fullseye

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 fullseye as fs; fs.ledger.ellipse_sinogram(size=256, ellipses=None, angles_deg=None, n_detectors=None) (実装を直接呼ぶなら import tomography; tomography.ellipse_sinogram(size=256, ellipses=None, angles_deg=None, n_detectors=None)、台帳から引くなら opstomography.get("ellipse_sinogram"))

使い方

The closed-form Radon transform of a sum of uniform ellipses.

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
• poc_ct_fidelity — py -3.11 examples/poc_ct_fidelity.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

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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.

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