typed op• 資料種類:cimage → feature
• 呼叫:fullseye.apply(img, "tb_cplx_cr_residual", a=0.5, b=0.5)(2-D 的模型是一張圖 + 兩個純量旋鈕 a,b∈[0,1])
*無圖: 該運算子以 cimage 為輸入。從影像開始的 Studio 程式無法到達該型別，請參見下方的可執行範例。*
取樣複數場的 Cauchy-Riemann 殘差——把「這個場是否全純？」量化成一個數值。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
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.
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• (尚無)
feature 作為輸入)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 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.