# 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, rotc_guess]) 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 [B11].

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_pc(proj1, proj2, tol=0.5, rotc_guess=None)[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 phase_cross_correlation function uses cross-correlation in Fourier space, optionally employing an upsampled matrix-multiplication DFT to achieve arbitrary subpixel precision. [B15].

Parameters
• proj1 (ndarray) – 2D projection data.

• proj2 (ndarray) – 2D projection data.

• tol (scalar, optional) – Subpixel accuracy

• rotc_guess (float, optional) – Initual guess value for the rotation center

Returns

float – Rotation axis location.

tomopy.recon.rotation.find_center_vo(tomo, ind=None, smin=- 50, smax=50, srad=6, step=0.25, ratio=0.5, drop=20)[source]

Find rotation axis location using Nghia Vo’s method. [B24].

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.

• 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.mask_empty_slice(tomo, threshold=0.25)[source]

Generate a mask to indicate whether current slice contains sample

At APS 1ID, some of the projection images contains large empty area above the sample, resulting in empty layers.

Parameters
• tomo (ndarray) – 3D tomographic data.

• threshold (float, optional) – determine whether a layer is considered to be empty

Returns

nparray – a mask indicate the emptyness of each layer

tomopy.recon.rotation.write_center(tomo, theta, dpath='tmp/center', cen_range=None, ind=None, mask=False, ratio=1.0, sinogram_order=False, algorithm='gridrec', filter_name='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 [B2].

‘bart’

Block algebraic reconstruction technique.

‘fbp’

Filtered back-projection algorithm.

‘gridrec’

Fourier grid reconstruction algorithm [B5], [B22].

‘mlem’

Maximum-likelihood expectation maximization algorithm [B3].

‘osem’

Ordered-subset expectation maximization algorithm [B17].

‘ospml_hybrid’

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

Ordered-subset penalized maximum likelihood algorithm with quadratic penalties.

‘pml_hybrid’

Penalized maximum likelihood algorithm with weighted linear and quadratic penalties [B18].

Penalized maximum likelihood algorithm with quadratic penalty.

‘sirt’

Simultaneous algebraic reconstruction technique.

‘tv’

Total Variation reconstruction technique [B8].

Gradient descent method with a constant step size

‘tikh’

Tikhonov regularization with identity Tikhonov matrix.

filter_namestr, 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.