PPubMed19 Jan 2022Cited 3×

Fast and noise-tolerant determination of the center of rotation in tomography Center of rotation in tomography

Everett Vacek, Chris Jacobsen

Abstract

A rapid phase symmetry method for finding the center of rotation in tomographic data using two images located 180° ± Δθ apart is introduced. The method is more robust against photon noise than image correlation methods, and shows good tolerance to Δθ ranging up to several degrees.

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Phase symmetry enables rapid, noise‑tolerant determination of the tomographic center of rotation using only two projections.

What’s new

i.Introduced a rapid phase‑symmetry method for finding the center of rotation using two images 180° ± Δθ apart
ii.Showed the method is more robust against photon noise than image‑correlation methods
iii.Demonstrated tolerance to angular deviations Δθ up to several degrees
iv.Provided open‑source Python implementation on GitHub
v.Achieved speedups of 32× over phase correlation and 640× over sinogram FFT

How they did it

Two projection images taken approximately 180° apart are summed into a reflection‑pair array, which is reshaped into a 1‑D vector and transformed with a single FFT. The phase of the lowest non‑zero spatial frequency is extracted, converted to a position shift, and reported as the center‑of‑rotation error. Normalization steps using TomoPy are applied to mitigate illumination gradients.

What they found

Phase‑symmetry calculation was 32 times faster than phase correlation and 640 times faster than the sinogram FFT approach
The method remained the most robust of the three tested approaches at low signal‑to‑noise ratios (Fig. 4)
Accurate COR recovery was maintained for angular departures up to ±30° and for very low per‑projection SNR (0.09)
Across multiple TomoBank data sets the phase‑symmetry approach reproduced the COR to within a fraction of a pixel

Caveats

✕Requires the object to remain fully within the field of view for all projections
✕Assumes the rotation axis is aligned with the detector axis
✕Sensitive to illumination gradients along the detector axis unless corrected
✕Relies on the lowest spatial frequency, so strong illumination gradients can affect accuracy

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