Approximation of XLD contours by ellipses or elliptic arcs.

::fit_ellipse_contour_xld approximates the XLD contours Contours 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 (Row, Column), the orientation of the main axis Phi, the length of the larger half axis Radius1, and the length of the smaller half axis Radius2 of the underlying ellipse. In addition to that, the angle corresponding to the start point and the end point StartPhi, EndPhi, and the point order along the boundary PointOrder is returned for elliptic arcs. These parameters are set to 0, 2*PI, and 'positive' for closed ellipses. The algorithm used for the fitting of ellipses can be selected via Algorithm: 'fitzgibbon': This approach minimizes the algebraic distance a*Xi^2 + b*Xi*Yi + c*Yi^2 + d*Xi + e*Yi + f between the contour points (Xi,Yi) and the resulting ellipse. The constraint 4ac - b^2 = 1 guarantees that the resulting polynom 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. 'ftukey': Similar to 'fitzgibbon'. Here the contour points are weighted to decrease the impact of outliers based on the approach of Tukey. '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 choosen 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. VossTabSize 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 VossTabSize) to ::fit_ellipse_contour_xld. 'focpoints': Each point P on an ellipse satisfies the constraint that the sum of distances to the focal points F1,F2 equals twice the length of the larger half axis a. In this approach, the deviation PF1 + PF2 - 2a 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. 'fptukey': Similar to 'focpoints'. Here a weighted least squares optimization is done to decrease the impact of outliers based on the approach of Tukey. 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 ClippingFactor (a scaling factor for the standard deviation) controls the amount of damping outliers: The smaller the value chosen for ClippingFactor the more outliers are detected. The detection of outliers and the least squares fitting in the mode 'focpoints' is repeated. The parameter Iterations specifies the number of iterations.

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 MaxNumPoints, only up to MaxNumPoints 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 refering to the main axis of the ellipse 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 ellipses instead of elliptic 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 at the beginning and at the end of a contour from the fitting of ellipses. However, they are still used for the determination of StartPhi and EndPhi.

read_image (Image, "caltab");
find_caltab (Image, &Caltab, "caltabBig.descr", 3, 112, 5)
reduce_domain (Image, Caltab, &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);

::fit_ellipse_contour_xld returns H_MSG_TRUE if all parameter values are correct, and ellipses 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.

::gen_contours_skeleton_xld, ::lines_gauss, ::lines_facet, ::edges_sub_pix, ::smooth_contours_xld

::gen_ellipse_contour_xld, ::disp_ellipse, ::get_points_ellipse

::fit_line_contour_xld

Sub-pixel operators