fit_circle_contour_xldfit_circle_contour_xldFitCircleContourXldFitCircleContourXldfit_circle_contour_xld (Operator)

Name

fit_circle_contour_xldfit_circle_contour_xldFitCircleContourXldFitCircleContourXldfit_circle_contour_xld — Approximate XLD contours by circles.

Signature

fit_circle_contour_xld(Contours : : Algorithm, MaxNumPoints, MaxClosureDist, ClippingEndPoints, Iterations, ClippingFactor : Row, Column, Radius, StartPhi, EndPhi, PointOrder)

Description

fit_circle_contour_xldfit_circle_contour_xldFitCircleContourXldFitCircleContourXldfit_circle_contour_xld approximates the XLD contours ContoursContoursContourscontourscontours by circles. It does not perform a segmentation of the input contours. Thus, one has to make sure that each contour corresponds to one and only one circle. The operator returns for each contour the center (RowRowRowrowrow, ColumnColumnColumncolumncolumn), and the RadiusRadiusRadiusradiusradius.

The algorithm used for the fitting of circles can be selected via AlgorithmAlgorithmAlgorithmalgorithmalgorithm:

'algebraic'"algebraic""algebraic""algebraic""algebraic": This approach minimizes the algebraic distance between the contour points and the resulting circle.
'ahuber'"ahuber""ahuber""ahuber""ahuber": Similar to 'algebraic'"algebraic""algebraic""algebraic""algebraic". Here the contour points are weighted to decrease the impact of outliers based on the approach of Huber (see below).
'atukey'"atukey""atukey""atukey""atukey": Similar to 'algebraic'"algebraic""algebraic""algebraic""algebraic". Here the contour points are weighted and outliers are ignored based on the approach of Tukey (see below).
'geometric'"geometric""geometric""geometric""geometric": This approach minimizes the geometric distance between the contour points and the resulting circle. The distance measure is statistically optimal, but takes more computational time. This option is recommended if the contour points are considerably distorted by noise.
'geohuber'"geohuber""geohuber""geohuber""geohuber": Similar to 'geometric'"geometric""geometric""geometric""geometric". Here the contour points are weighted to decrease the impact of outliers based on the approach of Huber (see below).
'geotukey'"geotukey""geotukey""geotukey""geotukey": Similar to 'geometric'"geometric""geometric""geometric""geometric". Here the contour points are weighted and outliers are ignored based on the approach of Tukey (see below).

For '*huber' and '*tukey' a robust error statistics is used to estimate the standard deviation of the distances from the contour points without outliers from the approximating circle. The parameter ClippingFactorClippingFactorClippingFactorclippingFactorclipping_factor (a scaling factor for the standard deviation) controls the amount of outliers: the smaller the value chosen for ClippingFactorClippingFactorClippingFactorclippingFactorclipping_factor the more outliers are detected. In the Tukey algorithm outliers are removed, whereas in the Huber algorithm outliers are only damped, or more precisely they are weighted linearly. Without any robust weighting the squares of the distances are taken as error values in the optimization, i.e., a least square formulation. In practice, the approach of Tukey is recommended.

The parameter IterationsIterationsIterationsiterationsiterations specifies the number of iterations for the algorithms 'algebraic'"algebraic""algebraic""algebraic""algebraic", 'ahuber'"ahuber""ahuber""ahuber""ahuber" and 'atukey'"atukey""atukey""atukey""atukey". This parameter is ignored for the algorithms 'geometric'"geometric""geometric""geometric""geometric", 'geohuber'"geohuber""geohuber""geohuber""geohuber" and 'geotukey'"geotukey""geotukey""geotukey""geotukey". If IterationsIterationsIterationsiterationsiterations is set to zero, the algorithm does not perform iterative improvements on the fitted circle, but only checks if the initial guess was already close enough depending on the chosen treatment of outliers.

To reduce the computational load, the fitting of circles can be restricted to a subset of the contour points: If a value other than -1 is assigned to MaxNumPointsMaxNumPointsMaxNumPointsmaxNumPointsmax_num_points, only up to MaxNumPointsMaxNumPointsMaxNumPointsmaxNumPointsmax_num_points points - uniformly distributed over the contour - are used.

