pytomography.utils
#
This module contains utility functions used in the other modules of PyTomography
Submodules#
Package Contents#
Classes#
Implementation of the Hamming filter given by \(\Pi(\omega) = \frac{1}{2}\left(1+\cos\left(\frac{\pi(|\omega|-\omega_L)}{\omega_H-\omega_L} \right)\right)\) for \(\omega_L \leq |\omega| < \omega_H\) and \(\Pi(\omega) = 1\) for \(|\omega| \leq \omega_L\) and \(\Pi(\omega) = 0\) for \(|\omega|>\omega_H\). Arguments |
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Implementation of the Ramp filter \(\Pi(\omega) = |\omega|\) |
Functions#
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Reverse cumulative sum along the first axis of a tensor of shape [batch_size, Lx, Ly, Lz]. |
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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 SPECT PSF modeling where the amount of blurring depends on thedistance from the detector. |
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Given an object tensor, finds the nearest neighbour (corresponding to |
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Obtains the number of blank z-slices at the sup ( |
Prints all the available SPECT collimator parameters |
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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 \(\phi = 3\pi/2 - \beta\). |
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Computes the pad width required such that subsequent rotation retains the entire image |
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Pads an image along the Lr axis |
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Pads object tensors by enough pixels in the xy plane so that subsequent rotations don't crop out any of the object |
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Unpads the image back to original Lr dimensions |
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Unpads a padded object tensor in the xy plane back to its original dimensions |
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Pads an object tensor along z. Useful for PSF modeling |
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Unpads an object along the z dimension |
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Function used for curve fitting of linear attenuation coefficient vs. photon energy curves from NIST. It's given by the functional form \(f(x) = c_1e^{-d_1\sqrt{x}} + c_2e^{-d_2\sqrt{x}}\). It was chosen purely because it gave good fit results. |
Return energy and linear attenuation data from NIST datafiles of mass attenuation coefficients between 50keV and 511keV. |
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Gets linear attenuation corresponding to a given energy in in the data from |
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- pytomography.utils.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 SPECT attenuation 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.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 SPECT PSF modeling 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.get_object_nearest_neighbour(object, shifts)[source]#
Given an object tensor, finds the nearest neighbour (corresponding to
shifts
) for each voxel (done by shifting object by i,j,k)- Parameters:
object (torch.Tensor) – Original object
shifts (list[int]) – List of three integers [i,j,k] corresponding to neighbour location
- Returns:
Shifted object whereby each voxel corresponding to neighbour [i,j,k] of the
object
.- Return type:
torch.Tensor
- pytomography.utils.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.print_collimator_parameters()[source]#
Prints all the available SPECT collimator parameters
- pytomography.utils.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.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.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.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.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.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.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.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.dual_sqrt_exponential(energy, c1, c2, d1, d2)[source]#
Function used for curve fitting of linear attenuation coefficient vs. photon energy curves from NIST. It’s given by the functional form \(f(x) = c_1e^{-d_1\sqrt{x}} + c_2e^{-d_2\sqrt{x}}\). It was chosen purely because it gave good fit results.
- Parameters:
energy (float) – Energy of photon
c1 (float) – Fit parameter 1
c2 (float) – Fit parameter 2
d1 (float) – Fit parameter 3
d2 (float) – Fit parameter 4
- Returns:
_description_
- Return type:
float
- pytomography.utils.get_E_mu_data_from_datasheet(file)[source]#
Return energy and linear attenuation data from NIST datafiles of mass attenuation coefficients between 50keV and 511keV.
- Parameters:
file (str) – Location of NIST data file. Corresponds to a particular element/material.
- Returns:
Energy and linear attenuation values.
- Return type:
tuple[np.array, np.array]
- pytomography.utils.get_mu_from_spectrum_interp(file, energy)[source]#
Gets linear attenuation corresponding to a given energy in in the data from
file
.- Parameters:
file (str) – Filepath of the mu-energy data
energy (float) – Energy at which mu is computed
- Returns:
Linear attenuation coefficient (in 1/cm) at the desired energies.
- Return type:
np.array
- pytomography.utils.compute_TEW(projection_lower, projection_upper, width_lower, width_upper, width_peak)[source]#
- class pytomography.utils.HammingFilter(wl, wh)[source]#
Implementation of the Hamming filter given by \(\Pi(\omega) = \frac{1}{2}\left(1+\cos\left(\frac{\pi(|\omega|-\omega_L)}{\omega_H-\omega_L} \right)\right)\) for \(\omega_L \leq |\omega| < \omega_H\) and \(\Pi(\omega) = 1\) for \(|\omega| \leq \omega_L\) and \(\Pi(\omega) = 0\) for \(|\omega|>\omega_H\). Arguments
wl
andwh
should be expressed as fractions of the Nyquist frequency (i.e.wh=0.93
represents 93% the Nyquist frequency).- __call__(w)#