transform op• 資料種類:image2d → image2d
• 呼叫:import photoncount; photoncount.anscombe_transform(image, gain=1.0, read_sigma=0.0, offset=0.0, clip=False)(或 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 -> :func:anscombe_inverse.
The generalised form (Starck/Murtagh/Bijaoui) also absorbs the sensor's
analogue chain, and takes exactly the parameters
:func: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
:func: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.