moments_any_points_xldmoments_any_points_xldMomentsAnyPointsXldMomentsAnyPointsXldmoments_any_points_xld (Operator)

Name

moments_any_points_xldmoments_any_points_xldMomentsAnyPointsXldMomentsAnyPointsXldmoments_any_points_xld — Arbitrary geometric moments of contours or polygons treated as point clouds.

Signature

Description

moments_any_points_xldmoments_any_points_xldMomentsAnyPointsXldMomentsAnyPointsXldMomentsAnyPointsXldmoments_any_points_xld calculates arbitrary moments MMMMmm of the point clouds given by the contours or polygons XLDXLDXLDXLDXLDxld (i.e., the order of the points in the contour or polygon is not taken into account).

The computed moments are normalized depending on the desired mode ModeModeModeModemodemode:

'unnormalized':

No normalization.

'unnormalized_central':

Shift the contour points by their centroid

'normalized':

Normalization by the area A = AreaAreaAreaAreaareaarea

'central':

Normalization by the area A = AreaAreaAreaAreaareaarea and a shift of the contour points by their centroid

For the normalization of the moments three specific values are used: The area AreaAreaAreaAreaareaarea and the coordinates CenterRowCenterRowCenterRowCenterRowcenterRowcenter_row,CenterColCenterColCenterColCenterColcenterColcenter_col of it's centroid (this values can be computed with area_center_points_xldarea_center_points_xldAreaCenterPointsXldAreaCenterPointsXldAreaCenterPointsXldarea_center_points_xld).

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_any_xldmoments_any_xldMomentsAnyXldMomentsAnyXldMomentsAnyXldmoments_any_xld 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_any_xldmoments_any_xldMomentsAnyXldMomentsAnyXldMomentsAnyXldmoments_any_xld does not produce useful results. To test whether the contours or polygons intersect themselves, test_self_intersection_xldtest_self_intersection_xldTestSelfIntersectionXldTestSelfIntersectionXldTestSelfIntersectionXldtest_self_intersection_xld can be used.

If more than one contour or polygon is passed, MMMMmm contains all desired moments of the first contour/polygon followed by all the moments of the second contour/polygon and so forth.

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

Complexity

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

Result

moments_any_points_xldmoments_any_points_xldMomentsAnyPointsXldMomentsAnyPointsXldMomentsAnyPointsXldmoments_any_points_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

area_center_points_xldarea_center_points_xldAreaCenterPointsXldAreaCenterPointsXldAreaCenterPointsXldarea_center_points_xld, gen_contours_skeleton_xldgen_contours_skeleton_xldGenContoursSkeletonXldGenContoursSkeletonXldGenContoursSkeletonXldgen_contours_skeleton_xld, smooth_contours_xldsmooth_contours_xldSmoothContoursXldSmoothContoursXldSmoothContoursXldsmooth_contours_xld, gen_polygons_xldgen_polygons_xldGenPolygonsXldGenPolygonsXldGenPolygonsXldgen_polygons_xld

Alternatives

moments_points_xldmoments_points_xldMomentsPointsXldMomentsPointsXldMomentsPointsXldmoments_points_xld, moments_any_xldmoments_any_xldMomentsAnyXldMomentsAnyXldMomentsAnyXldmoments_any_xld

See also

moments_points_xldmoments_points_xldMomentsPointsXldMomentsPointsXldMomentsPointsXldmoments_points_xld, area_center_points_xldarea_center_points_xldAreaCenterPointsXldAreaCenterPointsXldAreaCenterPointsXldarea_center_points_xld, moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd, area_centerarea_centerAreaCenterAreaCenterAreaCenterarea_center

Module

Foundation