geometry op• Data kinds: sinogram → measurement
• Call: import fullseye as fs; fs.ledger.sinogram_center_of_rotation(sinogram, angles_deg=None, min_condition=0.02) (implementation को सीधे call करना हो तो import tomography; tomography.sinogram_center_of_rotation(sinogram, angles_deg=None, min_condition=0.02), registry से लेना हो तो opstomography.get("sinogram_center_of_rotation"))
rotation axis वास्तव में कहाँ है, केंद्र से detector bin में।
> नीचे का विस्तृत विवरण मूल text में है — सारांश और headings का अनुवाद हो चुका है।
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.
• Sample data catalog (DL URL / license) — 2-D के लिए skimage.data (BSD/public) + synthetic, 3-D के लिए real data sources (Stanford/PDS आदि) के DL URL।
• Operators का स्रोत और संदर्भ — इस op family के मूल research/methods के स्रोत।
• Algorithm का मानक स्रोत (लेखक, वर्ष) और उपयोग ऊपर की family usage guide में दिए गए हैं।
• ct_reconstruction — py -3.11 examples/ct_reconstruction.py
measurement को input के रूप में लेते हैं)—
geometry)*Provenance: tomography.py — TOMOGRAPHY operator registry. यह per-op note tools/opdocs.py md से अपने-आप generate होता है (हाथ से edit न करें)।*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.