5.3.1. discorpy.proc.processing

Module of processing methods:

  • Fit lines of points to parabolas, find the center of distortion.

  • Calculate undistorted intercepts of gridlines.

  • Calculate distortion coefficients of the backward model, the forward model, and the backward-from-forward model.

  • Correct perspective distortion affecting curve lines.

  • Generate non-perspective points or lines from perspective points or lines.

  • Calculate perspective coefficients.

  • Correct perspective effect.

  • Find center of distortion based on using vanishing points.

Functions:

_para_fit_hor(list_lines, xcenter, ycenter)

Fit horizontal lines of points to parabolas.

_para_fit_ver(list_lines, xcenter, ycenter)

Fit vertical lines of points to parabolas.

find_cod_coarse(list_hor_lines, list_ver_lines)

Coarse estimation of the center of distortion.

find_cod_fine(list_hor_lines, ...)

Find the best center of distortion (CoD) by searching around the coarse estimation of the CoD.

_calc_undistor_intercept(list_hor_lines, ...)

Calculate the intercepts of undistorted lines.

calc_coef_backward(list_hor_lines, ...[, ...])

Calculate the distortion coefficients of a backward mode.

calc_coef_forward(list_hor_lines, ...[, ...])

Calculate the distortion coefficients of a forward mode.

calc_coef_backward_from_forward(...[, ...])

Calculate the distortion coefficients of a backward mode from a forward model.

transform_coef_backward_and_forward(list_fact)

Transform polynomial coefficients of a radial distortion model between forward mapping and backward mapping.

find_cod_bailey(list_hor_lines, list_ver_lines)

Find the center of distortion (COD) using the Bailey's approach (Ref.

_generate_non_perspective_parabola_coef(...)

Correct the deviation of fitted parabola coefficients of each line caused by perspective distortion.

_find_cross_point_between_parabolas(...)

Find a cross point between two parabolas in opposite direction.

regenerate_grid_points_parabola(...[, ...])

Regenerating grid points by finding cross points between horizontal lines and vertical lines using their parabola coefficients.

_generate_linear_coef(list_hor_lines, ...[, ...])

Get linear coefficients of horizontal and vertical lines from linear fit.

_find_cross_point_between_lines(...)

Find a cross point between two lines in opposite direction.

_calc_undistor_intercept_perspective(...[, ...])

Calculate the intercepts of undistorted lines from perspective distortion.

regenerate_grid_points_linear(...[, is_coef])

Regenerating grid points by finding cross points between horizontal lines and vertical lines using their linear coefficients.

generate_undistorted_perspective_lines(...)

Generate undistorted lines from perspective lines.

generate_source_target_perspective_points(...)

Generate source points (distorted) and target points (undistorted).

generate_4_source_target_perspective_points(points)

Generate 4 rectangular points corresponding to 4 perspective-distorted points.

calc_perspective_coefficients(source_points, ...)

Calculate perspective coefficients of a matrix to map from source points to target points (Ref.

update_center(list_lines, xcenter, ycenter)

Update the coordinates of points on lines.

correct_perspective_effect(list_hor_lines, ...)

Correct perspective effect of radial-distorted grid lines.

find_center_based_vanishing_points(...)

Find the center of distortion (COD) using vanishing points formed by the intersections of parapolas with opposite curves in the horizontal and vertical directions.

find_center_based_vanishing_points_iteration(...)

Find the center of distortion (COD) using vanishing points formed by the intersections of parapolas with lines of minimum curvature in the horizontal and vertical directions.
discorpy.proc.processing.find_cod_coarse(list_hor_lines, list_ver_lines)[source]

Coarse estimation of the center of distortion.

Parameters:

  • list_hor_lines (list of 2D arrays) – List of (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D arrays) – List of (y,x)-coordinates of points on each vertical line.

Returns:

  • xcenter (float) – Center of distortion in the x-direction.

