transform op• 資料種類:image2d → image2d
• 呼叫: import fullseye as fs; fs.ledger.anscombe_transform(image, gain=1.0, read_sigma=0.0, offset=0.0, clip=False)(要直接呼叫實作,import photoncount; photoncount.anscombe_transform(image, gain=1.0, read_sigma=0.0, offset=0.0, clip=False);從台帳取用則 opsphoton.get("anscombe_transform"))
Anscombe 變異數穩定化變換:卜瓦松計數 -> 變異數約為 1。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
Photon-limited data has signal-dependent noise, which every classical denoiser (Gaussian, bilateral, NLM, wavelet, BM3D) assumes away. The Anscombe transform A(x) = 2*sqrt(x + 3/8) makes the variance approximately 1 *independently of the signal*, so the standard route is transform -> denoise with a unit-sigma Gaussian denoiser -> anscombe_inverse.
The generalised form (Starck/Murtagh/Bijaoui) also absorbs the sensor's analogue chain, and takes exactly the parameters backends_aug.aug_read_noise injects::
A(x) = (2/g) * sqrt(g*(x - offset) + (3/8)*g^2 + sigma_r^2)
with *gain* g in ADU per photon, *read_sigma* the Gaussian read noise in ADU and *offset* the black level in ADU. The defaults g=1, sigma_r=0, offset=0 reduce it to the classical form exactly.
Measured stabilisation — var(A(X)) for X ~ Poisson(lambda), computed exactly by summing the Poisson pmf (no sampling, so anyone can reproduce these; tests/test_photoncount.py pins them and the sampled versions):
======== ========
lambda var(A)
======== ========
1 0.717443
2 0.924297
4 0.998754
10 1.000910
100 1.000006
======== ========
So "variance 1" is true from about 4 photons/pixel upward and false below it — at 1 photon/pixel the variance is 0.717, a 28% shortfall, which is the honest statement of the transform's low-count limit. Below a few photons an exact Poisson method (or the exact unbiased inverse, see anscombe_inverse) is required.
It does not help a linear smoother, and the tests say so. Measured on a two-level scene (4 and 64 photons/pixel, seed 5): a plain Gaussian filter applied to the raw counts reaches RMSE 2.387, and the same filter through the Anscombe route reaches 2.459 — i.e. *slightly worse*. That is expected:
averaging is already the right thing to do to Poisson counts, so stabilising the variance first buys nothing. The transform pays off for denoisers whose parameter is an absolute noise scale — thresholds, sigma filters, wavelet shrinkage, NLM, BM3D — because that parameter becomes one constant instead of a per-pixel function. Measured with a 5x5 sigma filter at a 3-sigma threshold on that same scene: 1.191 through the transform against 2.307 in the raw domain using the same 3-sigma rule with a globally estimated sigma. (An *oracle* raw threshold, swept against ground truth one does not have in practice, reaches 1.080 — so the honest headline is "one principled constant instead of a tuned guess", not "always better".)
Returns a float64 array of the same shape as *image*.
Raises ValueError: non-finite *image*, non-positive *gain*, negative *read_sigma*, and — unless clip=True — any pixel whose argument under the square root is negative (which can happen for real read-noise data dipping below the black level). clip=True floors the argument at 0 and is the documented, opt-in behaviour; the default refuses rather than quietly manufacturing a value.
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者、年份)與用途見上面的族使用指南。
• photon_timeresolved — py -3.11 examples/photon_timeresolved.py
image2d 作為輸入)photon_sample · photon_statistics · photon_uncertainty · anscombe_inverse
transform)*Provenance: photoncount.py — PHOTON 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.