How to get the calculate the RGB values of a pixel from the luminance?

Question

I want to compute the RGB values from the luminance.

The data that I know are :

• the new luminance (the value that I want to apply)
• the old luminance
• the old RGB values.

We can compute the luminance from the RGB values like this :
uint8_t luminance = R * 0.21 + G * 0.71 + B * 0.07;

My code is :

// We create a function to set the luminance of a pixel
void jpegImage::setLuminance(uint8_t newLuminance, unsigned int x, unsigned int y) {

  // If the X or Y value is out of range, we throw an error
  if(x >= width) {
    throw std::runtime_error("Error : in jpegImage::setLuminance : The X value is out of range");
  }
  else if(y >= height) {
    throw std::runtime_error("Error : in jpegImage::setLuminance : The Y value is out of range");
  }

  // If the image is monochrome
  if(pixelSize == 1) {

    // We set the pixel value to the luminance
    pixels[y][x] = newLuminance;
  }

  // Else if the image is colored, we throw an error
  else if(pixelSize == 3) {
    // I don't know how to proceed
    // My image is stored in a std::vector<std::vector<uint8_t>> pixels;

    // This is a list that contain the lines of the image
    // Each line contains the RGB values of the following pixels
    // For example an image with 2 columns and 3 lines
    // [[R, G, B, R, G, B], [R, G, B, R, G, B], [R, G, B, R, G, B]]

    // For example, the R value with x = 23, y = 12 is:
    // pixels[12][23 * pixelSize];
    // For example, the B value with x = 23, y = 12 is:
    // pixels[12][23 * pixelSize + 2];
    // (If the image is colored, the pixelSize will be 3 (R, G and B)
    // (If the image is monochrome the pixelSIze will be 1 (just the luminance value)
  }
}

How can I proceed ? Thanks !

Answer 1

You don't need the old luminance if you have the original RGB.

Referencing https://www.fourcc.org/fccyvrgb.php for YUV to RGB conversion.

Compute U and V from original RGB:

```
V =  (0.439 * R) - (0.368 * G) - (0.071 * B) + 128
U = -(0.148 * R) - (0.291 * G) + (0.439 * B) + 128
```

Y is the new luminance normalized to a value between 0 and 255

Then just convert back to RGB:

B = 1.164(Y - 16)                   + 2.018(U - 128)
G = 1.164(Y - 16) - 0.813(V - 128) - 0.391(U - 128)
R = 1.164(Y - 16) + 1.596(V - 128)

Make sure you clamp your computed values of each equation to be in range of 0..255. Some of these formulas can convert a YUV or RGB value to something less than 0 or higher than 255.

There's also multiple formula for converting between YUV and RGB. (Different constants). I noticed the page listed above has a different computation for Y than you cited. They are all relatively close with different precisions and adjustments. For just changing the brightness of a pixel, almost any formula will do.

Updated

I originally deleted this answer after the OP suggested it wasn't working for him. I was too busy for the last few days to investigate, but I wrote some sample code to confirm my hypothesis. At the bottom of this answer is a snippet of GDI+ based code increases the luminance of an image by a variable amount. Along with the code is an image that I tested this out on and two conversions. One at 130% brightness. Another at 170% brightness.

Here's a sample conversion

Original Image

Updated Image (at 130% Y)

Updated Image (at 170% Y)

Source:

#define CLAMP(val) {val = (val > 255) ? 255 : ((val < 0) ? 0 : val);}

void Brighten(Gdiplus::BitmapData& dataIn, Gdiplus::BitmapData& dataOut, const double YMultiplier=1.3)
{
    if ( ((dataIn.PixelFormat != PixelFormat24bppRGB) && (dataIn.PixelFormat != PixelFormat32bppARGB)) ||
         ((dataOut.PixelFormat != PixelFormat24bppRGB) && (dataOut.PixelFormat != PixelFormat32bppARGB)))
    {
        return;
    }

    if ((dataIn.Width != dataOut.Width) || (dataIn.Height != dataOut.Height))
    {
        // images sizes aren't the same
        return;
    }


    const size_t incrementIn = dataIn.PixelFormat == PixelFormat24bppRGB ? 3 : 4;
    const size_t incrementOut = dataOut.PixelFormat == PixelFormat24bppRGB ? 3 : 4;
    const size_t width = dataIn.Width;
    const size_t height = dataIn.Height;


    for (size_t y = 0; y < height; y++)
    {
        auto ptrRowIn = (BYTE*)(dataIn.Scan0) + (y * dataIn.Stride);
        auto ptrRowOut = (BYTE*)(dataOut.Scan0) + (y * dataOut.Stride);

        for (size_t x = 0; x < width; x++)
        {
            uint8_t B = ptrRowIn[0];
            uint8_t G = ptrRowIn[1];
            uint8_t R = ptrRowIn[2];
            uint8_t A = (incrementIn == 3) ? 0xFF : ptrRowIn[3];

            auto Y = (0.257 * R) + (0.504 * G) + (0.098 * B) + 16;
            auto V = (0.439 * R) - (0.368 * G) - (0.071 * B) + 128;
            auto U = -(0.148 * R) - (0.291 * G) + (0.439 * B) + 128;

            Y *= YMultiplier;

            auto newB = 1.164*(Y - 16) + 2.018*(U - 128);
            auto newG = 1.164*(Y - 16) - 0.813*(V - 128) - 0.391*(U - 128);
            auto newR = 1.164*(Y - 16) + 1.596*(V - 128);

            CLAMP(newR);
            CLAMP(newG);
            CLAMP(newB);

            ptrRowOut[0] = newB;
            ptrRowOut[1] = newG;
            ptrRowOut[2] = newR;
            if (incrementOut == 4)
            {
                ptrRowOut[3] = A; // keep original alpha
            }

            ptrRowIn += incrementIn;
            ptrRowOut += incrementOut;
        }
    }
}