moments_points_xldmoments_points_xldMomentsPointsXldmoments_points_xldMomentsPointsXldMomentsPointsXld (Operator)

Name

moments_points_xldmoments_points_xldMomentsPointsXldmoments_points_xldMomentsPointsXldMomentsPointsXld — Geometric moments , , and of contours or polygons treated as point clouds.

Signature

moments_points_xld(XLD : : : M11, M20, M02)

moments_points_xldmoments_points_xldMomentsPointsXldmoments_points_xldMomentsPointsXldMomentsPointsXld calculates the moments (M20M20M20M20M20m20, M02M02M02M02M02m02, and M11M11M11M11M11m11) of a point cloud given by a contour or a polygon XLDXLDXLDXLDXLDXLD (i.e., the order of the points in the contour or polygon is not taken into account). Therefore, the moments are given by

Here, is the centroid and n the number of points.

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.

moments_points_xldmoments_points_xldMomentsPointsXldmoments_points_xldMomentsPointsXldMomentsPointsXld should be used if the contour XLDXLDXLDXLDXLDXLD 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 moments_xldmoments_xldMomentsXldmoments_xldMomentsXldMomentsXld does not produce useful results. To test whether the contours or polygons intersect themselves, test_self_intersection_xldtest_self_intersection_xldTestSelfIntersectionXldtest_self_intersection_xldTestSelfIntersectionXldTestSelfIntersectionXld 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 XLDXLDXLDXLDXLDXLD.