vol_gaussian_psf — 3D `restoration` op

• Data kinds: measurement → voxel

• Call: import fullseye as fs; fs.ledger.vol_gaussian_psf(sigma, truncate=4.0) (to call the implementation directly, import volrestore; volrestore.vol_gaussian_psf(sigma, truncate=4.0); from the registry, ops3d.get("vol_gaussian_psf"))

Usage

A normalised (sums to 1) 3-D Gaussian PSF kernel. *sigma* is a scalar or

> The detailed description below is the original text — the summary and the headings are translated.

`(sz, sy, sx) in voxels; the kernel spans +-truncate*sigma` per axis

(odd size, centre at the middle voxel). The convenient companion to

:func:vol_richardson_lucy when the instrument PSF is well approximated

as Gaussian. Kernels above `PSF_MAX_ELEMENTS` (~256^3) raise

`ValueError` — a PSF that large is an input mistake, not an instrument.

形: 各軸の半径 `r = ceil(truncate * sigma)、辺長 2r + 1`(奇数)の

`(2rz+1, 2ry+1, 2rx+1) float64 配列。軸順は (z, y, x) で、sigma` を

`(sz, sy, sx)` で渡すとその順に対応する(異方 PSF)。3 本の 1-D Gaussian

`exp(-x^2 / (2 sigma^2))` の外積を全体和で割るので、合計はちょうど 1、中心

voxel が最大値。単位は voxel(mm の PSF 幅は spacing で割ってから渡す)。

引数と検証(`ValueError`):

• `sigma`: 正の有限スカラ、または長さ 3 の正の有限値。2 乗が 0 に

アンダーフローするほど小さい値(~1.5e-154 未満)は 0/0 になるので拒否。

• `truncate`: 正の有限値(既定 4.0 = 片側 4σ で打ち切り)。

• 要素数 `prod(2r+1) が PSF_MAX_ELEMENTS(2**24`)を超えると拒否

(σ≈300 で 64 GB を確保しかけた実測が動機)。

使いどころ: `vol_richardson_lucy(vol, psf) の psf`。RL 側でも合計 1 に

再正規化するので、ここで作ったカーネルをそのまま渡してよい。

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

• deconv_fft_restore — py -3.11 examples_3d/deconv_fft_restore.py

Ops the type connects to (they accept `voxel` as input)

voxel_to_mips · voxel_to_mesh · signed_distance_field · to_points · sobel3d · hessian3d · curvature_maps · edt_jfa

Same category (`restoration`)

vol_richardson_lucy

*Provenance: volrestore.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

vol_gaussian_psf — 3D restoration op