fit_ellipse_contour_xldfit_ellipse_contour_xldFitEllipseContourXldFitEllipseContourXldfit_ellipse_contour_xld (Operator)

Name

fit_ellipse_contour_xldfit_ellipse_contour_xldFitEllipseContourXldFitEllipseContourXldfit_ellipse_contour_xld — Approximate XLD contours by ellipses or elliptic arcs.

Signature

Description

fit_ellipse_contour_xldfit_ellipse_contour_xldFitEllipseContourXldFitEllipseContourXldFitEllipseContourXldfit_ellipse_contour_xld approximates the XLD contours ContoursContoursContoursContourscontourscontours by elliptic arcs or closed ellipses. 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 elliptic structure. The operator returns for each contour the center (RowRowRowRowrowrow, ColumnColumnColumnColumncolumncolumn), the orientation of the main axis PhiPhiPhiPhiphiphi, the length of the larger half axis Radius1Radius1Radius1Radius1radius1radius_1, and the length of the smaller half axis Radius2Radius2Radius2Radius2radius2radius_2 of the underlying ellipse. In addition to that, the angle corresponding to the start point and the end point StartPhiStartPhiStartPhiStartPhistartPhistart_phi, EndPhiEndPhiEndPhiEndPhiendPhiend_phi, and the point order along the boundary PointOrderPointOrderPointOrderPointOrderpointOrderpoint_order is returned for elliptic arcs. These parameters are set to 0, , and 'positive' for closed ellipses. The algorithm used for the fitting of ellipses can be selected via AlgorithmAlgorithmAlgorithmAlgorithmalgorithmalgorithm:

'fitzgibbon'

This approach minimizes the algebraic distance between the contour points and the resulting ellipse. The constraint 4ac - b^2 = 1 guarantees that the resulting polynomial characterizes an ellipse (instead of a hyperbola or a parabola).

'fhuber'

Similar to 'fitzgibbon'. Here the contour points are weighted to decrease the impact of outliers based on the approach of Huber (see below).

'ftukey'

Similar to 'fitzgibbon'. Here the contour points are weighted and outliers are ignored based on the approach of Tukey (see below).

'geometric'

This approach minimizes the geometric distance between the contour points and the resulting ellipse. The distance measure is statistically optimal, but takes more computational time, because the computation is an iterative process. This option is recommended if the contour points are considerably distorted by noise.

'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'

Similar to 'geometric'. Here the contour points are weighted and outliers are ignored based on the approach of Tukey (see below).

'voss'

Each input contour is transformed in an affine standard position. Based on the moments of the transformed contour (that is of the enclosed image region) the standard circular segment is chosen whose standard position matches best with the standard position of the contour. The ellipse corresponding to the standard position of the selected circular segment is re-transformed based on the affine transformation which produced the standard position of the contour resulting in the ellipse matching the original contour. VossTabSizeVossTabSizeVossTabSizeVossTabSizevossTabSizevoss_tab_size standard circular segments are used for this computation. To speed up the process the corresponding moments and other data is stored in a table which is created during the first call (with a specific value for VossTabSizeVossTabSizeVossTabSizeVossTabSizevossTabSizevoss_tab_size) to fit_ellipse_contour_xldfit_ellipse_contour_xldFitEllipseContourXldFitEllipseContourXldFitEllipseContourXldfit_ellipse_contour_xld.

'focpoints'

Each point P on an ellipse satisfies the constraint that the sum of distances to the focal points equals twice the length of the larger half axis a. In this approach, the deviation is minimized for all contour points by a least squares optimization.

'fphuber'

Similar to 'focpoints'. Here a weighted least squares optimization is done to decrease the impact of outliers based on the approach of Huber (see below).

'fptukey'

Similar to 'focpoints'. Here a weighted least squares optimization is done 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 ellipse. The parameter ClippingFactorClippingFactorClippingFactorClippingFactorclippingFactorclipping_factor (a scaling factor for the standard deviation) controls the amount of outliers: the smaller the value chosen for ClippingFactorClippingFactorClippingFactorClippingFactorclippingFactorclipping_factor the more points are classified as outliers. Every contour point is individually weighted and contributes according to its weight in the fitting process. The bundle of robust weighting and fitting can be iterated. The overall number of iterations is given by IterationsIterationsIterationsIterationsiterationsiterations. 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. If the algorithm does not find a fitting ellipse within this number of iterations, it fits a line; in this case Radius2Radius2Radius2Radius2radius2radius_2 is zero. 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 ellipses can be restricted to a subset of the contour points: If a value other than -1 is assigned to MaxNumPointsMaxNumPointsMaxNumPointsMaxNumPointsmaxNumPointsmax_num_points, only up to MaxNumPointsMaxNumPointsMaxNumPointsMaxNumPointsmaxNumPointsmax_num_points points - uniformly distributed over the contour - are used.

