elliptic_axis_xldelliptic_axis_xldEllipticAxisXldEllipticAxisXldelliptic_axis_xld (Operator)

Name

elliptic_axis_xldelliptic_axis_xldEllipticAxisXldEllipticAxisXldelliptic_axis_xld — Parameters of the equivalent ellipse of contours or polygons.

Signature

Description

The operator elliptic_axis_xldelliptic_axis_xldEllipticAxisXldEllipticAxisXldEllipticAxisXldelliptic_axis_xld calculates the radii and the orientations of the ellipses having the same orientation and the same aspect ratio as the input contours or polygons. The length of the major radius RaRaRaRarara and the minor radius RbRbRbRbrbrb as well as the orientation of the main axis with regard to the horizontal (PhiPhiPhiPhiphiphi) are determined. The angle is indicated in radians. It is assumed that the contours or polygons are closed. If this is not the case elliptic_axis_xldelliptic_axis_xldEllipticAxisXldEllipticAxisXldEllipticAxisXldelliptic_axis_xld will artificially close the contours or polygons.

Calculation: If the moments , and are normalized and passed to the area (see moments_xldmoments_xldMomentsXldMomentsXldMomentsXldmoments_xld), the radii RaRaRaRarara and RbRbRbRbrbrb are calculated as: The orientation PhiPhiPhiPhiphiphi is defined by:

It should be noted that elliptic_axis_xldelliptic_axis_xldEllipticAxisXldEllipticAxisXldEllipticAxisXldelliptic_axis_xld only returns useful results if the contour or polygon encloses a region in the plane. In particular, the contour or polygon must not intersect itself. This is particularly important if open contours or polygons are passed because they are closed automatically, which can produce a self-intersection. To test whether the contours or polygons intersect themselves, test_self_intersection_xldtest_self_intersection_xldTestSelfIntersectionXldTestSelfIntersectionXldTestSelfIntersectionXldtest_self_intersection_xld can be used. If the contour or polygon intersects itself, useful values for the ellipse parameters can be calculated with elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXldEllipticAxisPointsXldelliptic_axis_points_xld.

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 XLDXLDXLDXLDXLDxld.

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

If N is the number of contour or polygon points, the runtime complexity is O(N).

Result

elliptic_axis_xldelliptic_axis_xldEllipticAxisXldEllipticAxisXldEllipticAxisXldelliptic_axis_xld returns TRUE if the input is not empty. 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.

Possible Predecessors

gen_contours_skeleton_xldgen_contours_skeleton_xldGenContoursSkeletonXldGenContoursSkeletonXldGenContoursSkeletonXldgen_contours_skeleton_xld, edges_sub_pixedges_sub_pixEdgesSubPixEdgesSubPixEdgesSubPixedges_sub_pix, threshold_sub_pixthreshold_sub_pixThresholdSubPixThresholdSubPixThresholdSubPixthreshold_sub_pix, gen_contour_polygon_xldgen_contour_polygon_xldGenContourPolygonXldGenContourPolygonXldGenContourPolygonXldgen_contour_polygon_xld, test_self_intersection_xldtest_self_intersection_xldTestSelfIntersectionXldTestSelfIntersectionXldTestSelfIntersectionXldtest_self_intersection_xld

Possible Successors

area_center_xldarea_center_xldAreaCenterXldAreaCenterXldAreaCenterXldarea_center_xld, gen_ellipse_contour_xldgen_ellipse_contour_xldGenEllipseContourXldGenEllipseContourXldGenEllipseContourXldgen_ellipse_contour_xld

Alternatives

elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXldEllipticAxisPointsXldelliptic_axis_points_xld, smallest_rectangle2smallest_rectangle2SmallestRectangle2SmallestRectangle2SmallestRectangle2smallest_rectangle2

See also

moments_xldmoments_xldMomentsXldMomentsXldMomentsXldmoments_xld, smallest_circle_xldsmallest_circle_xldSmallestCircleXldSmallestCircleXldSmallestCircleXldsmallest_circle_xld, smallest_rectangle1_xldsmallest_rectangle1_xldSmallestRectangle1XldSmallestRectangle1XldSmallestRectangle1Xldsmallest_rectangle1_xld, smallest_rectangle2_xldsmallest_rectangle2_xldSmallestRectangle2XldSmallestRectangle2XldSmallestRectangle2Xldsmallest_rectangle2_xld, shape_trans_xldshape_trans_xldShapeTransXldShapeTransXldShapeTransXldshape_trans_xld

References

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

Module

Foundation