.0;
double sin = abs(std::sin(radians));
double cos = abs(std::cos(radians));

frame.copyTo(targetMat.rowRange(offsetY, offsetY + frame.rows).colRange(offsetX, offsetX + frame.cols));
Mat rot_mat = getRotationMatrix2D(src_center, theta, 1.0);
warpAffine(targetMat, frameRotated, rot_mat, targetMat.size());
 //Calculate bounding rect and for exact image
 //Reference:- https://stackoverflow.com/questions/19830477/find-the-bounding-rectangle-of-rotated-rectangle/19830964?noredirect=1#19830964
    Rect bound_Rect(frame.cols,frame.rows,0,0);

    int x1 = offsetX;
    int x2 = offsetX+frame.cols;
    int x3 = offsetX;
    int x4 = offsetX+frame.cols;

    int y1 = offsetY;
    int y2 = offsetY;
    int y3 = offsetY+frame.rows;
    int y4 = offsetY+frame.rows;

    Mat co_Ordinate = (Mat_<double>(3,4) << x1, x2, x3, x4,
                                            y1, y2, y3, y4,
                                            1,  1,  1,  1 );
    Mat RotCo_Ordinate = rot_mat * co_Ordinate;

    for(int i=0;i<4;i++){
       if(RotCo_Ordinate.at<double>(0,i)<bound_Rect.x)
         bound_Rect.x=(int)RotCo_Ordinate.at<double>(0,i); //access smallest 
       if(RotCo_Ordinate.at<double>(1,i)<bound_Rect.y)
        bound_Rect.y=RotCo_Ordinate.at<double>(1,i); //access smallest y
     }

     for(int i=0;i<4;i++){
       if(RotCo_Ordinate.at<double>(0,i)>bound_Rect.width)
         bound_Rect.width=(int)RotCo_Ordinate.at<double>(0,i); //access largest x
       if(RotCo_Ordinate.at<double>(1,i)>bound_Rect.height)
        bound_Rect.height=RotCo_Ordinate.at<double>(1,i); //access largest y
     }

    bound_Rect.width=bound_Rect.width-bound_Rect.x;
    bound_Rect.height=bound_Rect.height-bound_Rect.y;

    Mat cropedResult;
    Mat ROI = frameRotated(bound_Rect);
    ROI.copyTo(cropedResult);

    imshow("Result", cropedResult);
    imshow("frame", frame);
    imshow("rotated frame", frameRotated);
    char k=waitKey();
    if(k=='+') theta+=10;
    if(k=='-') theta-=10;
    if(k=='s') imwrite("rotated.jpg",cropedResult);
    if(k==27) break;

}

裁剪圖像

Answer 3

謝謝羅布拉！ 實際上，您不需要計算兩次正弦和余弦。

import cv2

def rotate_image(mat, angle):
  # angle in degrees

  height, width = mat.shape[:2]
  image_center = (width/2, height/2)

  rotation_mat = cv2.getRotationMatrix2D(image_center, angle, 1.)

  abs_cos = abs(rotation_mat[0,0])
  abs_sin = abs(rotation_mat[0,1])

  bound_w = int(height * abs_sin + width * abs_cos)
  bound_h = int(height * abs_cos + width * abs_sin)

  rotation_mat[0, 2] += bound_w/2 - image_center[0]
  rotation_mat[1, 2] += bound_h/2 - image_center[1]

  rotated_mat = cv2.warpAffine(mat, rotation_mat, (bound_w, bound_h))
  return rotated_mat

Answer 4

謝謝@哈里斯！ 這是 Python 版本：

def rotate_image(image, angle):
  '''Rotate image "angle" degrees.