For elliptic arcs, the points on the ellipse 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 main axis of the ellipse are returned in StartPhiStartPhiStartPhiStartPhistartPhistart_phi and EndPhiEndPhiEndPhiEndPhiendPhiend_phi, see also gen_ellipse_contour_xldgen_ellipse_contour_xldGenEllipseContourXldGenEllipseContourXldGenEllipseContourXldgen_ellipse_contour_xld. Contours, for which the distance between their start points and their end points is less or equal MaxClosureDistMaxClosureDistMaxClosureDistMaxClosureDistmaxClosureDistmax_closure_dist are considered to be closed. Thus, they are approximated by ellipses instead of elliptic arcs. The 'focpoints' algorithms determine the initial parameters for the optimization for closed contours in a faster and less accurate way than for open contours. As a result, in some cases more IterationsIterationsIterationsIterationsiterationsiterations may be necessary when applied to closed contours. Due to artifacts in the pre-processing the start and end points of a contour might be faulty. Therefore, it is possible to exclude ClippingEndPointsClippingEndPointsClippingEndPointsClippingEndPointsclippingEndPointsclipping_end_points points at the beginning and at the end of a contour from the fitting of ellipses. However, they are still used for the determination of StartPhiStartPhiStartPhiStartPhistartPhistart_phi and EndPhiEndPhiEndPhiEndPhiendPhiend_phi.

The minimum necessary number of contour points for fitting an ellipse is five. 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

read_image (Image, 'caltab')
find_caltab (Image, CalPlate, 'caltab_800mm.descr', 3, 112, 5)
reduce_domain (Image, CalPlate, ImageReduced)
edges_sub_pix (ImageReduced, Edges, 'lanser2', 0.5, 20, 40)
select_contours_xld (Edges, EdgesClosed, 'closed', 0, 2.0, 0, 0)
select_contours_xld (EdgesClosed, EdgesMarks, 'length', 20, 80, 0, 0)
fit_ellipse_contour_xld (EdgesMarks, 'fitzgibbon', -1, 2, 0, 200, 3, 2.0, \
                         Row, Column, Phi, Radius1, Radius2, StartPhi, \
                         EndPhi, PointOrder)
gen_ellipse_contour_xld (EllMarks, Row, Column, Phi, Radius1, Radius2, \
                         StartPhi, EndPhi, PointOrder, 1.5)
length_xld(EllMarks,Length)

read_image (Image, 'caltab')
find_caltab (Image, CalPlate, 'caltab_800mm.descr', 3, 112, 5)
reduce_domain (Image, CalPlate, ImageReduced)
edges_sub_pix (ImageReduced, Edges, 'lanser2', 0.5, 20, 40)
select_contours_xld (Edges, EdgesClosed, 'closed', 0, 2.0, 0, 0)
select_contours_xld (EdgesClosed, EdgesMarks, 'length', 20, 80, 0, 0)
fit_ellipse_contour_xld (EdgesMarks, 'fitzgibbon', -1, 2, 0, 200, 3, 2.0, \
                         Row, Column, Phi, Radius1, Radius2, StartPhi, \
                         EndPhi, PointOrder)
gen_ellipse_contour_xld (EllMarks, Row, Column, Phi, Radius1, Radius2, \
                         StartPhi, EndPhi, PointOrder, 1.5)
length_xld(EllMarks,Length)

read_image (Image, 'caltab')
find_caltab (Image, CalPlate, 'caltab_800mm.descr', 3, 112, 5)
reduce_domain (Image, CalPlate, ImageReduced)
edges_sub_pix (ImageReduced, Edges, 'lanser2', 0.5, 20, 40)
select_contours_xld (Edges, EdgesClosed, 'closed', 0, 2.0, 0, 0)
select_contours_xld (EdgesClosed, EdgesMarks, 'length', 20, 80, 0, 0)
fit_ellipse_contour_xld (EdgesMarks, 'fitzgibbon', -1, 2, 0, 200, 3, 2.0, \
                         Row, Column, Phi, Radius1, Radius2, StartPhi, \
                         EndPhi, PointOrder)
gen_ellipse_contour_xld (EllMarks, Row, Column, Phi, Radius1, Radius2, \
                         StartPhi, EndPhi, PointOrder, 1.5)
length_xld(EllMarks,Length)

