Overall

This is a project to create a character set which is most easily distinguishable at various scales.

Smallest-resolution characters

In min_res is the code to generate shift- and scale-invariant "characters" of 3 x 3 binary pixels.

I constrain the full characters to be coarse-grained to these fundamental characters, so that the characters are distinguishable at the smallest possible scale.

Scaling to greater resolutions

In upscale is the in-progress code to generate highly distinct character shapes which are appropriately rasterized to their minimum-resolution versions. I use a pretrained vision model, dinov2, to embed the candidate characters, and then optimize such that:

• The embeddings are far away from each other: minimize the "energy" of the set of characters ${c_i}$, $\sum_{i < j} |\text{embed}(c_i) - \text{embed}(c_j)|^{-1}$;
• The coarse-grained images have the same pattern of light and dark as the originals;
• The images are somewhat continuous: minimize the absolute differences in adjacent pixels $\sum_i \left(\sum_{x=1}^X \sum_{y=2}^Y |(c_i){x,y} - (c_i){x,y-1}| + \sum_{x=2}^X \sum_{y=1}^Y |(c_i){x,y} - (c_i){x-1,y}|\right)$; and
• The images are sharp (lacking in intermediate pixel values): minimize the sum over all pixels of $p(1-p)$

Results and plans

Here are the results of training according to this scheme:

These figures are reasonably visually distinct, but they are less figural than existing character sets. I'm considering optimizing the parameters of a set of Bézier curves directly in order to get a result that looks more like a standard character set.

Development

The upscale project uses uv for dependency management. After installing uv, run:

cd upscale
uv sync
uv run python src/tests.py