  • ycenter (float) – Center of distortion in the y-direction.

discorpy.proc.processing.find_cod_fine(list_hor_lines, list_ver_lines, xcenter, ycenter, point_dist)[source]

Find the best center of distortion (CoD) by searching around the coarse estimation of the CoD.

Parameters:

  • list_hor_lines (list of 2D arrays) – List of the (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D arrays) – List of the (y,x)-coordinates of points on each vertical line.

  • xcenter (float) – Coarse estimation of the CoD in x-direction.

  • ycenter (float) – Coarse estimation of the CoD in y-direction.

  • point_dist (float) – Median distance of two nearest points.

Returns:

  • xcenter (float) – Center of distortion in x-direction.

  • ycenter (float) – Center of distortion in y-direction.

discorpy.proc.processing.calc_coef_backward(list_hor_lines, list_ver_lines, xcenter, ycenter, num_fact, optimizing=False, threshold=0.3)[source]

Calculate the distortion coefficients of a backward mode.

Parameters:

  • list_hor_lines (list of 2D arrays) – List of the (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D arrays) – List of the (y,x)-coordinates of points on each vertical line.

  • xcenter (float) – Center of distortion in x-direction.

  • ycenter (float) – Center of distortion in y-direction.

  • num_fact (int) – Number of the factors of polynomial.

  • optimizing (bool, optional) – Apply optimization if True.

  • threshold (float) – To determine if there are missing lines. Larger is less sensitive.

Returns:

list_fact (list of float) – Coefficients of the polynomial.

discorpy.proc.processing.calc_coef_forward(list_hor_lines, list_ver_lines, xcenter, ycenter, num_fact, optimizing=False, threshold=0.3)[source]

Calculate the distortion coefficients of a forward mode.

Parameters:

  • list_hor_lines (list of 2D arrays) – List of the (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D arrays) – List of the (y,x)-coordinates of points on each vertical line.

  • xcenter (float) – Center of distortion in x-direction.

  • ycenter (float) – Center of distortion in y-direction.

  • num_fact (int) – Number of the factors of polynomial.

  • optimizing (bool, optional) – Apply optimization if True.

  • threshold (float) – To determine if there are missing lines. Larger is less sensitive.

Returns:

list_fact (list of float) – Coefficients of the polynomial.

discorpy.proc.processing.calc_coef_backward_from_forward(list_hor_lines, list_ver_lines, xcenter, ycenter, num_fact, optimizing=False, threshold=0.3)[source]

Calculate the distortion coefficients of a backward mode from a forward model.

Parameters:

  • list_hor_lines (list of 2D arrays) – List of the (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D arrays) – List of the (y,x)-coordinates of points on each vertical line.

  • xcenter (float) – Center of distortion in x-direction.

  • ycenter (float) – Center of distortion in y-direction.

  • num_fact (int) – Number of the factors of polynomial.

  • optimizing (bool, optional) – Apply optimization if True.

  • threshold (float) – To determine if there are missing lines. Larger is less sensitive.

Returns:

  • list_ffact (list of floats) – Polynomial coefficients of the forward model.

  • list_bfact (list of floats) – Polynomial coefficients of the backward model.

discorpy.proc.processing.transform_coef_backward_and_forward(list_fact, mapping='backward', ref_points=None)[source]

Transform polynomial coefficients of a radial distortion model between forward mapping and backward mapping.

Parameters:

  • list_fact (list of floats) – Polynomial coefficients of the radial distortion model.

  • mapping ({‘backward’, ‘forward’}) – Transformation direction.

  • ref_points (list of 1D-arrays, optional) – List of the (y,x)-coordinates of points used for the transformation. Generated if None given.

Returns:

list of floats – Polynomial coefficients of the reversed model.

discorpy.proc.processing.find_cod_bailey(list_hor_lines, list_ver_lines, iteration=2)[source]

Find the center of distortion (COD) using the Bailey’s approach (Ref. [1]).

