transform op• 데이터 종류: image2d → image2d
• 호출: import photoncount; photoncount.anscombe_transform(image, gain=1.0, read_sigma=0.0, offset=0.0, clip=False)(또는 opsphoton.get("anscombe_transform"))
Anscombe 분산 안정화 변환: 푸아송 계수 -> 분산 약 1.
> 아래 상세 설명은 원문입니다 —— 요약과 제목은 번역되어 있습니다.
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.
• 샘플 데이터 카탈로그(DL URL / 라이선스) —— 2-D 는 skimage.data(BSD/public)+ 합성, 3-D 는 실데이터 소스(Stanford/PDS 등)의 DL URL.
• 연산자의 내력·참고문헌 —— 이 연산자 족의 바탕이 된 연구/기법의 출처.
• 알고리즘의 정전(저자·연도)과 용도는 위의 패밀리 사용 가이드에 적혀 있습니다.
• photon_timeresolved — py -3.11 examples/photon_timeresolved.py
image2d 를 입력으로 받는 것)photon_sample · photon_statistics · photon_uncertainty · anscombe_inverse
transform)*Provenance: photoncount.py — PHOTON 연산자 레지스트리. 이 op 노트는 tools/opdocs.py md 가 자동 생성합니다(직접 편집하지 마세요).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.