How to get the real RGBA or ARGB color values without premultiplied alpha? - iphone

Question

I'm creating an bitmap context using CGBitmapContextCreate with the kCGImageAlphaPremultipliedFirst option.
I made a 5 x 5 test image with some major colors (pure red, green, blue, white, black), some mixed colors (i.e. purple) combined with some alpha variations. Every time when the alpha component is not 255, the color value is wrong.
I found that I could re-calculate the color when I do something like:
almostCorrectRed = wrongRed * (255 / alphaValue);
almostCorrectGreen = wrongGreen * (255 / alphaValue);
almostCorrectBlue = wrongBlue * (255 / alphaValue);
But the problem is, that my calculations are sometimes off by 3 or even more. So for example I get a value of 242 instead of 245 for green, and I am 100% sure that it must be exactly 245. Alpha is 128.
Then, for the exact same color just with different alpha opacity in the PNG bitmap, I get alpha = 255 and green = 245 as it should be.
If alpha is 0, then red, green and blue are also 0. Here all data is lost and I can't figure out the color of the pixel.
How can I avoid or undo this alpha premultiplication alltogether so that I can modify pixels in my image based on the true R G B pixel values as they were when the image was created in Photoshop? How can I recover the original values for R, G, B and A?
Background info (probably not necessary for this question):
What I'm doing is this: I take a UIImage, draw it to a bitmap context in order to perform some simple image manipulation algorithms on it, shifting the color of each pixel depending on what color it was before. Nothing really special. But my code needs the real colors. When a pixel is transparent (meaning it has alpha less than 255) my algorithm shouldn't care about this, it should just modify R,G,B as needed while Alpha remains at whatever it is. Sometimes though it will shift alpha up or down too. But I see them as two separate things. Alpha contorls transparency, while R G B control the color.

Answer 1

This is a fundamental problem with premultiplication in an integral type:
245 * (128/255) = 122.98
122.98 truncated to an integer = 122
122 * (255/128) = 243.046875
I'm not sure why you're getting 242 instead of 243, but this problem remains either way, and it gets worse the lower the alpha goes.
The solution is to use floating-point components instead. The Quartz 2D Programming Guide gives the full details of the format you'll need to use.
Important point: You'd need to use floating-point from the creation of the original image (and I don't think it's even possible to save such an image as PNG; you might have to use TIFF). An image that was already premultiplied in an integral type has already lost that precision; there is no getting it back.
The zero-alpha case is the extreme version of this, to such an extent that even floating-point cannot help you. Anything times zero (alpha) is zero, and there is no recovering the original unpremultiplied value from that point.

Answer 2

Pre-multiplying alpha with an integer color type is an information lossy operation. Data is destroyed during the quantization process (rounding to 8 bits).
Since some data is destroy (by rounding), there is no way to recover the exact original pixel color (except for some lucky values). You have to save the colors of your photoshop image before you draw it into a bitmap context, and use that original color data, not the multiplied color data from the bitmap.

Answer 3

I ran into this same problem when trying to read image data, render it to another image with CoreGraphics, and then save the result as non-premultiplied data. The solution I found that worked for me was to save a table that contains the exact mapping that CoreGraphics uses to map non-premultiplied data to premultiplied data. Then, estimate what the original premultipled value would be with a mult and floor() call. Then, if the estimate and the result from the table lookup do not match, just check the value below the estimate and the one above the estimate in the table for the exact match.
// Execute premultiply logic on RGBA components split into componenets.
// For example, a pixel RGB (128, 0, 0) with A = 128
// would return (255, 0, 0) with A = 128
static
inline
uint32_t premultiply_bgra_inline(uint32_t red, uint32_t green, uint32_t blue, uint32_t alpha)
{
const uint8_t* const restrict alphaTable = &extern_alphaTablesPtr[alpha * PREMULT_TABLEMAX];
uint32_t result = (alpha << 24) | (alphaTable[red] << 16) | (alphaTable[green] << 8) | alphaTable[blue];
return result;
}
static inline
int unpremultiply(const uint32_t premultRGBComponent, const float alphaMult, const uint32_t alpha)
{
float multVal = premultRGBComponent * alphaMult;
float floorVal = floor(multVal);
uint32_t unpremultRGBComponent = (uint32_t)floorVal;
assert(unpremultRGBComponent >= 0);
if (unpremultRGBComponent > 255) {
unpremultRGBComponent = 255;
}
// Pass the unpremultiplied estimated value through the
// premultiply table again to verify that the result
// maps back to the same rgb component value that was
// passed in. It is possible that the result of the
// multiplication is smaller or larger than the
// original value, so this will either add or remove
// one int value to the result rgb component to account
// for the error possibility.
uint32_t premultPixel = premultiply_bgra_inline(unpremultRGBComponent, 0, 0, alpha);
uint32_t premultActualRGBComponent = (premultPixel >> 16) & 0xFF;
if (premultRGBComponent != premultActualRGBComponent) {
if ((premultActualRGBComponent < premultRGBComponent) && (unpremultRGBComponent < 255)) {
unpremultRGBComponent += 1;
} else if ((premultActualRGBComponent > premultRGBComponent) && (unpremultRGBComponent > 0)) {
unpremultRGBComponent -= 1;
} else {
// This should never happen
assert(0);
}
}
return unpremultRGBComponent;
}
You can find the complete static table of values at this github link.
Note that this approach will not recover information "lost" when the original unpremultiplied pixel was premultiplied. But, it does return the smallest unpremultiplied pixel that will become the premultiplied pixel once run through the premultiply logic again. This is useful when the graphics subsystem only accepts premultiplied pixels (like CoreGraphics on OSX). If the graphics subsystem only accepts premultipled pixels, then you are better off storing only the premultipled pixels, since less space is consumed as compared to the unpremultiplied pixels.