pytomography.utils.helper_functions#

Module Contents#

Functions#

rev_cumsum(x)

Reverse cumulative sum along the first axis of a tensor of shape [batch_size, Lx, Ly, Lz].

rotate_detector_z(x, angles[, mode, negative])

Returns an object tensor in a rotated reference frame such that the scanner is located at the +x axis. Note that the scanner angle \(\beta\) is related to \(\phi\) (azimuthal angle) by \(\phi = 3\pi/2 - \beta\).

get_distance(Lx, r, dx)

Given the radial distance to center of object space from the scanner, computes the distance

compute_pad_size(width)

Computes the pad width required such that subsequent rotation retains the entire image

compute_pad_size_padded(width)

Computes the width by which an object was padded, given its padded size.

pad_object(object[, mode])

Pads object tensors by enough pixels in the xy plane so that subsequent rotations don't crop out any of the object

unpad_object(object)

Unpads a padded object tensor in the xy plane back to its original dimensions

pad_image(image[, mode, value])

Pads an image along the Lr axis

unpad_image(image)

Unpads the image back to original Lr dimensions

pad_object_z(object, pad_size[, mode])

Pads an object tensor along z. Useful for PSF modeling

unpad_object_z(object, pad_size)

Unpads an object along the z dimension

get_object_nearest_neighbour(object, shifts)

get_blank_below_above(image)

Obtains the number of blank z-slices at the sup (blank_above) and inf (blank_below) of the projection data. This method is entirely empircal, and looks for z slices where there are zero detected counts.

bilinear_transform(arr, a1, b1, a2, b2)

Converts an array of Hounsfield Units into linear attenuation coefficient using the bilinear transformation \(f(x)=a_1x+b_1\) for positive \(x\) and \(f(x)=a_2x+b_2\) for negative \(x\).

pytomography.utils.helper_functions.rev_cumsum(x)[source]#

Reverse cumulative sum along the first axis of a tensor of shape [batch_size, Lx, Ly, Lz]. since this is used with CT correction, the initial voxel only contributes 1/2.

Parameters:

x (torch.tensor[batch_size,Lx,Ly,Lz]) – Tensor to be summed

Returns:

The cumulatively summed tensor.

Return type:

torch.tensor[batch_size, Lx, Ly, Lz]

pytomography.utils.helper_functions.rotate_detector_z(x, angles, mode='bilinear', negative=False)[source]#

Returns an object tensor in a rotated reference frame such that the scanner is located at the +x axis. Note that the scanner angle \(\beta\) is related to \(\phi\) (azimuthal angle) by \(\phi = 3\pi/2 - \beta\).

Parameters:
  • x (torch.tensor[batch_size, Lx, Ly, Lz]) – Tensor aligned with cartesian coordinate system specified

  • manual. (by the) –

  • angles (torch.Tensor) – The angles \(\beta\) where the scanner is located for each element in the batch x.

  • mode (str, optional) – Method of interpolation used to get rotated image. Defaults to bilinear.

  • negative (bool, optional) – If True, applies an inverse rotation. In this case, the tensor

:param x is an object in a coordinate system aligned with \(\beta\): :param and the function rotates the: :param x back to the original cartesian coordinate system specified by the users manual. In particular: :param if one: :param uses this function on a tensor with negative=False: :param then applies this function to that returned: :param tensor with negative=True: :param it should return the same tensor. Defaults to False.:

Returns:

Rotated tensor.

Return type:

torch.tensor[batch_size, Lx, Ly, Lz]

Parameters:
  • x (torch.Tensor) –

  • angles (torch.tensor) –

  • mode (str) –

  • negative (bool) –

pytomography.utils.helper_functions.get_distance(Lx, r, dx)[source]#
Given the radial distance to center of object space from the scanner, computes the distance

between each parallel plane (i.e. (y-z plane)) and a detector located at +x. This function is used for point spread function (PSF) blurring where the amount of blurring depends on thedistance from the detector.

Parameters:
  • Lx (int) – The number of y-z planes to compute the distance of

  • r (float) – The radial distance between the central y-z plane and the detector at +x.

  • dx (float) – The spacing between y-z planes in Euclidean distance.

Returns:

An array of distances for each y-z plane to the detector.

