How to alpha blend with transparency masks

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I have figured out how to do alpha blend with transparency masks, but as with most things OpenCV, I suspect I'm not doing it as efficiently as could be.

I know how to copy an image with a mask onto another using cv::Mat::copyTo(). But when I do that, the 2nd image is copied 100% onto the destination. What I want is to copy it at 30% or some other value, like in the 3rd "blended" window in this example:

Note how the text "starry night blend test" is partially see-through in that final blended image?

The only way I could figure out how to do that is like this:

// compile with:  g++ test.cpp $(pkg-config --libs opencv)
#include <opencv2/opencv.hpp>

int main()
{
    const auto fontface         = cv::FONT_HERSHEY_PLAIN;
    const auto fontscale        = 3.0;
    const auto fontthickness    = 3;

    const std::string text("starry night blend test");
    const cv::Scalar purple(255, 0, 255);
    const cv::Scalar white(255, 255, 255);

    cv::Mat background  = cv::imread("starrynight.jpg");

    // Create the layers on which we'll write the text.  Layers start out as
    // pure black.
    cv::Mat font_layer  = cv::Mat::zeros(background.size(), CV_8UC3);
    cv::Mat mask_layer  = cv::Mat::zeros(background.size(), CV_8UC1); // <- note the mask is 1 channel

    // Write the text in colour on the "font" layer.  In my actual application
    // there are many layers, and it is more complicated than just a line of
    // text.
    const cv::Point p(20, 100);
    cv::putText(font_layer, text, p, fontface, fontscale, purple, fontthickness, cv::LINE_8);

    // I also have a mask of the "font" layer.  In this example, the easiest
    // way to produce that mask is to write out the same text, with the exact
    // same options, but onto the single channel mat.
    cv::putText(mask_layer, text, p, fontface, fontscale, white, fontthickness, cv::LINE_8);

    // The function copyTo() has an optional "mask" parameter which we can use
    // to copy parts of an image onto another.  In this case, we copy the text
    // onto a clone of the image.
    cv::Mat tmp = background.clone();
    font_layer.copyTo(tmp, mask_layer);

    // This is the cool part of the code.  We do an alpha blend between the
    // two mats.  One of which is just the background, and the other is the
    // background with bright purple text.  When blended, it will appear as
    // if the text layer is semi-transparent.  0.3 == 30%
    const double alpha = 0.3;
    const double beta = 1.0 - alpha;
    cv::Mat blended;
    cv::addWeighted(tmp, alpha, background, beta, 0, blended);

    cv::imshow("tmp"        , tmp       );
    cv::imshow("blended"    , blended   );
    cv::imshow("background" , background);
    cv::waitKey(0);

    return 0;
}

The thing I don't like about this solution is the multiple copies:

1. First I copy the entire background image into "tmp"
2. Then I copy the font layer onto tmp using the mask
3. Then I "copy" again when I call into cv::addWeighted().

Is this the way I should be doing this, or is there a better solution?