Calculate OpenCV warpPerspective Map For Reuse (C++)

At work, I was working on an OpenCV project that utilized warpPerspective quite extensively for real-time perspective correction.  It worked great, but it was slow.  When I profiled my solution, warpPerspective was taking ~20% of the CPU on my MacBook Pro.

Now, if you look at the code for warpPerspective, it's essentially doing quite a bit of matrix multiplication for each pixel.  Since I'm assuming that my camera won't change position during a run, that's a lot of wasted effort.

I use the following code to calculate the map that is generated by warpPerspective up front so I can use it in a remap call later to get the same results for less than half the CPU cost.  I store the final map in cv::Mats named transformation_x and transformation_y.

transformationMatrix = cv::getPerspectiveTransform(originalCorners, destinationCorners);

// Since the camera won't be moving, let's pregenerate the remap LUT
cv::Mat inverseTransMatrix;
cv::invert(transformationMatrix, inverseTransMatrix);

// Generate the warp matrix
cv::Mat map_x, map_y, srcTM;
srcTM = inverseTransMatrix.clone(); // If WARP_INVERSE, set srcTM to transformationMatrix

map_x.create(sourceFrame.size(), CV_32FC1);
map_y.create(sourceFrame.size(), CV_32FC1);

double M11, M12, M13, M21, M22, M23, M31, M32, M33;
M11 = srcTM.at<double>(0,0);
M12 = srcTM.at<double>(0,1);
M13 = srcTM.at<double>(0,2);
M21 = srcTM.at<double>(1,0);
M22 = srcTM.at<double>(1,1);
M23 = srcTM.at<double>(1,2);
M31 = srcTM.at<double>(2,0);
M32 = srcTM.at<double>(2,1);
M33 = srcTM.at<double>(2,2);

for (int y = 0; y < sourceFrame.rows; y++) {
  double fy = (double)y;
  for (int x = 0; x < sourceFrame.cols; x++) {
    double fx = (double)x;
    double w = ((M31 * fx) + (M32 * fy) + M33);
    w = w != 0.0f ? 1.f / w : 0.0f;
    float new_x = (float)((M11 * fx) + (M12 * fy) + M13) * w;
    float new_y = (float)((M21 * fx) + (M22 * fy) + M23) * w;
    map_x.at<float>(y,x) = new_x;
    map_y.at<float>(y,x) = new_y;
  }
}

// This creates a fixed-point representation of the mapping resulting in ~4% CPU savings
transformation_x.create(sourceFrame.size(), CV_16SC2);
transformation_y.create(sourceFrame.size(), CV_16UC1);
cv::convertMaps(map_x, map_y, transformation_x, transformation_y, false);

// If the fixed-point representation causes issues, replace it with this code
//transformation_x = map_x.clone();
//transformation_y = map_y.clone();

I then apply the map using a remap call:

cv::remap(sourceImage, destinationImage, transformation_x, transformation_y, CV_INTER_LINEAR); 

Ended up dropping CPU usage for the call down to ~8%.  I'll take it.