elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXldelliptic_axis_points_xld (Operator)

Name

elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXldelliptic_axis_points_xld — Parameters of the equivalent ellipse of contours or polygons treated as point clouds.

Signature

Description

The operator elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXldelliptic_axis_points_xld calculates the radii (RaRaRarara, RbRbRbrbrb) and the orientation (PhiPhiPhiphiphi, in radians) of the ellipse having the same orientation and the same aspect ratio as the point cloud given by the contour or polygon XLDXLDXLDXLDxld (i.e., the order of the points in the contour or polygon is not taken into account). If the contour or polygon is closed (end point = start point), the end point of the contour or polygon is not taken into account to avoid that it receives twice the weight of the other points.

Calculation: If the moments , and are normalized to the area (see moments_points_xldmoments_points_xldMomentsPointsXldMomentsPointsXldmoments_points_xld), the major radius RaRaRarara and the minor radius RbRbRbrbrb are calculated as: The orientation PhiPhiPhiphiphi, i.e., the angle between the major axis and the x (column) axis, is defined by:

elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXldelliptic_axis_points_xld should be used if the contour XLDXLDXLDXLDxld intersects itself or if it is not possible to close the contour using a line from end to start point without self-intersection, because in this case elliptic_axis_xldelliptic_axis_xldEllipticAxisXldEllipticAxisXldelliptic_axis_xld does not produce useful results. To test whether the contours or polygons intersect themselves, test_self_intersection_xldtest_self_intersection_xldTestSelfIntersectionXldTestSelfIntersectionXldtest_self_intersection_xld can be used.

If more than one contour or polygon is passed, the results are stored in tuples in the same order as the respective contours or polygons in XLDXLDXLDXLDxld.

Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Automatically parallelized on tuple level.

Parameters

Complexity

Let n be the number of points of the contour or polygon. Then the run time is O(n).

Result

elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXldelliptic_axis_points_xld returns 2 ( H_MSG_TRUE) if the input is not empty. If the input is empty the behavior can be set via set_system(::'no_object_result',<Result>:). If necessary, an exception is raised.

Possible Predecessors

gen_contours_skeleton_xldgen_contours_skeleton_xldGenContoursSkeletonXldGenContoursSkeletonXldgen_contours_skeleton_xld, edges_sub_pixedges_sub_pixEdgesSubPixEdgesSubPixedges_sub_pix, threshold_sub_pixthreshold_sub_pixThresholdSubPixThresholdSubPixthreshold_sub_pix, gen_contour_polygon_xldgen_contour_polygon_xldGenContourPolygonXldGenContourPolygonXldgen_contour_polygon_xld, test_self_intersection_xldtest_self_intersection_xldTestSelfIntersectionXldTestSelfIntersectionXldtest_self_intersection_xld

Possible Successors

area_center_points_xldarea_center_points_xldAreaCenterPointsXldAreaCenterPointsXldarea_center_points_xld, gen_ellipse_contour_xldgen_ellipse_contour_xldGenEllipseContourXldGenEllipseContourXldgen_ellipse_contour_xld

Alternatives

elliptic_axis_xldelliptic_axis_xldEllipticAxisXldEllipticAxisXldelliptic_axis_xld, smallest_rectangle2smallest_rectangle2SmallestRectangle2SmallestRectangle2smallest_rectangle2

See also

moments_xldmoments_xldMomentsXldMomentsXldmoments_xld, smallest_circle_xldsmallest_circle_xldSmallestCircleXldSmallestCircleXldsmallest_circle_xld, smallest_rectangle1_xldsmallest_rectangle1_xldSmallestRectangle1XldSmallestRectangle1Xldsmallest_rectangle1_xld, smallest_rectangle2_xldsmallest_rectangle2_xldSmallestRectangle2XldSmallestRectangle2Xldsmallest_rectangle2_xld, shape_trans_xldshape_trans_xldShapeTransXldShapeTransXldshape_trans_xld

References

R. Haralick, L. Shapiro “Computer and Robot Vision” Addison-Wesley, 1992, pp. 73-75

Module

Foundation