OpenCV minimum upright bounding rect of a RotatedRect

Question

I'm trying to determin minimum bouding rect of a rotated rectangle. I tried a couple of samples like this from RotatedRect reference or from this tutorial about ellipses and bounding boxes. Nothing with satisfactory results. On the image bellow, yellow rectangle is the desired result.

Example data for my test:

Image:
    Width: 1500
    Height: 843

RotatedRect:
    Center:
        X: 783.490417
        Y: 433.673492
    Size:
        Width: 810.946899
        Height: 841.796997
    Angle: 95.4092407

Sample code:

cv::RotatedRect r(cv::Point2f(783.490417, 433.673492), 
    cv::Size2f(810.946899, 841.796997), 
    95.4092407);

cv::Mat img = Mat::zeros(843, 1500, CV_8UC3);

cv::Rect rect  = r.boundingRect();
cv::ellipse(img, r, cv::Scalar(0, 0, 255)); // RED

Point2f vertices[4];
r.points(vertices);

for (int i = 0; i < 4; i++)
    line(img, vertices[i], vertices[(i + 1) % 4], Scalar(0, 255, 0)); // GREEN

rectangle(img, rect, Scalar(255, 0, 0)); // BLUE
cv::imshow("Result", img);

• RED - RotatedRect for which min bouding rect is calculated
• BLUE - r.boundingRect()
• GREEN - r.points()
• YELLOW - desired result

Answer 1

i think here you can find a function doing your desired result.

#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"


using namespace cv;

int main( int argc, char**)
{
    RotatedRect r ;
    r.center =  cv::Point2f(783.490417, 433.673492);
    r.angle = 95.4092407;
    r.size = cv::Size2f(810.946899, 841.796997);

    cv::Mat img = Mat::zeros(843, 1500, CV_8UC3);

    cv::Rect rect  = r.boundingRect();
    cv::ellipse(img, r, cv::Scalar(0, 0, 255)); // RED

    Point2f vertices[4];
    r.points(vertices);

    for (int i = 0; i < 4; i++)
        line(img, vertices[i], vertices[(i + 1) % 4], Scalar(0, 255, 0)); // GREEN

    rectangle(img, rect, Scalar(255, 0, 0)); // BLUE


    float degree = r.angle*3.1415/180;
    float majorAxe = r.size.width/2;
    float minorAxe = r.size.height/2;
    float x = r.center.x;
    float y = r.center.y;
    float c_degree = cos(degree);
    float s_degree = sin(degree);
    float t1 = atan(-(majorAxe*s_degree)/(minorAxe*c_degree));
    float c_t1 = cos(t1);
    float s_t1 = sin(t1);
    float w1 = majorAxe*c_t1*c_degree;
    float w2 = minorAxe*s_t1*s_degree;
    float maxX = x + w1-w2;
    float minX = x - w1+w2;

    t1 = atan((minorAxe*c_degree)/(majorAxe*s_degree));
    c_t1 = cos(t1);
    s_t1 = sin(t1);
    w1 = minorAxe*s_t1*c_degree;
    w2 = majorAxe*c_t1*s_degree;
    float maxY = y + w1+w2;
    float minY = y - w1-w2;
    if (minY > maxY)
    {
        float temp = minY;
        minY = maxY;
        maxY = temp;
    }
    if (minX > maxX)
    {
        float temp = minX;
        minX = maxX;
        maxX = temp;
    }
    Rect yellowrect(minX,minY,maxX-minX+1,maxY-minY+1);

    rectangle(img, yellowrect, Scalar(0, 255, 255)); // YELLOW
    cv::imshow("Result", img);
    waitKey();
}