Parameters:

  • list_hor_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on each vertical line.

Returns:

  • xcenter (float) – Center of distortion in x-direction.

  • ycenter (float) – Center of distortion in y-direction.

References

[1].. https://www-ist.massey.ac.nz/dbailey/sprg/pdfs/2002_IVCNZ_59.pdf

discorpy.proc.processing.regenerate_grid_points_parabola(list_hor_lines, list_ver_lines, perspective=False, find_center=False)[source]

Regenerating grid points by finding cross points between horizontal lines and vertical lines using their parabola coefficients.

Parameters:

  • list_hor_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on each vertical line.

  • perspective (bool, optional) – If True, apply perspective correction and set “find_center” to True.

  • find_center (bool, optional) – If True, calculate distortion center, translate the coordinates of points to the center, apply parabola fitting, and translate the coordinates back

Returns:

  • new_hor_lines (list of 2D-arrays) – List of the updated (y,x)-coordinates of points on each horizontal line.

  • new_ver_lines (list of 2D-arrays) – List of the updated (y,x)-coordinates of points on each vertical line.

discorpy.proc.processing.regenerate_grid_points_linear(list_hor_lines, list_ver_lines, is_coef=False)[source]

Regenerating grid points by finding cross points between horizontal lines and vertical lines using their linear coefficients.

Parameters:

  • list_hor_lines (list of 2D-arrays) – List of the (y, x)-coordinates of points on each horizontal line, or list of linear fitted coefficients of lines (if is_coef=True).

  • list_ver_lines (list of 2D-arrays) – List of the (y, x)-coordinates of points on each vertical line, or list of linear fitted coefficients of lines (if is_coef=True).

  • is_coef (bool, optional) – Whether the input is linear fitted coefficients of lines. If False, linear fitting will be applied to the input lines.

Returns:

  • new_hor_lines (list of 2D-arrays) – List of the updated (y,x)-coordinates of points on each horizontal line.

  • new_ver_lines (list of 2D-arrays) – List of the updated (y,x)-coordinates of points on each vertical line.

discorpy.proc.processing.generate_undistorted_perspective_lines(list_hor_lines, list_ver_lines, equal_dist=True, scale='mean', optimizing=True)[source]

Generate undistorted lines from perspective lines.

Parameters:

  • list_hor_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on each vertical line.

  • equal_dist (bool) – Use the condition that lines are equidistant if True.

  • scale ({‘mean’, ‘median’, ‘min’, ‘max’, float}) – Scale option for the undistorted grid.

  • optimizing (bool) – Apply optimization for finding line-distance if True.

Returns:

  • list_uhor_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on undistorted horizontal lines.

  • list_uver_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on undistorted vertical lines.

discorpy.proc.processing.generate_source_target_perspective_points(list_hor_lines, list_ver_lines, equal_dist=True, scale='mean', optimizing=True)[source]

Generate source points (distorted) and target points (undistorted).

Parameters:

  • list_hor_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on each vertical line.

  • equal_dist (bool) – Use the condition that lines are equidistant if True.

  • scale ({‘mean’, ‘median’, ‘min’, ‘max’, float}) – Scale option for the undistorted grid.

  • optimizing (bool) – Apply optimization for finding line-distance if True.

Returns:

  • source_points (list of 1D-arrays) – List of the (y,x)-coordinates of distorted points.

  • target_points (list of 1D-arrays) – List of the (y,x)-coordinates of undistorted points.

discorpy.proc.processing.generate_4_source_target_perspective_points(points, input_order='yx', equal_dist=False, scale='mean')[source]

Generate 4 rectangular points corresponding to 4 perspective-distorted points.

Parameters:

  • points (list of 1D-arrays) – List of the coordinates of 4 perspective-distorted points.

  • input_order ({‘yx’, ‘xy’}) – Order of the coordinates of input-points.

  • equal_dist (bool) – Use the condition that the rectangular making of 4-points is square if True.

