tomopy.prep.alignment

Functions:

align_seq(prj, ang[, fdir, iters, pad, …]) Aligns the projection image stack using the sequential re-projection algorithm [C8].
align_joint(prj, ang[, fdir, iters, pad, …]) Aligns the projection image stack using the joint re-projection algorithm [C8].
add_jitter(prj[, low, high]) Simulates jitter in projection images.
add_noise(prj[, ratio]) Adds Gaussian noise with zero mean and a given standard deviation as a ratio of the maximum value in data.
blur_edges(prj[, low, high]) Blurs the edge of the projection images.
shift_images(prj, sx, sy) Shift projections images for a given set of shift values in horizontal and vertical directions.
scale(prj) Linearly scales the projection images in the range between -1 and 1.
tilt(obj[, rad, phi]) Tilt object at a given angle from the rotation axis.
tomopy.prep.alignment.align_seq(prj, ang, fdir='.', iters=10, pad=(0, 0), blur=True, center=None, algorithm='sirt', upsample_factor=10, rin=0.5, rout=0.8, save=False, debug=True)[source]

Aligns the projection image stack using the sequential re-projection algorithm [C8].

Parameters:

  • prj (ndarray) – 3D stack of projection images. The first dimension is projection axis, second and third dimensions are the x- and y-axes of the projection image, respectively.

  • ang (ndarray) – Projection angles in radians as an array.

  • iters (scalar, optional) – Number of iterations of the algorithm.

  • pad (list-like, optional) – Padding for projection images in x and y-axes.

  • blur (bool, optional) – Blurs the edge of the image before registration.

  • center (array, optional) – Location of rotation axis.

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

    ‘art’

    Algebraic reconstruction technique [C2].

    ‘gridrec’

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

    ‘mlem’

    Maximum-likelihood expectation maximization algorithm [C3].

    ‘sirt’

    Simultaneous algebraic reconstruction technique.

    ‘tv’

    Total Variation reconstruction technique [C7].

    ‘grad’

    Gradient descent method with a constant step size

  • upsample_factor (integer, optional) – The upsampling factor. Registration accuracy is inversely propotional to upsample_factor.

  • rin (scalar, optional) – The inner radius of blur function. Pixels inside rin is set to one.

  • rout (scalar, optional) – The outer radius of blur function. Pixels outside rout is set to zero.

  • save (bool, optional) – Saves projections and corresponding reconstruction for each algorithm iteration.

  • debug (book, optional) – Provides debugging info such as iterations and error.
Returns:

  • ndarray – 3D stack of projection images with jitter.
  • ndarray – Error array for each iteration.
tomopy.prep.alignment.align_joint(prj, ang, fdir='.', iters=10, pad=(0, 0), blur=True, center=None, algorithm='sirt', upsample_factor=10, rin=0.5, rout=0.8, save=False, debug=True)[source]

Aligns the projection image stack using the joint re-projection algorithm [C8].

Parameters:

  • prj (ndarray) – 3D stack of projection images. The first dimension is projection axis, second and third dimensions are the x- and y-axes of the projection image, respectively.

  • ang (ndarray) – Projection angles in radians as an array.

  • iters (scalar, optional) – Number of iterations of the algorithm.

  • pad (list-like, optional) – Padding for projection images in x and y-axes.

  • blur (bool, optional) – Blurs the edge of the image before registration.

  • center (array, optional) – Location of rotation axis.

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

    ‘art’

    Algebraic reconstruction technique [C2].

    ‘gridrec’

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

    ‘mlem’

    Maximum-likelihood expectation maximization algorithm [C3].

    ‘sirt’

    Simultaneous algebraic reconstruction technique.

    ‘tv’

    Total Variation reconstruction technique [C7].

    ‘grad’

    Gradient descent method with a constant step size

  • upsample_factor (integer, optional) – The upsampling factor. Registration accuracy is inversely propotional to upsample_factor.

  • rin (scalar, optional) – The inner radius of blur function. Pixels inside rin is set to one.

  • rout (scalar, optional) – The outer radius of blur function. Pixels outside rout is set to zero.

  • save (bool, optional) – Saves projections and corresponding reconstruction for each algorithm iteration.

  • debug (book, optional) – Provides debugging info such as iterations and error.
Returns:

  • ndarray – 3D stack of projection images with jitter.
  • ndarray – Error array for each iteration.
tomopy.prep.alignment.scale(prj)[source]

Linearly scales the projection images in the range between -1 and 1.

Parameters:prj (ndarray) – 3D stack of projection images. The first dimension is projection axis, second and third dimensions are the x- and y-axes of the projection image, respectively.
Returns:ndarray – Scaled 3D stack of projection images.
tomopy.prep.alignment.tilt(obj, rad=0, phi=0)[source]

Tilt object at a given angle from the rotation axis.

Warning

Not implemented yet.

Parameters:
  • obj (ndarray) – 3D discrete object.
  • rad (scalar, optional) – Radius in polar cordinates to define tilt angle. The value is between 0 and 1, where 0 means no tilt and 1 means a tilt of 90 degrees. The tilt angle can be obtained by arcsin(rad).
  • phi (scalar, optional) – Angle in degrees to define tilt direction from the rotation axis. 0 degree means rotation in sagittal plane and 90 degree means rotation in coronal plane.
Returns:

ndarray – Tilted 3D object.
tomopy.prep.alignment.add_jitter(prj, low=0, high=1)[source]

Simulates jitter in projection images. The jitter is simulated by drawing random samples from a uniform distribution over the half-open interval [low, high).

Parameters:
  • prj (ndarray) – 3D stack of projection images. The first dimension is projection axis, second and third dimensions are the x- and y-axes of the projection image, respectively.
  • low (float, optional) – Lower boundary of the output interval. All values generated will be greater than or equal to low. The default value is 0.
  • high (float) – Upper boundary of the output interval. All values generated will be less than high. The default value is 1.0.
Returns:

ndarray – 3D stack of projection images with jitter.
tomopy.prep.alignment.add_noise(prj, ratio=0.05)[source]

Adds Gaussian noise with zero mean and a given standard deviation as a ratio of the maximum value in data.

Parameters:
  • prj (ndarray) – 3D stack of projection images. The first dimension is projection axis, second and third dimensions are the x- and y-axes of the projection image, respectively.
  • ratio (float, optional) – Ratio of the standard deviation of the Gaussian noise distribution to the maximum value in data.
Returns:

ndarray – 3D stack of projection images with added Gaussian noise.
tomopy.prep.alignment.blur_edges(prj, low=0, high=0.8)[source]

Blurs the edge of the projection images.

Parameters:
  • prj (ndarray) – 3D stack of projection images. The first dimension is projection axis, second and third dimensions are the x- and y-axes of the projection image, respectively.
  • low (scalar, optional) – Min ratio of the blurring frame to the image size.
  • high (scalar, optional) – Max ratio of the blurring frame to the image size.
Returns:

ndarray – Edge-blurred 3D stack of projection images.
tomopy.prep.alignment.shift_images(prj, sx, sy)[source]

Shift projections images for a given set of shift values in horizontal and vertical directions.