tomopy.recon.rotation

Module for functions related to finding axis of rotation.

Functions:

find_center(tomo, theta[, ind, init, tol, …]) Find rotation axis location.
find_center_vo(tomo[, ind, smin, smax, …]) Find rotation axis location using Nghia Vo’s method.
find_center_pc(proj1, proj2[, tol]) Find rotation axis location by finding the offset between the first projection and a mirrored projection 180 degrees apart using phase correlation in Fourier space.
write_center(tomo, theta[, dpath, …]) Save images reconstructed with a range of rotation centers.
tomopy.recon.rotation.find_center(tomo, theta, ind=None, init=None, tol=0.5, mask=True, ratio=1.0, sinogram_order=False)[source]

Find rotation axis location.

The function exploits systematic artifacts in reconstructed images due to shifts in the rotation center. It uses image entropy as the error metric and ‘’Nelder-Mead’’ routine (of the scipy optimization module) as the optimizer [C10].

Parameters:
  • tomo (ndarray) – 3D tomographic data.
  • theta (array) – Projection angles in radian.
  • ind (int, optional) – Index of the slice to be used for reconstruction.
  • init (float) – Initial guess for the center.
  • tol (scalar) – Desired sub-pixel accuracy.
  • mask (bool, optional) – If True, apply a circular mask to the reconstructed image to limit the analysis into a circular region.
  • ratio (float, optional) – The ratio of the radius of the circular mask to the edge of the reconstructed image.
  • sinogram_order (bool, optional) – Determins whether data is a stack of sinograms (True, y-axis first axis) or a stack of radiographs (False, theta first axis).
Returns:

float – Rotation axis location.
tomopy.recon.rotation.find_center_vo(tomo, ind=None, smin=-50, smax=50, srad=6, step=0.5, ratio=0.5, drop=20)[source]

Find rotation axis location using Nghia Vo’s method. [C22].

Parameters:
  • tomo (ndarray) – 3D tomographic data.
  • ind (int, optional) – Index of the slice to be used for reconstruction.
  • smin, smax (int, optional) – Coarse search radius. Reference to the horizontal center of the sinogram.
  • srad (float, optional) – Fine search radius.
  • step (float, optional) – Step of fine searching.
  • ratio (float, optional) – The ratio between the FOV of the camera and the size of object. It’s used to generate the mask.
  • drop (int, optional) – Drop lines around vertical center of the mask.
Returns:

float – Rotation axis location.
tomopy.recon.rotation.find_center_pc(proj1, proj2, tol=0.5)[source]

Find rotation axis location by finding the offset between the first projection and a mirrored projection 180 degrees apart using phase correlation in Fourier space. The register_translation function uses cross-correlation in Fourier space, optionally employing an upsampled matrix-multiplication DFT to achieve arbitrary subpixel precision. [C14].

Parameters:
  • proj1 (ndarray) – 2D projection data.
  • proj2 (ndarray) – 2D projection data.
  • tol (scalar, optional) – Subpixel accuracy
Returns:

float – Rotation axis location.
tomopy.recon.rotation.write_center(tomo, theta, dpath=u'tmp/center', cen_range=None, ind=None, mask=False, ratio=1.0, sinogram_order=False, algorithm=u'gridrec', filter_name=u'parzen')[source]

Save images reconstructed with a range of rotation centers.

Helps finding the rotation center manually by visual inspection of images reconstructed with a set of different centers.The output images are put into a specified folder and are named by the center position corresponding to the image.

Parameters:

  • tomo (ndarray) – 3D tomographic data.

  • theta (array) – Projection angles in radian.

  • dpath (str, optional) – Folder name to save output images.

  • cen_range (list, optional) – [start, end, step] Range of center values.

  • ind (int, optional) – Index of the slice to be used for reconstruction.

  • mask (bool, optional) – If True, apply a circular mask to the reconstructed image to limit the analysis into a circular region.

  • ratio (float, optional) – The ratio of the radius of the circular mask to the edge of the reconstructed image.

  • sinogram_order (bool, optional) – Determins whether data is a stack of sinograms (True, y-axis first axis) or a stack of radiographs (False, theta first axis).

  • algorithm ({str, function}) – One of the following string values.

    ‘art’

    Algebraic reconstruction technique [C2].

    ‘bart’

    Block algebraic reconstruction technique.

    ‘fbp’

    Filtered back-projection algorithm.

    ‘gridrec’

    Fourier grid reconstruction algorithm [C5], [C21].

    ‘mlem’

    Maximum-likelihood expectation maximization algorithm [C3].

    ‘osem’

    Ordered-subset expectation maximization algorithm [C16].

    ‘ospml_hybrid’

    Ordered-subset penalized maximum likelihood algorithm with weighted linear and quadratic penalties.

    ‘ospml_quad’

    Ordered-subset penalized maximum likelihood algorithm with quadratic penalties.

    ‘pml_hybrid’

    Penalized maximum likelihood algorithm with weighted linear and quadratic penalties [C17].

    ‘pml_quad’

    Penalized maximum likelihood algorithm with quadratic penalty.

    ‘sirt’

    Simultaneous algebraic reconstruction technique.

    ‘tv’

    Total Variation reconstruction technique [C7].

    ‘grad’

    Gradient descent method with a constant step size

  • filter_name (str, optional) – Name of the filter for analytic reconstruction.

    ‘none’

    No filter.

    ‘shepp’

    Shepp-Logan filter (default).

    ‘cosine’

    Cosine filter.

    ‘hann’

    Cosine filter.

    ‘hamming’

    Hamming filter.

    ‘ramlak’

    Ram-Lak filter.

    ‘parzen’

    Parzen filter.

    ‘butterworth’

    Butterworth filter.

    ‘custom’

    A numpy array of size next_power_of_2(num_detector_columns)/2 specifying a custom filter in Fourier domain. The first element of the filter should be the zero-frequency component.

    ‘custom2d’

    A numpy array of size num_projections*next_power_of_2(num_detector_columns)/2 specifying a custom angle-dependent filter in Fourier domain. The first element of each filter should be the zero-frequency component.