BGR -> YCbCr conversion not working correctly - c++

Question

I am trying to manually convert an image from RBG (BGR in OpenCV) to the YCbCr color space.
My image is a png color image, 800 width and 600 height, 3 channels, 16 bit depth.
Here's how I tried solving this.
cv::Mat convertToYCbCr(cv::Mat image) {
// converts an RGB image to YCbCr
// cv::Mat: B-G-R
std::cout << "Converting image to YCbCr color space." << std::endl;
int i, j;
for (i = 0; i <= image.cols; i++) {
for (j = 0; j <= image.rows; j++) {
// R, G, B values
auto R = image.at<cv::Vec3d>(j, i)[2];
auto G = image.at<cv::Vec3d>(j, i)[1];
auto B = image.at<cv::Vec3d>(j, i)[0];
// Y'
auto Y = image.at<cv::Vec3d>(j,i)[0] = 0.299 * R + 0.587 * G + 0.114 * B + 16;
// Cb
auto Cb = image.at<cv::Vec3d>(j,i)[1] = 128 + (-0.169 * R -0.331 * G + 0.5 * B);
// Cr
auto Cr = image.at<cv::Vec3d>(j,i)[2] = 128 + (0.5 * R -0.419 * G -0.081 * B);
std::cout << "At conversion: Y = " << Y << ", Cb = " << Cb << ", "
<< Cr << std::endl;
}
}
std::cout << "Converting finished." << std::endl;
return image;
}
The image I receive looks like this:
What I am expecting is this (using OpenCV method):
The vertical lines hint maybe at something? Is my loop wrong? Can I even just "replace" the RGB values with YCbCr values and expect the image to look like the example? typeid() returns the same value for both images, N2cv3MatE.

Answer 1

The primary reason for incorrect results being observed is the incorrect data-type used to access the image. The correct type for accessing 16 bit unsigned pixels is cv::Vec3w (not cv::Vec3d).
The next issue is that the coefficients that are being using for conversion are designed for analog signals ( YPbPr ). For digital images, we have to use coefficients designed for digital images ( YCbCr ). You can find more details on the Wikipedia article on YCbCr in section ITU-R BT.601 conversion.
The piece of information missing from the article is that how will the coefficients change if the images are of 16 bit unsigned depth or 32 bit floating point depth? The answer to this is that we will have to scale the coefficients according to the bit depth of our image.
For images with 16 bit unsigned depth, the scaling should be performed as follows:
auto Y = (R * 65.481f * scale) + (G * 128.553f * scale) + (B * 24.966f * scale) + (16.0f * offset);
auto Cb = (R * -37.797f * scale) + (G * -74.203f * scale) + (B * 112.0f * scale) + (128.0f * offset);
auto Cr = (R * 112.0f * scale) + (G * -93.786f * scale) + (B * -18.214f * scale) + (128.0f * offset);
where scale is equal to 257.0/65535.0 and offset is equal to 257.0.
This conversion technique has been adopted from MATLAB source code for rgb2ycbcr function which references the following book describing the scaling:
C.A. Poynton, "A Technical Introduction to Digital Video", John Wiley
& Sons, Inc., 1996, Chapter 9, Page 175`
Now that the conversion has been done, the third issue we face is the visualization of image similar to that of OpenCV. When we perform color conversion with OpenCV, the output image is stored in the order YCrCb instead of the usual YCbCr. So to get the same image with our custom conversion logic, we have to store values in the relevant order.
A sample conversion code may look like this:
if(image.type() == CV_16UC3)
{
const float scale = 257.0f / 65535.0f;
const float offset = 257.0f;
for (int i = 0; i < image.cols; i++)
{
for (int j = 0; j < image.rows; j++)
{
auto R = image.at<cv::Vec3w>(j, i)[2];
auto G = image.at<cv::Vec3w>(j, i)[1];
auto B = image.at<cv::Vec3w>(j, i)[0];
auto Y = (R * 65.481f * scale) + (G * 128.553f * scale) + (B * 24.966f * scale) + (16.0f * offset);
auto Cb = (R * -37.797f * scale) + (G * -74.203f * scale) + (B * 112.0f * scale) + (128.0f * offset);
auto Cr = (R * 112.0f * scale) + (G * -93.786f * scale) + (B * -18.214f * scale) + (128.0f * offset);
image.at<cv::Vec3w>(j, i)[0] = (unsigned short)Y;
image.at<cv::Vec3w>(j, i)[1] = (unsigned short)Cr;
image.at<cv::Vec3w>(j, i)[2] = (unsigned short)Cb;
}
}
}

Answer 2

You should use cv::cvtColor
cvtColor(src, target_image, cv::COLOR_RGB2YCrCb);
Then just flip the second and third channels.
Though you could be getting that error because you're not casting the resulting values to ints.