gaussian_transport_map — COLORTRANSPORT `matching` op

• Data kinds: points × points → matrix

• Call: import colortransport; colortransport.gaussian_transport_map(src_samples, ref_samples) (or opscolortransport.get("gaussian_transport_map"))

Usage

The Monge map `(A, b)` when two point sets are taken to be normal distributions.

> The detailed description below is the original text — the summary and the headings are translated.

`x -> A (x - m1) + m2 で、A` は

`S1^-1/2 (S1^1/2 S2 S1^1/2)^1/2 S1^-1/2`(Bures 幾何の閉じた形)。

共分散ごと運ぶので、チャネル間の相関が保たれる。

退化(片方の共分散が特異)では逆平方根が作れない ―― 疑似逆で誤魔化すと

「運べていないのに運んだ顔をした」写像になるので `ValueError`。

Background guides (the physics and conventions behind this op)

• colorimetry — 測色と分光の知識 — 色は「分光 × 光源 × 観測者」でしか決まらない

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• color_transport — py -3.11 examples/color_transport.py

Ops the type connects to (they accept `matrix` as input)

sinkhorn · sinkhorn_distance · sinkhorn_divergence · transport_cost

Same category (`matching`)

histogram_match · color_transfer

*Provenance: colortransport.py — COLORTRANSPORT operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

gaussian_transport_map — COLORTRANSPORT matching op