typed op• 데이터 종류: cimage → feature
• 호출: fullseye.apply(img, "tb_cplx_cr_residual", a=0.5, b=0.5)(2-D 는 이미지 1 장 + 스칼라 노브 2 개 a,b∈[0,1] 모델)
*그림 없음: 이 연산자는 cimage를 입력으로 받습니다. 이미지에서 시작하는 Studio 프로그램으로는 그 타입에 닿지 않으므로 아래의 실행 가능한 예제를 보세요.*
표본화된 복소수 장의 코시-리만 잔차 — "이 장은 정칙(holomorphic)인가?"를 하나의 수치로 나타낸 것.
> 아래 상세 설명은 원문입니다 —— 요약과 제목은 번역되어 있습니다.
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.
• 샘플 데이터 카탈로그(DL URL / 라이선스) —— 2-D 는 skimage.data(BSD/public)+ 합성, 3-D 는 실데이터 소스(Stanford/PDS 등)의 DL URL.
• 연산자의 내력·참고문헌 —— 이 연산자 족의 바탕이 된 연구/기법의 출처.
• (아직 없음)
feature 를 입력으로 받는 것)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 연산자 레지스트리. 이 op 노트는 tools/opdocs.py md 가 자동 생성합니다(직접 편집하지 마세요).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.