For circular arcs, the points on the circle closest to the start points and end points of the original contours are chosen as start and end points. The corresponding angles referring to the X-axis are returned in StartPhiStartPhiStartPhistartPhistart_phi and EndPhiEndPhiEndPhiendPhiend_phi, see also gen_ellipse_contour_xldgen_ellipse_contour_xldGenEllipseContourXldGenEllipseContourXldgen_ellipse_contour_xld. Contours, for which the distance between their start points and their end points is less or equal MaxClosureDistMaxClosureDistMaxClosureDistmaxClosureDistmax_closure_dist are considered to be closed. Thus, they are approximated by circles instead of circular arcs. Due to artifacts in the pre-processing the start and end points of a contour might be faulty. Therefore, it is possible to exclude ClippingEndPointsClippingEndPointsClippingEndPointsclippingEndPointsclipping_end_points points at the beginning and at the end of a contour from the fitting of circles. However, they are still used for the determination of StartPhiStartPhiStartPhistartPhistart_phi and EndPhiEndPhiEndPhiendPhiend_phi.

The minimum necessary number of contour points for fitting a circle is three. Therefore, it is required that the number of contour points is at least .

Execution Information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters

ContoursContoursContourscontourscontours (input_object) xld_cont(-array) → object

Input contours.

AlgorithmAlgorithmAlgorithmalgorithmalgorithm (input_control) string → (string)

Algorithm for the fitting of circles.

Default: 'algebraic' "algebraic" "algebraic" "algebraic" "algebraic"

List of values: 'ahuber'"ahuber""ahuber""ahuber""ahuber", 'algebraic'"algebraic""algebraic""algebraic""algebraic", 'atukey'"atukey""atukey""atukey""atukey", 'geohuber'"geohuber""geohuber""geohuber""geohuber", 'geometric'"geometric""geometric""geometric""geometric", 'geotukey'"geotukey""geotukey""geotukey""geotukey"

MaxNumPointsMaxNumPointsMaxNumPointsmaxNumPointsmax_num_points (input_control) integer → (integer)

Maximum number of contour points used for the computation (-1 for all points).

Default: -1

Restriction: MaxNumPoints >= 3

MaxClosureDistMaxClosureDistMaxClosureDistmaxClosureDistmax_closure_dist (input_control) real → (real)

Maximum distance between the end points of a contour to be considered as 'closed'.

Default: 0.0

Restriction: MaxClosureDist >= 0.0

ClippingEndPointsClippingEndPointsClippingEndPointsclippingEndPointsclipping_end_points (input_control) integer → (integer)

Number of points at the beginning and at the end of the contours to be ignored for the fitting.

Default: 0

Restriction: ClippingEndPoints >= 0

IterationsIterationsIterationsiterationsiterations (input_control) integer → (integer)

Maximum number of iterations for the robust weighted fitting.

Default: 3

Restriction: Iterations >= 0

ClippingFactorClippingFactorClippingFactorclippingFactorclipping_factor (input_control) real → (real)

Clipping factor for the elimination of outliers (typical: 1.0 for Huber and 2.0 for Tukey).

Default: 2.0

Suggested values: 1.0, 1.5, 2.0, 2.5, 3.0

Restriction: ClippingFactor > 0

RowRowRowrowrow (output_control) circle.center.y(-array) → (real)

Row coordinate of the center of the circle.

ColumnColumnColumncolumncolumn (output_control) circle.center.x(-array) → (real)

Column coordinate of the center of the circle.

RadiusRadiusRadiusradiusradius (output_control) circle.radius(-array) → (real)

Radius of circle.

StartPhiStartPhiStartPhistartPhistart_phi (output_control) angle.rad(-array) → (real)

Angle of the start point [rad].

EndPhiEndPhiEndPhiendPhiend_phi (output_control) angle.rad(-array) → (real)

Angle of the end point [rad].

PointOrderPointOrderPointOrderpointOrderpoint_order (output_control) string(-array) → (string)

Point order along the boundary.

List of values: 'negative'"negative""negative""negative""negative", 'positive'"positive""positive""positive""positive"

Result

fit_circle_contour_xldfit_circle_contour_xldFitCircleContourXldFitCircleContourXldfit_circle_contour_xld returns 2 ( H_MSG_TRUE) if all parameter values are correct, and circles could be fitted to the input contours. If the input is empty the behavior can be set via set_system('no_object_result',<Result>)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)set_system("no_object_result",<Result>). If necessary, an exception is raised. If the parameter ClippingFactorClippingFactorClippingFactorclippingFactorclipping_factor is chosen too small, i.e., all points are classified as outliers, the error 3264 is raised.