read_image (Image, 'caltab')
find_caltab (Image, CalPlate, 'caltab_800mm.descr', 3, 112, 5)
reduce_domain (Image, CalPlate, ImageReduced)
edges_sub_pix (ImageReduced, Edges, 'lanser2', 0.5, 20, 40)
select_contours_xld (Edges, EdgesClosed, 'closed', 0, 2.0, 0, 0)
select_contours_xld (EdgesClosed, EdgesMarks, 'length', 20, 80, 0, 0)
fit_ellipse_contour_xld (EdgesMarks, 'fitzgibbon', -1, 2, 0, 200, 3, 2.0, \
                         Row, Column, Phi, Radius1, Radius2, StartPhi, \
                         EndPhi, PointOrder)
gen_ellipse_contour_xld (EllMarks, Row, Column, Phi, Radius1, Radius2, \
                         StartPhi, EndPhi, PointOrder, 1.5)
length_xld(EllMarks,Length)

read_image (Image, 'caltab')
find_caltab (Image, CalPlate, 'caltab_800mm.descr', 3, 112, 5)
reduce_domain (Image, CalPlate, ImageReduced)
edges_sub_pix (ImageReduced, Edges, 'lanser2', 0.5, 20, 40)
select_contours_xld (Edges, EdgesClosed, 'closed', 0, 2.0, 0, 0)
select_contours_xld (EdgesClosed, EdgesMarks, 'length', 20, 80, 0, 0)
fit_ellipse_contour_xld (EdgesMarks, 'fitzgibbon', -1, 2, 0, 200, 3, 2.0, \
                         Row, Column, Phi, Radius1, Radius2, StartPhi, \
                         EndPhi, PointOrder)
gen_ellipse_contour_xld (EllMarks, Row, Column, Phi, Radius1, Radius2, \
                         StartPhi, EndPhi, PointOrder, 1.5)
length_xld(EllMarks,Length)

Result

fit_ellipse_contour_xldfit_ellipse_contour_xldFitEllipseContourXldFitEllipseContourXldFitEllipseContourXldfit_ellipse_contour_xld returns 2 (H_MSG_TRUE) if all parameter values are correct, and ellipses 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>)SetSystem("no_object_result",<Result>)set_system("no_object_result",<Result>). If necessary, an exception is raised. If the parameter ClippingFactorClippingFactorClippingFactorClippingFactorclippingFactorclipping_factor 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_xldGenContoursSkeletonXldGenContoursSkeletonXldGenContoursSkeletonXldgen_contours_skeleton_xld, lines_gausslines_gaussLinesGaussLinesGaussLinesGausslines_gauss, lines_facetlines_facetLinesFacetLinesFacetLinesFacetlines_facet, edges_sub_pixedges_sub_pixEdgesSubPixEdgesSubPixEdgesSubPixedges_sub_pix, smooth_contours_xldsmooth_contours_xldSmoothContoursXldSmoothContoursXldSmoothContoursXldsmooth_contours_xld

Possible Successors

gen_ellipse_contour_xldgen_ellipse_contour_xldGenEllipseContourXldGenEllipseContourXldGenEllipseContourXldgen_ellipse_contour_xld, disp_ellipsedisp_ellipseDispEllipseDispEllipseDispEllipsedisp_ellipse, get_points_ellipseget_points_ellipseGetPointsEllipseGetPointsEllipseGetPointsEllipseget_points_ellipse

See also

fit_line_contour_xldfit_line_contour_xldFitLineContourXldFitLineContourXldFitLineContourXldfit_line_contour_xld, fit_circle_contour_xldfit_circle_contour_xldFitCircleContourXldFitCircleContourXldFitCircleContourXldfit_circle_contour_xld, fit_rectangle2_contour_xldfit_rectangle2_contour_xldFitRectangle2ContourXldFitRectangle2ContourXldFitRectangle2ContourXldfit_rectangle2_contour_xld

Module

Foundation