transform op• Data kinds: image2d → image2d
• Call: import fullseye as fs; fs.ledger.anscombe_transform(image, gain=1.0, read_sigma=0.0, offset=0.0, clip=False) (to call the implementation directly, import photoncount; photoncount.anscombe_transform(image, gain=1.0, read_sigma=0.0, offset=0.0, clip=False); from the registry, opsphoton.get("anscombe_transform"))
Anscombe variance-stabilising transform: Poisson counts -> ~unit-variance.
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.
• photon_timeresolved family guide
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• photon_timeresolved — py -3.11 examples/photon_timeresolved.py
image2d as input)photon_sample · photon_statistics · photon_uncertainty · anscombe_inverse
transform)*Provenance: photoncount.py — PHOTON operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.