Indexed export (GIF, PNG-8, BMP, TIFF) finds each pixel's nearest
palette entry with a linear scan, and the k-means refinement in median
cut does the same once per cell per pass. With the 256-entry palettes
this code produces, that is 256 distance evaluations per query.
PaletteIndex is an exact nearest-neighbour kd-tree over the palette,
balanced at the widest weighted axis, with tight channel bounds in every
subtree so branch-and-bound can skip whole boxes. Small palettes (12 or
fewer entries) keep the scan, which is cheaper than tree traversal.
Results match the linear scan exactly, including ties: an equal-distance
entry with a smaller index still wins. The bound uses the same weighted
squared f32 form as dist() rather than a transformed space, so rounding
cannot change which entry is chosen.
Three tests: randomized parity against the original scan across palette
sizes spanning the cutoff, three weight vectors, duplicate colours and
fractional query points; explicit tie-breaking cases; and an opt-in
benchmark comparing 100k queries at both, behind -- --ignored.
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