具有指定角度的 OpenCV RotatedRect

I have the situation that I have a small binary image that has one shape, around which I want to find the best fitting rotated rectangle (not bounding rectangle). I know that there is cv::minAreaRect() that you apply on the result found by cv::findContours(), but this has delivered poor results in my case, because the data is noisy (coming from MS Kinect, see example picture where rotation changes due to the input data (contour) being slightly different). What I did instead was to calculate the principal axis using PCA on my binary image (which is less sensitive to noise), which yields angle "a", and now I want to create a RotatedRect around my shape, given the angle of the principal axis, a).

I have an illustration, made with my superb Paint skills!

那么我的问题是：你们有代码片段或具体建议来解决这个问题吗？恐怕我必须进行多次布雷森汉姆迭代，希望有一个聪明的方法。

顺便说一句，对于那些不太熟悉 openCV 的 RotatedRect 数据结构的人来说：它是由高度、宽度、角度和中心点定义的，假设中心点实际上位于矩形的中心。

Cheers!

好的，我的解决方案： 方法：

1. PCA，给出旋转矩形中心的角度和第一近似值
2. 获取二元形状的轮廓，将其旋转到直立位置，获取 X 和 Y 坐标的最小/最大，以获得边界矩形的宽度和高度
3. 从最大 X (Y) 中减去宽度（高度）的一半，即可得到“直立空间”中的中心点

4. 通过逆旋转矩阵将该中心点向后旋转

   cv::RotatedRect Utilities::getBoundingRectPCA( cv::Mat& binaryImg ) {
   cv::RotatedRect result;
   
   //1. convert to matrix that contains point coordinates as column vectors
   int count = cv::countNonZero(binaryImg);
   if (count == 0) {
       std::cout << "Utilities::getBoundingRectPCA() encountered 0 pixels in binary image!" << std::endl;
       return cv::RotatedRect();
   }
   
   cv::Mat data(2, count, CV_32FC1);
   int dataColumnIndex = 0;
   for (int row = 0; row < binaryImg.rows; row++) {
       for (int col = 0; col < binaryImg.cols; col++) {
           if (binaryImg.at<unsigned char>(row, col) != 0) {
               data.at<float>(0, dataColumnIndex) = (float) col; //x coordinate
               data.at<float>(1, dataColumnIndex) = (float) (binaryImg.rows - row); //y coordinate, such that y axis goes up
               ++dataColumnIndex;
           }
       }
   }
   
   //2. perform PCA
   const int maxComponents = 1;
   cv::PCA pca(data, cv::Mat() /*mean*/, CV_PCA_DATA_AS_COL, maxComponents);
   //result is contained in pca.eigenvectors (as row vectors)
   //std::cout << pca.eigenvectors << std::endl;
   
   //3. get angle of principal axis
   float dx = pca.eigenvectors.at<float>(0, 0);
   float dy = pca.eigenvectors.at<float>(0, 1);
   float angle = atan2f(dy, dx)  / (float)CV_PI*180.0f;
   
   //find the bounding rectangle with the given angle, by rotating the contour around the mean so that it is up-right
   //easily finding the bounding box then
   cv::Point2f center(pca.mean.at<float>(0,0), binaryImg.rows - pca.mean.at<float>(1,0));
   cv::Mat rotationMatrix = cv::getRotationMatrix2D(center, -angle, 1);
   cv::Mat rotationMatrixInverse = cv::getRotationMatrix2D(center, angle, 1);
   
   std::vector<std::vector<cv::Point> > contours;
   cv::findContours(binaryImg, contours, CV_RETR_EXTERNAL, CV_CHAIN_APPROX_SIMPLE);
   if (contours.size() != 1) {
       std::cout << "Warning: found " << contours.size() << " contours in binaryImg (expected one)" << std::endl;
       return result;
   }
   
   //turn vector of points into matrix (with points as column vectors, with a 3rd row full of 1's, i.e. points are converted to extended coords)
   cv::Mat contourMat(3, contours[0].size(), CV_64FC1);
   double* row0 = contourMat.ptr<double>(0);
   double* row1 = contourMat.ptr<double>(1);
   double* row2 = contourMat.ptr<double>(2);
   for (int i = 0; i < (int) contours[0].size(); i++) {
       row0[i] = (double) (contours[0])[i].x;
       row1[i] = (double) (contours[0])[i].y;
       row2[i] = 1;
   }
   
   cv::Mat uprightContour = rotationMatrix*contourMat;
   
   //get min/max in order to determine width and height
   double minX, minY, maxX, maxY;
   cv::minMaxLoc(cv::Mat(uprightContour, cv::Rect(0, 0, contours[0].size(), 1)), &minX, &maxX); //get minimum/maximum of first row
   cv::minMaxLoc(cv::Mat(uprightContour, cv::Rect(0, 1, contours[0].size(), 1)), &minY, &maxY); //get minimum/maximum of second row
   
   int minXi = cvFloor(minX);
   int minYi = cvFloor(minY);
   int maxXi = cvCeil(maxX);
   int maxYi = cvCeil(maxY);
   
   //fill result
   result.angle = angle;
   result.size.width = (float) (maxXi - minXi);
   result.size.height = (float) (maxYi - minYi);
   
   //Find the correct center:
   cv::Mat correctCenterUpright(3, 1, CV_64FC1);
   correctCenterUpright.at<double>(0, 0) = maxX - result.size.width/2;
   correctCenterUpright.at<double>(1,0) = maxY - result.size.height/2;
   correctCenterUpright.at<double>(2,0) = 1;
   cv::Mat correctCenterMat = rotationMatrixInverse*correctCenterUpright;
   cv::Point correctCenter = cv::Point(cvRound(correctCenterMat.at<double>(0,0)), cvRound(correctCenterMat.at<double>(1,0)));
   
   result.center = correctCenter;
   
   return result;
   

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