  How it works:
    - Creates a blank image that fits any rotation of the image. To achieve
      this, set the height and width to be the image's diagonal.
    - Copy the original image to the center of this blank image
    - Rotate using warpAffine, using the newly created image's center
      (the enlarged blank image center)
    - Translate the four corners of the source image in the enlarged image
      using homogenous multiplication of the rotation matrix.
    - Crop the image according to these transformed corners
  '''

  diagonal = int(math.sqrt(pow(image.shape[0], 2) + pow(image.shape[1], 2)))
  offset_x = (diagonal - image.shape[0])/2
  offset_y = (diagonal - image.shape[1])/2
  dst_image = np.zeros((diagonal, diagonal, 3), dtype='uint8')
  image_center = (diagonal/2, diagonal/2)

  R = cv2.getRotationMatrix2D(image_center, angle, 1.0)
  dst_image[offset_x:(offset_x + image.shape[0]), \
            offset_y:(offset_y + image.shape[1]), \
            :] = image
  dst_image = cv2.warpAffine(dst_image, R, (diagonal, diagonal), flags=cv2.INTER_LINEAR)

  # Calculate the rotated bounding rect
  x0 = offset_x
  x1 = offset_x + image.shape[0]
  x2 = offset_x
  x3 = offset_x + image.shape[0]

  y0 = offset_y
  y1 = offset_y
  y2 = offset_y + image.shape[1]
  y3 = offset_y + image.shape[1]

  corners = np.zeros((3,4))
  corners[0,0] = x0
  corners[0,1] = x1
  corners[0,2] = x2
  corners[0,3] = x3
  corners[1,0] = y0
  corners[1,1] = y1
  corners[1,2] = y2
  corners[1,3] = y3
  corners[2:] = 1

  c = np.dot(R, corners)

  x = int(c[0,0])
  y = int(c[1,0])
  left = x
  right = x
  up = y
  down = y

  for i in range(4):
    x = int(c[0,i])
    y = int(c[1,i])
    if (x < left): left = x
    if (x > right): right = x
    if (y < up): up = y
    if (y > down): down = y
  h = down - up
  w = right - left

  cropped = np.zeros((w, h, 3), dtype='uint8')
  cropped[:, :, :] = dst_image[left:(left+w), up:(up+h), :]
  return cropped

Answer 5

在四處尋找一個干凈且易於理解的解決方案並通讀上面的答案試圖理解它們之后，我最終想出了一個使用三角學的解決方案。

我希望這對某人有所幫助:)

import cv2
import math

def rotate_image(mat, angle):
    height, width = mat.shape[:2]
    image_center = (width / 2, height / 2)

    rotation_mat = cv2.getRotationMatrix2D(image_center, angle, 1)

    radians = math.radians(angle)
    sin = math.sin(radians)
    cos = math.cos(radians)
    bound_w = int((height * abs(sin)) + (width * abs(cos)))
    bound_h = int((height * abs(cos)) + (width * abs(sin)))

    rotation_mat[0, 2] += ((bound_w / 2) - image_center[0])
    rotation_mat[1, 2] += ((bound_h / 2) - image_center[1])

    rotated_mat = cv2.warpAffine(mat, rotation_mat, (bound_w, bound_h))
    return rotated_mat

編輯：請參閱下面@Remi Cuingnet 的回答。

Answer 6

增加圖像畫布（從中心開始，不改變圖像大小），使其適合旋轉后的圖像，然后應用warpAffine ：

Mat img = imread ("/path/to/image", 1);
double offsetX, offsetY;
double angle = -45;
double width = img.size().width;
double height = img.size().height;
Point2d center = Point2d (width / 2, height / 2);
Rect bounds = RotatedRect (center, img.size(), angle).boundingRect();
Mat resized = Mat::zeros (bounds.size(), img.type());
offsetX = (bounds.width - width) / 2;
offsetY = (bounds.height - height) / 2;
Rect roi = Rect (offsetX, offsetY, width, height);
img.copyTo (resized (roi));
center += Point2d (offsetX, offsetY);
Mat M = getRotationMatrix2D (center, angle, 1.0);
warpAffine (resized, resized, M, resized.size());

