fit_circle_contour_xldfit_circle_contour_xldfit_circle_contour_xldFitCircleContourXldFitCircleContourXld (Operator)

Name

fit_circle_contour_xldfit_circle_contour_xldfit_circle_contour_xldFitCircleContourXldFitCircleContourXld — Approximate XLD contours by circles.

Signature

Description

fit_circle_contour_xldfit_circle_contour_xldfit_circle_contour_xldFitCircleContourXldFitCircleContourXld 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'. 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'. Here the contour points are weighted to decrease the impact of outliers 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 destorted by noise.

'geohuber'"geohuber""geohuber""geohuber""geohuber"

Similar to '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'. Here the contour points are weighted to decrease the impact of outliers 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 ClippingFactorClippingFactorClippingFactorClippingFactorclippingFactor (a scaling factor for the standard deviation) controls the amount of damping outliers: the smaller the value chosen for ClippingFactorClippingFactorClippingFactorClippingFactorclippingFactor the more outliers are detected. The detection of outliers together with the least squares fitting can be repeated. The parameter IterationsIterationsIterationsIterationsiterations specifies the number of iterations. This parameter is of relevance for all algorithms except the two based on the geometric distance, i.e. 'geohuber' and 'geotukey', where this parameter is ignored. 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.

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 MaxNumPointsMaxNumPointsMaxNumPointsMaxNumPointsmaxNumPoints, only up to MaxNumPointsMaxNumPointsMaxNumPointsMaxNumPointsmaxNumPoints 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 refering to the X-axis are returned in StartPhiStartPhiStartPhiStartPhistartPhi and EndPhiEndPhiEndPhiEndPhiendPhi, see also gen_ellipse_contour_xldgen_ellipse_contour_xldgen_ellipse_contour_xldGenEllipseContourXldGenEllipseContourXld. Contours, for which the distance between their start points and their end points is less or equal MaxClosureDistMaxClosureDistMaxClosureDistMaxClosureDistmaxClosureDist are considered to be closed. Thus, they are approximated by circles instead of circular arcs. Due to artefacts in the pre-processing the start and end points of a contour might be faulty. Therefore, it is possible to exclude ClippingEndPointsClippingEndPointsClippingEndPointsClippingEndPointsclippingEndPoints 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 StartPhiStartPhiStartPhiStartPhistartPhi and EndPhiEndPhiEndPhiEndPhiendPhi.

The minimun necessary number of contour points for fitting a circle is three. Therefore, it is required that the number of contour points is at least 3 + 2*ClippingEndPointsClippingEndPointsClippingEndPointsClippingEndPointsclippingEndPoints .

Parallelization

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

Parameters

Result

fit_circle_contour_xldfit_circle_contour_xldfit_circle_contour_xldFitCircleContourXldFitCircleContourXld 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 behaviour can be set via set_system('no_object_result',<Result>)set_system("no_object_result",<Result>)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>). If necessary, an exception is raised. If the parameter ClippingFactorClippingFactorClippingFactorClippingFactorclippingFactor is chosen too small, i.e., all points are classified as outliers, the error 3264 is raised.

Possible Predecessors

gen_contours_skeleton_xldgen_contours_skeleton_xldgen_contours_skeleton_xldGenContoursSkeletonXldGenContoursSkeletonXld, lines_gausslines_gausslines_gaussLinesGaussLinesGauss, lines_facetlines_facetlines_facetLinesFacetLinesFacet, edges_sub_pixedges_sub_pixedges_sub_pixEdgesSubPixEdgesSubPix, smooth_contours_xldsmooth_contours_xldsmooth_contours_xldSmoothContoursXldSmoothContoursXld

Possible Successors

gen_ellipse_contour_xldgen_ellipse_contour_xldgen_ellipse_contour_xldGenEllipseContourXldGenEllipseContourXld, disp_circledisp_circledisp_circleDispCircleDispCircle, get_points_ellipseget_points_ellipseget_points_ellipseGetPointsEllipseGetPointsEllipse

See also

fit_ellipse_contour_xldfit_ellipse_contour_xldfit_ellipse_contour_xldFitEllipseContourXldFitEllipseContourXld, fit_line_contour_xldfit_line_contour_xldfit_line_contour_xldFitLineContourXldFitLineContourXld

Module

Foundation