fit_circle_contour_xld — Approximate XLD contours by circles.
fit_circle_contour_xld approximates the XLD contours Contours 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 (Row, Column), and the Radius.
The algorithm used for the fitting of circles can be selected via Algorithm:
This approach minimizes the algebraic distance between the contour points and the resulting circle.
Similar to 'algebraic'. Here the contour points are weighted to decrease the impact of outliers based on the approach of Huber (see below).
Similar to 'algebraic'. Here the contour points are weighted to decrease the impact of outliers based on the approach of Tukey (see below).
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.
Similar to 'geometric'. Here the contour points are weighted to decrease the impact of outliers based on the approach of Huber (see below).
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 ClippingFactor (a scaling factor for the standard deviation) controls the amount of outliers: the smaller the value chosen for ClippingFactor 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 Iterations specifies the number of iterations for the algorithms 'algebraic', 'ahuber' and 'atukey'. This parameter is ignored for the algorithms 'geometric', 'geohuber' and 'geotukey'. If Iterations 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 MaxNumPoints, only up to MaxNumPoints 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 StartPhi and EndPhi, see also gen_ellipse_contour_xld. Contours, for which the distance between their start points and their end points is less or equal MaxClosureDist 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 ClippingEndPoints 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 StartPhi and EndPhi.
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*ClippingEndPoints .
Algorithm for the fitting of circles.
Default value: 'algebraic'
List of values: 'ahuber', 'algebraic', 'atukey', 'geohuber', 'geometric', 'geotukey'
Maximum number of contour points used for the computation (-1 for all points).
Default value: -1
Restriction: MaxNumPoints >= 3
Maximum distance between the end points of a contour to be considered as 'closed'.
Default value: 0.0
Restriction: MaxClosureDist >= 0.0
Number of points at the beginning and at the end of the contours to be ignored for the fitting.
Default value: 0
Restriction: ClippingEndPoints >= 0
Maximum number of iterations for the robust weighted fitting.
Default value: 3
Restriction: Iterations >= 0
Clipping factor for the elimination of outliers (typical: 1.0 for Huber and 2.0 for Tukey).
Default value: 2.0
List of values: 1.0, 1.5, 2.0, 2.5, 3.0
Restriction: ClippingFactor > 0
Row coordinate of the center of the circle.
Column coordinate of the center of the circle.
Radius of circle.
Angle of the start point [rad].
Angle of the end point [rad].
Point order along the boundary.
List of values: 'negative', 'positive'
fit_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 behaviour can be set via set_system('no_object_result',<Result>). If necessary, an exception is raised. If the parameter ClippingFactor is chosen too small, i.e., all points are classified as outliers, the error 3264 is raised.
gen_contours_skeleton_xld, lines_gauss, lines_facet, edges_sub_pix, smooth_contours_xld
gen_ellipse_contour_xld, disp_circle, get_points_ellipse
fit_ellipse_contour_xld, fit_line_contour_xld, fit_rectangle2_contour_xld