robust op• データ種: matrix × signal → table
• 呼び出し: import fullseye as fs; fs.ledger.residue_crt(residues, periods, weights=None, lo=0.0, hi=None) -> 'dict' (実装を直接呼ぶなら import residue; residue.residue_crt(residues, periods, weights=None, lo=0.0, hi=None) -> 'dict'、台帳から引くなら opsresidue.get("residue_crt"))
実数の周期に対する重み付きの頑健な中国剰余定理 -> dict。
> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。
Solve v ≡ residues[i] (mod periods[i]) for v in [lo, hi). residues has the band axis first, shape (N,) or (N, ...) — every trailing element is solved independently (one pixel, one sample). weights (same shape, or (N,)) say how much each band is trusted — typically the product of the two amplitudes the phase came from, so a band with no contrast gets no vote.
Method: every candidate v = r_ref + k p_ref of the longest period inside the range is scored by phasor agreement sum_i w_i cos(2 pi (v - r_i)/p_i) (the maximum-likelihood criterion for von-Mises phase noise); the best one is refined by the inverse-variance-weighted mean of the signed residuals.
Returns {"value", "score", "margin", "residual", "n_candidates", "unambiguous_range"}: score in [-1, 1] (1 = all bands agree exactly), margin = best minus runner-up score (small = the answer was a near tie — treat as unreliable), residual per band in the units of v. hi defaults to lo + the least common multiple of the periods (when they are commensurate); a range wider than that is refused, because two values in it would have identical residues.
Exactness: integer residues of pairwise-coprime integer periods reproduce residue_integer_crt exactly. Robustness: with periods Γ M_i (M_i coprime integers) a value is recovered exactly whenever every residue error is below Γ/4 (Wang & Xia's bound); beyond it the margin collapses first.
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• poc_residue_crt — py -3.11 examples/poc_residue_crt.py
table を入力に取れる)—
robust)*Provenance: residue.py — RESIDUE operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.