ellipse_sinogram — TOMOGRAPHY forward op

• データ種: なし → sinogram(引数だけで決まる op —— 画像やデータの入力を取らない)

• 呼び出し: import tomography; tomography.ellipse_sinogram(size=256, ellipses=None, angles_deg=None, n_detectors=None) (または opstomography.get("ellipse_sinogram"))

使い方

一様な楕円の和の閉じた式による Radon 変換。

> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。

The ground truth this module is tested against, and a usable operator in its

own right: a sinogram with no discretisation error to feed a reconstruction,

so that any error in the picture belongs to the reconstruction and not to the

projector.

For one ellipse with centre `(x0, y0), semi-axes (a, b)`, rotation

`phi and density rho, the line integral along `x cos(t) + y sin(t) =

s`` is::

A(t)^2 = a^2 cos^2(t - phi) + b^2 sin^2(t - phi)

s' = s - (x0 cos t + y0 sin t)

p = 2 rho a b sqrt(A^2 - s'^2) / A^2 for |s'| < A, else 0

which for a disc (`a = b = r, rho = 1`) collapses to the chord length

`2 sqrt(r^2 - s^2)`. Densities add, so a sum of ellipses projects to a sum

of these.

The result is in the same pixel units as :func:radon_transform applied

to :func:ellipse_phantom at the same *size*: the normalised half-width is

`size/2` pixels, and a line integral scales with length, so the closed form

is multiplied by `size/2`. Getting that factor wrong is invisible in the

picture — a sinogram has no absolute scale — and shows up only as a

reconstruction whose density is off by a constant, which is why it is pinned

by a test rather than by a comment.

:param size: the pixel grid the units refer to (as in :func:ellipse_phantom).

:param ellipses: as :func:ellipse_phantom; `None -> :data:SHEPP_LOGAN`.

:param angles_deg: view angles; `None -> `linspace(0, 180, 180,

endpoint=False)``.

:param n_detectors: detector bins; `None` -> enough to cover the diagonal.

:returns: `(n_angles, n_detectors)` float64 sinogram.

:raises ValueError: on a degenerate ellipse or a sinogram over

:data:MAX_SINOGRAM_ELEMENTS.

参考(サンプルデータ・文献)

• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。

• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。

• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• ct_reconstruction — py -3.11 examples/ct_reconstruction.py

型が繋がる次の op(sinogram を入力に取れる)

backproject_sinogram · filtered_backprojection · sart_reconstruct · beam_hardening_apply · beam_hardening_correct · ring_artifact_apply · ring_artifact_remove · metal_trace_interpolate

同カテゴリ(forward)

ellipse_phantom · radon_transform

*Provenance: tomography.py — TOMOGRAPHY operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.