How does one convert 16-bit RGB565 to 24-bit RGB888?

You want to map each of these from a 5/6 bit space to an 8 bit space.

• 5 bits = 32 values
• 6 bits = 64 values
• 8 bits = 256 values

The code you're using is taking the naive approach that x5 * 256/32 = x8 where 256/32 = 8 and multiplying by 8 is left shift 3 but, as you say, this doesn't necessarily fill the new number space "correctly". 5 to 8 for max value is 31 to 255 and therein lies your clue to the solution.

x8 = 255/31 * x5
x8 = 255/63 * x6

where x5, x6 and x8 are 5, 6 and 8 bit values respectively.

Now there is a question about the best way to implement this. It does involve division and with integer division you will lose any remainder result (round down basically) so the best solution is probably to do floating point arithmetic and then round half up back to an integer.

This can be sped up considerably by simply using this formula to generate a lookup table for each of the 5 and 6 bit conversions.

My few cents:

If you care about precise mapping, yet fast algorithm you can consider this:

R8 = ( R5 * 527 + 23 ) >> 6;
G8 = ( G6 * 259 + 33 ) >> 6;
B8 = ( B5 * 527 + 23 ) >> 6;

It uses only: MUL, ADD and SHR -> so it is pretty fast! From the other side it is compatible in 100% to floating point mapping with proper rounding:

// R8 = (int) floor( R5 * 255.0 / 31.0 + 0.5);
// G8 = (int) floor( G6 * 255.0 / 63.0 + 0.5);
// B8 = (int) floor( R5 * 255.0 / 31.0 + 0.5);

Some extra cents: If you are interested in 888 to 565 conversion, this works very well too:

R5 = ( R8 * 249 + 1014 ) >> 11;
G6 = ( G8 * 253 +  505 ) >> 10;
B5 = ( B8 * 249 + 1014 ) >> 11;

Constants were found using brute force search with somę early rejections to speed thing up a bit.

You could shift and then or with the most significant bits; i.e.

Red 10101 becomes 10101000 | 101 => 10101101
    12345         12345---   123    12345123

This has the property you seek, but it's not the most linear mapping of values from one space to the other. It's fast, though. :)

Cletus' answer is more complete and probably better. :)

iOS vImage Conversion

The iOS Accelerate Framework documents the following algorithm for the vImageConvert_RGB565toARGB8888 function:

Pixel8 alpha = alpha
Pixel8 red   = (5bitRedChannel   * 255 + 15) / 31
Pixel8 green = (6bitGreenChannel * 255 + 31) / 63
Pixel8 blue  = (5bitBlueChannel  * 255 + 15) / 31

For a one-off conversion this will be fast enough, but if you want to process many frames you want to use something like the iOS vImage conversion or implement this yourself using NEON intrinsics.

From ARMs Community Forum Tutorial

First, we will look at converting RGB565 to RGB888. We assume there are eight 16-bit pixels in register q0, and we would like to separate reds, greens and blues into 8-bit elements across three registers d2 to d4.

 vshr.u8      q1, q0, #3      @ shift red elements right by three bits,
                                @  discarding the green bits at the bottom of
                                @  the red 8-bit elements.
vshrn.i16    d2, q1, #5      @ shift red elements right and narrow,
                                @  discarding the blue and green bits.
vshrn.i16    d3, q0, #5      @ shift green elements right and narrow,
                                @  discarding the blue bits and some red bits
                                @  due to narrowing.
vshl.i8      d3, d3, #2      @ shift green elements left, discarding the
                                @  remaining red bits, and placing green bits
                                @  in the correct place.
vshl.i16  q0, q0, #3      @ shift blue elements left to most-significant
                                @  bits of 8-bit color channel.
vmovn.i16    d4, q0          @ remove remaining red and green bits by
                                @  narrowing to 8 bits.

The effects of each instruction are described in the comments above, but in summary, the operation performed on each channel is: Remove color data for adjacent channels using shifts to push the bits off either end of the element. Use a second shift to position the color data in the most-significant bits of each element, and narrow to reduce element size from 16 to eight bits.

Note the use of element sizes in this sequence to address 8 and 16 bit elements, in order to achieve some of the masking operations.

A small problem

You may notice that, if you use the code above to convert to RGB888 format, your whites aren't quite white. This is because, for each channel, the lowest two or three bits are zero, rather than one; a white represented in RGB565 as (0x1F, 0x3F, 0x1F) becomes (0xF8, 0xFC, 0xF8) in RGB888. This can be fixed using shift with insert to place some of the most-significant bits into the lower bits.

For an Android specific example I found a YUV-to-RGB conversion written in intrinsics.