  • scale ({‘mean’, ‘min’, ‘max’, float}) – Scale option for the undistorted points.

Returns:

  • source_points (list of 1D-arrays) – List of the (y,x)-coordinates of distorted points.

  • target_points (list of 1D-arrays) – List of the (y,x)-coordinates of undistorted points.

discorpy.proc.processing.calc_perspective_coefficients(source_points, target_points, mapping='backward')[source]

Calculate perspective coefficients of a matrix to map from source points to target points (Ref. [1]). Note that the coordinate of a point are in (y,x)-order. This is to be consistent with other functions in the module.

Parameters:

  • source_points (array_like) – List of the (y,x)-coordinates of distorted points.

  • target_points (array_like) – List of the (y,x)-coordinates of undistorted points.

  • mapping ({‘backward’, ‘forward’}) – To select mapping direction.

Returns:

array_like – 1D array of 8 coefficients.

References

[1].. https://doi.org/10.1016/S0262-8856(98)00183-8

discorpy.proc.processing.update_center(list_lines, xcenter, ycenter)[source]

Update the coordinates of points on lines.

Parameters:

  • list_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on lines.

  • xcenter (float) – X-origin of the coordinate system.

  • ycenter (float) – Y-origin of the coordinate system.

Returns:

list of 2D-arrays.

discorpy.proc.processing.correct_perspective_effect(list_hor_lines, list_ver_lines, xcenter, ycenter, method='mean', scale='mean')[source]

Correct perspective effect of radial-distorted grid lines.

Parameters:

  • list_hor_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D-arrays) – List of the (y,x)-coordinates of points on each vertical line.

  • xcenter (float) – Center of radial distortion in x-direction.

  • ycenter (float) – Center of radial distortion in y-direction.

  • method ({‘mean’, ‘median’, ‘min’, ‘max’}) – Method to find 4 representative straight lines of parabolas with opposite curves in each direction. 4 intersection points of these lines are used to calculate perspective coefficients.

  • scale ({‘mean’, ‘median’, ‘min’, ‘max’, float}) – Scale option for perspective-corrected grid.

Returns:

  • corr_hor_lines (list of 2D-arrays) – List of the corrected (y,x)-coordinates of points on each horizontal line.

  • corr_ver_lines (list of 2D-arrays) – List of the corrected (y,x)-coordinates of points on each vertical line.

discorpy.proc.processing.find_center_based_vanishing_points(list_hor_lines, list_ver_lines)[source]

Find the center of distortion (COD) using vanishing points formed by the intersections of parapolas with opposite curves in the horizontal and vertical directions. Valid only for barrel distortion.

Parameters:

  • list_hor_lines (list of 2D-arrays) – List of (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D-arrays) – List of (y,x)-coordinates of points on each vertical line.

Returns:

  • xcenter (float) – Center of distortion in the x-direction.

  • ycenter (float) – Center of distortion in the y-direction.

discorpy.proc.processing.find_center_based_vanishing_points_iteration(list_hor_lines, list_ver_lines, iteration=2, method='mean')[source]

Find the center of distortion (COD) using vanishing points formed by the intersections of parapolas with lines of minimum curvature in the horizontal and vertical directions. This approach is more robust than the others when there’s significant perspective distortion.

Parameters:

  • list_hor_lines (list of 2D-arrays) – List of (y,x)-coordinates of points on each horizontal line.

  • list_ver_lines (list of 2D-arrays) – List of (y,x)-coordinates of points on each vertical line.

  • iteration (int, optional) – Iteration number

  • method ({‘mean’, ‘median’, ‘min’, ‘max’}) – Method to find 4 representative straight lines of parabolas with opposite curves in each direction. 4 intersection points of these lines are used to correct perspective distortion.

Returns:

  • xcenter (float) – Center of distortion in the x-direction.

  • ycenter (float) – Center of distortion in the y-direction.