typed op• データ種: cimage → feature
• 呼び出し: fullseye.apply(img, "tb_cplx_cr_residual", a=0.5, b=0.5) (2-D は 1 画像 + 2 スカラつまみ a,b∈[0,1] のモデル)
*図なし: この op は cimage を入力に取る。画像から始まる Studio のプログラムでは型が届かないので、下の「実行できる例」で使い方を見ること。*
Cauchy-Riemann residual of a sampled complex field — "is this field
holomorphic?" as a number.
With `f = u + i v` sampled on a uniform grid, holomorphy means
`u_x = v_y and u_y = -v_x` (Cauchy-Riemann). This returns the
relative residual `max(|u_x - v_y|, |u_y + v_x|) / max|grad|`
(central differences, `numpy.gradient): 0` = the samples satisfy CR to
the discretisation limit, `2` = the field is the conjugate of a
holomorphic one (`conj(z)` gives exactly 2), values in between = partly
analytic or noisy.
Grid convention (it decides the sign of the answer): `f[i, j]` is the
field at `z = x0 + j*spacing + i*spacing*1j` — rows index the *increasing
imaginary* axis, columns the real axis. Image arrays usually run rows
*downward*; feeding one directly measures the conjugate field, whose
residual is `2, not 0. Flip rows (f[::-1]`) to use image data.
Discretisation, honestly: central differences are exact for polynomials of
degree <= 2, so `f = z**2` returns exactly 0; for higher order the
residual floors at `O(h^2 * |f'''|) (measured: f = z**3` on a
`[-1,1]^2 grid returns 1.7e-3 at h` and 4.2e-4 at
`h/2` — a factor 4.00, the expected second order). Read a
small value as "consistent with holomorphic at this resolution", never as
proof.
A constant field returns `0.0 (it is holomorphic; the 0/0` of the
normalisation is resolved by that limit, and stated here rather than left
to numpy).
Raises `ValueError`: not a 2-D array, either dimension below 3 (no
central difference exists), non-finite/masked input, over-cap size,
non-finite or non-positive *spacing*.
HALCON: no operator (`derivate_gauss` supplies the real-valued
derivatives one would build this from).
Typed bridge of the math op `cplx_cr_residual into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. a drives spacing (default 1); b` is unused.
• 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。
• (まだありません)
feature を入力に取れる)typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_angle_3points · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal
*Provenance: ops.py — 2D 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.