2Tokens in a tree
The tokenizer asks SAM 2.1 hiera-base-plus (int8-quantized from 277
to 69 MB, executed by onnxruntime in WebAssembly) to segment the scene at
64 equally spaced points — and that number has a story. We first
built a learned proposer (a field-trained U-Net suggesting one prompt per
region, the segmenteverygrain pattern of Sylvester et al.), then ran the
control: a plain grid of dots, no learning at all. Against hand-labelled
Landsat the dots won — 28/34 labelled circles against the U-Net's
22/34, with half the tokens — so the dots shipped, and the U-Net is
reported in the repository as a falsified hypothesis. OpenCV traces every mask
into a polygon (Suzuki–Abe findContours,
Ramer–Douglas–Peucker approxPolyDP); near-duplicates
are rejected; a second half-stride grid round covers what the first missed;
and whatever remains becomes classical tokens, so no pixel is left
unowned. Quantization is nearly free: int8 masks are essentially identical
to full precision on both validation sites. The decoder you are running was
then fine-tuned on our own archive: 65k point→mask pairs from 38
Landsat spot-histories (1985–2025), where each target is the
track’s multi-decade consensus boundary rather than one noisy
pass. On the same hand-labelled harness it lifts recall from 28/34 to
31/34 circles, trading looser coverage (the classical remainder
partition absorbs it) for tighter, object-scale masks — so expect more,
smaller tokens. The model downloads once, on your first press of the button.
The traced regions are nested by area into a laminar tree: any two regions are
either disjoint or one contains the other. Laminarity is not a stylistic choice. It
is the condition under which the statistics of a region are well defined at all. The
worst bug of this project was two boundary-sharing regions slipping in as siblings,
which silently zeroed every statistic beneath them; one containment test, applied on
points pulled slightly toward the interior, fixed it.
Because the scene is a tree, each token's position in it can be written down once
and kept forever: a 64-bit address, eight bits per level, encoding the path from the
root. Containment then needs no geometry. Token B is inside token A exactly when
(addr(B) ≫ 8·Δd) ⊕ addr(A) = 0, one shift and one XOR. On the test
scene this agrees with the polygon geometry on all 1,369 ordered pairs. The tree is
also small: a 37-shape scene flattens to 74 tokens in 865 bytes, and a full landscape
hierarchy ships in 120 to 250 KB at 0.95 to 0.97 IoU, roughly 2,000 times smaller
than its dense masks.
Figure 2: the tokenizer running in this tab. Each traced outline is one token. When the run finishes, scroll to section 3 and click a shape.
THE CODE: core/laminar.py (the laminar tree built above)
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