7.5.1. algotom.util.calibration

Module of calibration methods:

  • Correcting the non-uniform background of an image.

  • Binarizing an image.

  • Calculating the distance between two point-like objects segmented from two images. Useful for determining pixel-size in helical scans.

  • Find the tilt and roll of a parallel-beam tomography system given coordinates of a point-like object scanned in the range of [0, 360] degrees.

Functions:

normalize_background(mat[, size])

Correct a non-uniform background of an image using the median filter.

normalize_background_based_fft(mat[, sigma, ...])

Correct a non-uniform background of an image using a Fourier Gaussian filter.

invert_dot_contrast(mat)

Invert the contrast of a 2D binary array to make sure that a dot is white.

calculate_threshold(mat[, bgr])

Calculate threshold value based on Algorithm 4 in Ref.

binarize_image(mat[, threshold, bgr, norm, ...])

Binarize an image.

get_dot_size(mat[, size_opt])

Get size of binary dots given the option.

check_dot_size(mat, min_size, max_size)

Check if the size of a dot is in a range.

select_dot_based_size(mat, dot_size[, ratio])

Select dots having a certain size.

calculate_distance(mat1, mat2[, size_opt, ...])

Calculate the distance between two point-like objects segmented from two images.

fit_points_to_ellipse(x, y)

Fit an ellipse to a set of points.

find_tilt_roll(x, y[, method])

Find the tilt and roll of a parallel-beam tomography system given coordinates of a point-like object scanned in the range of [0, 360] degrees.
algotom.util.calibration.normalize_background(mat, size=51)[source]

Correct a non-uniform background of an image using the median filter.

Parameters

  • mat (array_like) – 2D array.

  • size (int) – Size of the median filter.

Returns

array_like – 2D array. Corrected image.

algotom.util.calibration.normalize_background_based_fft(mat, sigma=5, pad=None, mode='reflect')[source]

Correct a non-uniform background of an image using a Fourier Gaussian filter.

Parameters

  • mat (array_like) – 2D array.

  • sigma (int) – Sigma of the Gaussian.

  • pad (int) – Padding for the Fourier transform.

  • mode (str, list of str, or tuple of str) – Padding method. One of options : ‘reflect’, ‘edge’, ‘constant’. Full list is at: https://numpy.org/doc/stable/reference/generated/numpy.pad.html

Returns

array_like – 2D array. Corrected image.

algotom.util.calibration.invert_dot_contrast(mat)[source]

Invert the contrast of a 2D binary array to make sure that a dot is white.

Parameters

mat (array_like) – 2D binary array.

Returns

array_like – 2D array.

algotom.util.calibration.calculate_threshold(mat, bgr='bright')[source]

Calculate threshold value based on Algorithm 4 in Ref. [1].

Parameters

  • mat (array_like) – 2D array.

  • bgr ({“bright”, “dark”}) – To indicate the brightness of the background against image features.

Returns

float – Threshold value.

References

[1] : https://doi.org/10.1364/OE.26.028396

algotom.util.calibration.binarize_image(mat, threshold=None, bgr='bright', norm=False, denoise=True, invert=True)[source]

Binarize an image.

Parameters

  • mat (array_like) – 2D array.

  • threshold (float, optional) – Threshold value for binarization. Automatically calculated using Algorithm 4 in Ref. [1] if None.

  • bgr ({“bright”, “dark”}) – To indicate the brightness of the background against image features.

  • norm (bool, optional) – Apply normalization if True.

  • denoise (bool, optional) – Apply denoising if True.

  • invert (bool, optional) – Invert the contrast if needed.

Returns

array_like – 2D binary array.

References

[1] : https://doi.org/10.1364/OE.26.028396

algotom.util.calibration.get_dot_size(mat, size_opt='max')[source]

Get size of binary dots given the option.

Parameters

  • mat (array_like) – 2D binary array.

  • size_opt ({“max”, “min”, “median”, “mean”}) – Select options.

Returns

dot_size (float) – Size of the dot.

algotom.util.calibration.check_dot_size(mat, min_size, max_size)[source]

Check if the size of a dot is in a range.

Parameters

  • mat (array_like) – 2D array.

  • min_size (float) – Minimum size.

  • max_size (float) – Maximum size.

Returns

bool

algotom.util.calibration.select_dot_based_size(mat, dot_size, ratio=0.01)[source]

Select dots having a certain size.

Parameters

  • mat (array_like) – 2D array.

  • dot_size (float) – Size of the standard dot.

  • ratio (float) – Used to calculate the acceptable range. [dot_size - ratio*dot_size; dot_size + ratio*dot_size]

Returns

array_like – 2D array. Selected dots.

algotom.util.calibration.calculate_distance(mat1, mat2, size_opt='max', threshold=None, bgr='bright', norm=False, denoise=True, invert=True)[source]

Calculate the distance between two point-like objects segmented from two images. Useful for measuring pixel-size in helical scans (Ref. [1]).

Parameters

  • mat1 (array_like) – 2D array.

  • mat2 (array_like) – 2D array.

  • size_opt ({“max”, “min”, “median”, “mean”}) – Options to select binary objects based on their size.

  • threshold (float, optional) – Threshold value for binarization. Automatically calculated using Algorithm 4 in Ref. [2] if None.

  • bgr ({“bright”, “dark”}) – To indicate the brightness of the background against image features.

  • norm (bool, optional) – Apply normalization if True.

  • denoise (bool, optional) – Apply denoising if True.

  • invert (bool, optional) – Invert the contrast if needed.

References

[1] : https://doi.org/10.1364/OE.418448

[2] : https://doi.org/10.1364/OE.26.028396

algotom.util.calibration.fit_points_to_ellipse(x, y)[source]

Fit an ellipse to a set of points.

Parameters

  • x (ndarray) – x-coordinates of the points.

  • y (ndarray) – y-coordinates of the points.

Returns

  • roll_angle (float) – Rotation angle of the ellipse in degree.

  • a_major (float) – Length of the major axis.

  • b_minor (float) – Length of the minor axis.

  • xc (float) – x-coordinate of the ellipse center.

  • yc (float) – y-coordinate of the ellipse center.

algotom.util.calibration.find_tilt_roll_based_linear_fit(x, y)[source]

Find the tilt and roll of a parallel-beam tomography system given coordinates of a point-like object scanned in the range of [0, 360] degrees. Uses a linear-fit-based approach [1].

Parameters

  • x (ndarray) – x-coordinates of the points.

  • y (ndarray) – y-coordinates of the points.

Returns

  • tilt (float) – Tilt angle in degree.

  • roll (float) – Roll angle in degree.

References

[1] : https://doi.org/10.1098/rsta.2014.0398

algotom.util.calibration.find_tilt_roll_based_ellipse_fit(x, y)[source]

Find the tilt and roll of a parallel-beam tomography system given coordinates of a point-like object scanned in the range of [0, 360] degrees. Uses an ellipse-fit-based approach.

Parameters

  • x (ndarray) – x-coordinates of the points.

  • y (ndarray) – y-coordinates of the points.

Returns

  • tilt (float) – Tilt angle in degree.

  • roll (float) – Roll angle in degree.

algotom.util.calibration.find_tilt_roll(x, y, method='ellipse')[source]

Find the tilt and roll of a parallel-beam tomography system given coordinates of a point-like object scanned in the range of [0, 360] degrees.

Parameters

  • x (ndarray) – x-coordinates of the points.

  • y (ndarray) – y-coordinates of the points.

  • method ({“linear”, “ellipse”}) – Method for finding tilt and roll.

Returns

  • tilt (float) – Tilt angle in degree.

  • roll (float) – Roll angle in degree.