typed op• データ種: counts → counts
• 呼び出し: fullseye.apply(img, "tb_tcspc_coates_correct", a=0.5, b=0.5) (2-D は 1 画像 + 2 スカラつまみ a,b∈[0,1] のモデル)
*図は合成の入力 128×128 で実際に走らせた出力。左が入力、右が出力。点群は上から見た散布(明るさ = z)、1-D 列は折れ線、体積は z 方向の最大値投影、動画は中央フレーム、複素画像は振幅、絵にならない返り値は値そのもの。*
*つまみ a は出力を変えない(実測: 0.1 / 0.5 / 0.9 で同一)。*
*つまみ b は出力を変えない(実測: 0.1 / 0.5 / 0.9 で同一)。*
段階(前置きの op → この op。左から順):
▸ tb_tcspc_coates_correct: 段階の図 (docs サイト)
別の画像でも(合成シーン / 写真 / 硬貨。上段が入力、下段がその出力。つまみは既定):
▸ tb_tcspc_coates_correct: 別の画像での出力 (docs サイト)
Undo TCSPC pile-up exactly (Coates's estimator) — the early-photon bias.
Classical TCSPC records at most one photon per excitation cycle: the first one. Late bins are therefore starved, because the cycles in which an early photon arrived never reach them, and the measured histogram is biased toward short arrival times — a dToF depth read straight off a piled-up histogram is *too close*, and a fluorescence lifetime is *too short*.
Coates's estimator inverts that exactly. With N_k the measured counts in bin k and C the number of excitation cycles, the number of cycles that survived to reach bin k is D_k = C - sum_{j<k} N_j, the per-cycle detection probability in that bin is p_k = N_k / D_k and the pile-up-free per-cycle intensity is lambda_k = -ln(1 - p_k). This op returns C * lambda_k — the histogram the same scene would have produced if the detector could record every photon — so it is directly comparable to the measured one.
This is an exact inverse, not a linearisation: build a histogram from a known lambda through the forward model N_k = C * exp(-sum_{j<k} lambda_j) * (1 - exp(-lambda_k)) and Coates returns lambda to machine precision (measured max relative error 1.6e-15 in the tests, on a pile-up so severe that the last bin was suppressed to 14.8% of its true counts).
*hist* is the 1-D measured histogram (counts per bin); *cycles* the number of excitation cycles (laser pulses) that produced it.
Raises ValueError: negative, non-finite or non-1-D *hist*, a non-positive or non-integer *cycles*, a histogram whose total exceeds *cycles* (impossible: at most one photon per cycle — a sure sign that *cycles* is wrong or the data are not first-photon TCSPC), and any bin that consumed every remaining cycle (p_k = 1, where -ln(0) is inf).
Typed bridge of the photon op tcspc_coates_correct into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. This op has no tunable parameter; a and b are unused.
• 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。
下のプログラムは実際に走ることを確かめてある(図と同じ入力)。Studio のヘルプではこのブロックがボタンになり、その場で読み込んで実行できる。
img_to_counts 0.50 0.50 tb_tcspc_coates_correct 0.50 0.50
次の例は元の台帳 op tcspc_coates_correct を呼ぶもの。この橋渡し op は同じ実装を fn(v, a, b) 規約に合わせただけなので、挙動はそのまま当てはまる(呼び出し形だけ違う)。
• photon_timeresolved — py -3.11 examples/photon_timeresolved.py
• poc_dtof_ranging — py -3.11 examples/poc_dtof_ranging.py
counts を入力に取れる)identity · tb_spad_deadtime_apply · tb_spad_deadtime_correct · tb_tcspc_irf_convolve · tb_tcspc_background_subtract · tb_dtof_depth · tb_countrate_to_counts · tb_counts_to_countrate
typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*Provenance: ops.py — 2D 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.