geometry op• 데이터 종류: sinogram → measurement
• 호출: import fullseye as fs; fs.ledger.sinogram_center_of_rotation(sinogram, angles_deg=None, min_condition=0.02)(구현을 직접 호출하려면 import tomography; tomography.sinogram_center_of_rotation(sinogram, angles_deg=None, min_condition=0.02), 원장에서 가져오려면 opstomography.get("sinogram_center_of_rotation"))
회전축이 실제로 어디에 있는가(중심에서 검출기 빈 몇 개).
> 아래 상세 설명은 원문입니다 —— 요약과 제목은 번역되어 있습니다.
The centre-of-mass identity, which is exact and needs no reconstruction: the first moment of a projection is the projection of the object's centre of mass, so::
s_cm(theta) = x0 cos(theta) + y0 sin(theta) + c
with (x0, y0) the centre of mass in the slice and c the offset of the rotation axis from the detector centre. Fitting the three unknowns by least squares over all views gives *c* directly. Measured on the Shepp-Logan phantom with 180 views, recovering a deliberately introduced shift, together with the cost of not correcting it (normalised RMS error of the FBP reconstruction against the truth):
true shift estimated error uncorrected after this fix
0.00 px +0.0029 px 0.0029 0.0250 0.0249
0.50 px +0.5029 px 0.0029 0.0537 0.0358
1.00 px +1.0029 px 0.0029 0.1016 0.0249
2.00 px +2.0029 px 0.0029 0.1630 0.0249
Three things in that table are worth reading twice. Half a pixel already doubles the error (0.0250 -> 0.0537) and does not look like a mistake — it looks like a slightly soft reconstruction, which is why this is a measurement and not an inspection. The estimator's own bias is a constant 0.0029 px across every shift, so it is a property of the phantom and the detector sampling, not of the size of the error being measured. And the half-pixel row is the only one the fix does not fully repair (0.0358 against 0.0249), because correcting a *fractional* shift means resampling, and the linear interpolation costs more than the integer shifts do — see sinogram_center_shift.
Two things this needs, both refused rather than assumed. The object must be entirely inside the field of view — the identity is about the whole mass, and a truncated object has a different mass at every angle. And the views must span enough angle for [cos, sin, 1] to be independent: over a narrow wedge, cos(theta) and the constant are nearly the same vector and the fit puts the object's own offset into *c*. The condition number is checked and a degenerate design is refused.
:param sinogram: (n_angles, n_detectors), rows = angles. :param angles_deg: view angles; None -> uniform [0, 180). :param min_condition: smallest acceptable reciprocal condition number of the
[cos, sin, 1] design matrix. The default of 0.02 is calibrated,
not chosen — the reciprocal condition number and the error it lets
through, on a sinogram with a true 1.00-px shift:
span rcond estimate error
180 deg 2.15e-01 +0.9939 0.0061 px
120 deg 8.92e-02 +0.9900 0.0100 px
90 deg 4.85e-02 +0.9485 0.0515 px
60 deg 2.09e-02 +0.8993 0.1007 px <- the default admits this
45 deg 1.17e-02 +0.7041 0.2959 px <- and refuses this
20 deg 2.26e-03 +1.7113 0.7113 px
10 deg 5.54e-04 -6.9765 7.9765 px
The 10-degree row is why the check exists at all: the answer is finite,
the sign is wrong, and the magnitude is eight pixels on a one-pixel
error. Nothing about it looks like a failure.
:returns: float — the axis offset in detector bins, positive towards
higher bin indices.
:raises ValueError: on a sinogram whose total mass is zero, on fewer than 3
views, or on an angular span too narrow to separate the offset from the
object's own position.
• 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.
• 알고리즘의 정전(저자·연도)과 용도는 위의 패밀리 사용 가이드에 적혀 있습니다.
• ct_reconstruction — py -3.11 examples/ct_reconstruction.py
measurement 를 입력으로 받는 것)—
geometry)*Provenance: tomography.py — TOMOGRAPHY 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.