Return type:

np.array[Lx]

pytomography.utils.helper_functions.compute_pad_size(width)[source]#

Computes the pad width required such that subsequent rotation retains the entire image

Parameters:

width (int) – width of the corresponding axis (i.e. number of elements in the dimension)

Returns:

the number of pixels by which the axis needs to be padded on each side

Return type:

int

pytomography.utils.helper_functions.compute_pad_size_padded(width)[source]#

Computes the width by which an object was padded, given its padded size.

Parameters:

width (int) – width of the corresponding axis (i.e. number of elements in the dimension)

Returns:

the number of pixels by which the object was padded to get to this width

Return type:

int

pytomography.utils.helper_functions.pad_object(object, mode='constant')[source]#

Pads object tensors by enough pixels in the xy plane so that subsequent rotations don’t crop out any of the object

Parameters:
  • object (torch.Tensor[batch_size, Lx, Ly, Lz]) – object tensor to be padded

  • mode (str, optional) – _description_. Defaults to ‘constant’.

Returns:

_description_

Return type:

_type_

pytomography.utils.helper_functions.unpad_object(object)[source]#

Unpads a padded object tensor in the xy plane back to its original dimensions

Parameters:

object (torch.Tensor[batch_size, Lx', Ly', Lz]) – padded object tensor

Returns:

Object tensor back to it’s original dimensions.

Return type:

torch.Tensor[batch_size, Lx, Ly, Lz]

pytomography.utils.helper_functions.pad_image(image, mode='constant', value=0)[source]#

Pads an image along the Lr axis

Parameters:
  • image (torch.Tensor[batch_size, Ltheta, Lr, Lz]) – Image tensor.

  • mode (str, optional) – Padding mode to use. Defaults to ‘constant’.

  • value (float, optional) – If padding mode is constant, fill with this value. Defaults to 0.

Returns:

Padded image tensor.

Return type:

torch.Tensor[batch_size, Ltheta, Lr’, Lz]

pytomography.utils.helper_functions.unpad_image(image)[source]#

Unpads the image back to original Lr dimensions

Parameters:

image (torch.Tensor[batch_size, Ltheta, Lr', Lz]) – Padded image tensor

Returns:

Unpadded image tensor

Return type:

torch.Tensor[batch_size, Ltheta, Lr, Lz]

pytomography.utils.helper_functions.pad_object_z(object, pad_size, mode='constant')[source]#

Pads an object tensor along z. Useful for PSF modeling

Parameters:
  • object (torch.Tensor[batch_size, Lx, Ly, Lz]) – Object tensor

  • pad_size (int) – Amount by which to pad in -z and +z

  • mode (str, optional) – Padding mode. Defaults to ‘constant’.

Returns:

Padded object tensor along z.

Return type:

torch.Tensor[torch.Tensor[batch_size, Lx, Ly, Lz’]]

pytomography.utils.helper_functions.unpad_object_z(object, pad_size)[source]#

Unpads an object along the z dimension

Parameters:
  • object (torch.Tensor[batch_size, Lx, Ly, Lz']) – Padded object tensor along z.

  • pad_size (int) – Amount by which the padded tensor was padded in the z direcion

Returns:

Unpadded object tensor.

Return type:

torch.Tensor[batch_size, Lx, Ly, Lz]

pytomography.utils.helper_functions.get_object_nearest_neighbour(object, shifts)[source]#
Parameters:
  • object (torch.Tensor) –

  • shifts (list[int]) –

pytomography.utils.helper_functions.get_blank_below_above(image)[source]#

Obtains the number of blank z-slices at the sup (blank_above) and inf (blank_below) of the projection data. This method is entirely empircal, and looks for z slices where there are zero detected counts.

Parameters:

image (torch.tensor) – Image data from a scanner

Returns:

A tuple of two elements corresponding to the number of blank slices at the inf, and the number of blank slices at the sup.

Return type:

Sequence[int]

pytomography.utils.helper_functions.bilinear_transform(arr, a1, b1, a2, b2)[source]#

Converts an array of Hounsfield Units into linear attenuation coefficient using the bilinear transformation \(f(x)=a_1x+b_1\) for positive \(x\) and \(f(x)=a_2x+b_2\) for negative \(x\).

Parameters:
  • arr (np.array) – Array to be transformed using bilinear transformation

  • a1 (float) – Bilinear slope for negative input values

  • b1 (float) – Bilinear intercept for negative input values

  • a2 (float) – Bilinear slope for positive input values

  • b2 (float) – Bilinear intercept for positive input values

Returns:

Transformed array.

Return type:

np.array