One much simpler way you could do that is to check the image pixels and find the minimum/maximum coordinates of non-black pixels.
Something like this:
int maxx,maxy,minx,miny;
maxx=maxy=-std::numeric_limits<int>::max();
minx=miny=std::numeric_limits<int>::min();
for(int y=0; y<img.rows; ++y)
{
for(int x=0; x<img.cols; ++x)
{
const cv::Vec3b &px = img.at<cv::Vec3b>(y,x);
if(px(0)==0 && px(1)==0 && px(2)==0)
continue;
if(x<minx) minx=x;
if(x>maxx) maxx=x;
if(y<miny) miny=y;
if(y>maxy) maxy=y;
}
}
cv::Mat subimg;
img(cv::Rect(cv::Point(minx,miny),cv::Point(maxx,maxy))).copyTo(subimg);
In my opinion, this approach is more reliable since you don't have to detect any contour, which could lead to false detections depending on the input image.