Answer 7

旋轉圖像並控制填充的黑色區域的 Python 版本，您可以使用scipy.ndimage.rotate 。 下面是一個例子：

from skimage import io
from scipy import ndimage

image = io.imread('https://www.pyimagesearch.com/wp- 
content/uploads/2019/12/tensorflow2_install_ubuntu_header.jpg')
io.imshow(image)
plt.show()

rotated = ndimage.rotate(image, angle=234, mode='nearest')
rotated = cv2.resize(rotated, (image.shape[:2]))
# rotated = cv2.cvtColor(rotated, cv2.COLOR_BGR2RGB)
# cv2.imwrite('rotated.jpg', rotated)
io.imshow(rotated)
plt.show()

Answer 8

感謝大家的這篇文章，它非常有用。 但是，當旋轉 90º 時，我發現左上和上一些黑線（使用 Rose 的 python 版本）。 問題似乎是一些 int() 四舍五入。 除此之外，我還改變了角度的符號，使其順時針增長。

def rotate_image(image, angle):
    '''Rotate image "angle" degrees.

    How it works:
    - Creates a blank image that fits any rotation of the image. To achieve
      this, set the height and width to be the image's diagonal.
    - Copy the original image to the center of this blank image
    - Rotate using warpAffine, using the newly created image's center
      (the enlarged blank image center)
    - Translate the four corners of the source image in the enlarged image
      using homogenous multiplication of the rotation matrix.
    - Crop the image according to these transformed corners
    '''

    diagonal = int(math.ceil(math.sqrt(pow(image.shape[0], 2) + pow(image.shape[1], 2))))
    offset_x = (diagonal - image.shape[0])/2
    offset_y = (diagonal - image.shape[1])/2
    dst_image = np.zeros((diagonal, diagonal, 3), dtype='uint8')
    image_center = (float(diagonal-1)/2, float(diagonal-1)/2)

    R = cv2.getRotationMatrix2D(image_center, -angle, 1.0)
    dst_image[offset_x:(offset_x + image.shape[0]), offset_y:(offset_y + image.shape[1]), :] = image
    dst_image = cv2.warpAffine(dst_image, R, (diagonal, diagonal), flags=cv2.INTER_LINEAR)

    # Calculate the rotated bounding rect
    x0 = offset_x
    x1 = offset_x + image.shape[0]
    x2 = offset_x + image.shape[0]
    x3 = offset_x

    y0 = offset_y
    y1 = offset_y
    y2 = offset_y + image.shape[1]
    y3 = offset_y + image.shape[1]

    corners = np.zeros((3,4))
    corners[0,0] = x0
    corners[0,1] = x1
    corners[0,2] = x2
    corners[0,3] = x3
    corners[1,0] = y0
    corners[1,1] = y1
    corners[1,2] = y2
    corners[1,3] = y3
    corners[2:] = 1

    c = np.dot(R, corners)

    x = int(round(c[0,0]))
    y = int(round(c[1,0]))
    left = x
    right = x
    up = y
    down = y

    for i in range(4):
        x = c[0,i]
        y = c[1,i]
        if (x < left): left = x
        if (x > right): right = x
        if (y < up): up = y
        if (y > down): down = y
    h = int(round(down - up))
    w = int(round(right - left))
    left = int(round(left))
    up = int(round(up))

    cropped = np.zeros((w, h, 3), dtype='uint8')
    cropped[:, :, :] = dst_image[left:(left+w), up:(up+h), :]
    return cropped

Answer 9

@robula 和 @remi-cuingnet 的 Go 版本（使用 gocv）

func rotateImage(mat *gocv.Mat, angle float64) *gocv.Mat {
        height := mat.Rows()
        width := mat.Cols()

        imgCenter := image.Point{X: width/2, Y: height/2}

        rotationMat := gocv.GetRotationMatrix2D(imgCenter, -angle, 1.0)

        absCos := math.Abs(rotationMat.GetDoubleAt(0, 0))
        absSin := math.Abs(rotationMat.GetDoubleAt(0, 1))

        boundW := float64(height) * absSin + float64(width) * absCos
        boundH := float64(height) * absCos + float64(width) * absSin

