transform op• Data kinds: image2d → table
• Call: import fullseye as fs; fs.ledger.hankel_image(image, *, center=None, spacing: 'float' = 1.0, n: 'int' = 256, r_max: 'float | None' = None) -> 'dict' (to call the implementation directly, import mathtransforms; mathtransforms.hankel_image(image, *, center=None, spacing: 'float' = 1.0, n: 'int' = 256, r_max: 'float | None' = None) -> 'dict'; from the registry, opsmath.get("hankel_image"))
> This operator's description has not been translated yet. The original text follows as it is.
軸対称な画像(円い開口・ガウスの塊・回折の輪)の 2 次元フーリエ変換を、動径の 1 本の Hankel 変換で求める。
画像を中心からの距離で 1 画素幅の輪に分けて平均し(動径の分布)、`hankel_transform`(0 次)にかける。
軸対称なら 2 次元の変換が1 本の積分で済み(輪で平均するので雑音も 1/√(輪の画素数) に減る)、軸対称から
どれだけ崩れているか(`asymmetry`)を数で返す。周波数の刻みは 2-D FFT と同じく 1/(2·半径) 程度で、細かくはならない。
Args:
image: 2-D の実画像。
center: 中心 (行, 列)。省略すると明るさの重心。
spacing: 1 画素の長さ(周波数の単位を決める)。
n: Hankel 変換の標本数。
r_max: 使う半径の上限(既定 = 中心から画像の縁までの最短距離。角の欠けた輪は使わない)。
Returns:
`nu(周波数)・F(2-D フーリエ変換の動径断面、∬ f e^{−2πi k·x} dx の値)・r・profile`(動径の分布)・
`center・asymmetry` = ‖画像 − 分布から作り直した軸対称の画像‖ / ‖画像‖(0 なら軸対称。暗い背景で薄めない)。
門: 半径 R の円板は F(ν) = R J₁(2πνR)/ν(Airy)、exp(−π r²/σ²) は σ² exp(−π σ² ν²)(自己双対の拡大)、
2-D FFT の動径断面と一致。
Every mathops op validates its input before computing (nothing slips through silently):
• **complex input raises ValueError** — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• **masked arrays with masked elements raise ValueError** — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• **NaN/Inf raises ValueError on every input** (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• 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.
• transforms_tour — py -3.11 examples/transforms_tour.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
transform)abel_transform · abel_inverse · abel_inverse_image · abel_revolve · hankel_transform · tf_poles_zeros · tf_freq_response · tf_impulse_response
*Provenance: mathtransforms.py — MATH 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.