A few notes and thoughts about compressing images to 140 characters for use on Twitter.

The first I read about this "competition" was ​here.

Discussion

Bit availability

Twitter allows for 140 characters in a message. UTF-8 is allowed.

UTF-8 is restricted to the formal Unicode definition by RFC 3629. It means that the only legal UTF-8 characters range from U+0000 to U+10FFFF. The following restrictions must also be added:

• The 2¹¹ high and low surrogates, used for UTF-16 encoding, restricting the Unicode range to U+0000..U+D7FF and U+E000..U+10FFFF.
• The 66 non-characters.

The final size of this set is:

The number of bits that can be encoded using 140 such characters is computed as follows:

In theory, 2811 bits is therefore the maximum we can stuff into a Twitter message. However, a lot of these characters are undefined, not yet allocated or are control characters. As of Unicode 5.1 there are 100507 graphic characters, reducing the number of expressed bits to:

We'll go on with this value of 2326 encodable bits.

Bit allocation

A compressed image usually contains the following information:

• The image geometry information (width and height)
• Optional colour information (palette)
• Elementary picture elements (encoded as pixels, triangles, vectors...)

Given the amount of compression we are doing, there is little point in compressing images larger than 512×512. This reduces image geometry information to 18 bits, leaving us with 2308 bits to encode the image information.

Whether to use a palette or to encode colour information into the picture elements is undecided yet. We'll cover both options.

Strategy 1: colour information in picture elements

Each picture element will hold data for:

• coordinates
• colour information
• additional control information

Coordinates could be absolute (therefore requiring 16 or 14 bits, maybe 12) or relative. I would favour a coordinate system relative to predefined image cells because there is a good chance that each cell will hold a point. Assuming at least 8 horizontal and vertical subdivisions, 6 bits can be gained this way. The final coordinate bit allocation is now 10, 8 or 6. We'll pick 8 to be safe for now: 16 X values and 16 Y values.

Using 7 bits per colour allows for the following options:

• full bit range usage: 4 red values, 8 green values, 4 blue values
• almost full bit range usage: 5 red values, 5 green values, 5 blue values

Finally, a weight value could be added, using a final bit.

The proposed allocation is then 16, allowing 144 points to be stored in the following configurations:

• 12×12
• 10×14 (wasting 4 point slots)
• 9×16
• 8×18
• 7×20 (wasting 4 point slots)
• 6×24

Strategy 2: colour information in a separate palette

To do.

Image reconstruction

Image reconstruction is an interpolation problem on a Delaunay triangulation. We use the natural neighbour coordinates to interpolate between nodes and obtain a first-order smooth image.

Results

Here are the results of img2twit using 140 characters, restricted to U+4e00..U+9fa5 (CJK Unified Ideographs):