        rotationMat.SetDoubleAt(0, 2, rotationMat.GetDoubleAt(0, 2) + (boundW / 2) - float64(imgCenter.X))
        rotationMat.SetDoubleAt(1, 2, rotationMat.GetDoubleAt(1, 2) + (boundH / 2) - float64(imgCenter.Y))

        gocv.WarpAffine(*mat, mat, rotationMat, image.Point{ X: int(boundW), Y: int(boundH) })

        return mat
}

我在內存中的同一個矩陣中旋轉，如果你不想改變它，請制作一個新矩陣

Answer 10

如果您有圖像的旋轉和縮放：

#include "opencv2/opencv.hpp"
#include <functional>
#include <vector>

bool compareCoords(cv::Point2f p1, cv::Point2f p2, char coord)
{
    assert(coord == 'x' || coord == 'y');

    if (coord == 'x')
        return p1.x < p2.x;

    return p1.y < p2.y;
}


int main(int argc, char** argv)
{

    cv::Mat image = cv::imread("../lenna.png");

    cv::Mat warpedImage;
    float angle = 45.0;  // degrees
    float scale = 0.5;
    cv::Mat_<float> rot_mat = cv::getRotationMatrix2D( cv::Point2f( 0.0f, 0.0f ), angle, scale );
    
    // Image corners
    cv::Point2f pA = cv::Point2f(0.0f, 0.0f);
    cv::Point2f pB = cv::Point2f(image.cols, 0.0f);
    cv::Point2f pC = cv::Point2f(image.cols, image.rows);
    cv::Point2f pD = cv::Point2f(0.0f, image.rows);

    std::vector<cv::Point2f> pts = { pA, pB, pC, pD };
    std::vector<cv::Point2f> ptsTransf;
    cv::transform(pts, ptsTransf, rot_mat );

    using namespace std::placeholders;
    float minX = std::min_element(ptsTransf.begin(), ptsTransf.end(), std::bind(compareCoords, _1, _2, 'x'))->x;
    float maxX = std::max_element(ptsTransf.begin(), ptsTransf.end(), std::bind(compareCoords, _1, _2, 'x'))->x;
    float minY = std::min_element(ptsTransf.begin(), ptsTransf.end(), std::bind(compareCoords, _1, _2, 'y'))->y;
    float maxY = std::max_element(ptsTransf.begin(), ptsTransf.end(), std::bind(compareCoords, _1, _2, 'y'))->y;

    int newW = maxX - minX;
    int newH = maxY - minY;

    cv::Mat_<float> trans_mat = (cv::Mat_<float>(2,3) << 0, 0, -minX, 0, 0, -minY);
    cv::Mat_<float> M = rot_mat + trans_mat;
    cv::warpAffine( image, warpedImage, M, cv::Size(newW, newH) );

    cv::imshow("lena", image);
    cv::imshow("Warped lena", warpedImage);

    cv::waitKey();
    cv::destroyAllWindows();
    return 0;
}

Answer 11

如果只是旋轉 90 度，也許這段代碼會有用。

    Mat img = imread("images.jpg");
    Mat rt(img.rows, img.rows, CV_8U);
    Point2f pc(img.cols / 2.0, img.rows / 2.0);
    Mat r = getRotationMatrix2D(pc, 90, 1);
    warpAffine(img, rt, r, rt.size());
    imshow("rotated", rt);

希望它有用。

Answer 12

順便說一句，僅對於 90º 旋轉，這里有一個更高效 + 准確的函數：

def rotate_image_90(image, angle):
    angle = -angle
    rotated_image = image
    if angle == 0:
        pass
    elif angle == 90:
        rotated_image = np.rot90(rotated_image)
    elif angle == 180 or angle == -180:
        rotated_image = np.rot90(rotated_image)
        rotated_image = np.rot90(rotated_image)
    elif angle == -90:
        rotated_image = np.rot90(rotated_image)
        rotated_image = np.rot90(rotated_image)
        rotated_image = np.rot90(rotated_image)
    return rotated_image