moments_region_centralmoments_region_centralmoments_region_centralMomentsRegionCentralMomentsRegionCentral (Operator)

Name

moments_region_centralmoments_region_centralmoments_region_centralMomentsRegionCentralMomentsRegionCentral — Geometric moments of regions.

Signature

Description

The operator moments_region_centralmoments_region_centralmoments_region_centralMomentsRegionCentralMomentsRegionCentral calculates the central moments (I1I1I1I1i1, I2I2I2I2i2, I3I3I3I3i3, I4I4I4I4i4).

 Calculation: Then the moments Ii  are defined by:

      I1 = MU20 MU02 - MU11^2
      I2 = (MU30 MU03 - MU21  MU12)^2
           -4(MU30 MU12 - MU21^2)(MU21  MU03 - MU12^2)
      I3 = MU20 (MU21 MU03 - MU12^2) - MU11(MU30 MU03
           - MU21  MU12) + MU02 (MU30 MU12 - MU21^2)
      I4 = MU30^2 MU02^3 - 6 MU30 MU21 MU11 MU02^2 +
           6 MU30 MU12  MU02 (2 MU11^2 - MU20  MU02)
           + MU30 MU03 (6 MU20 MU11 MU02 - 8 MU11^3) +
           9{MU21^2} MU20 MU02^2 - 18 MU21 MU12 MU20 MU11 MU02
           + 6 MU21 MU03 MU20 (2 MU11^2 - MU20 MU02)+
           9 MU12^2 MU20^2 MU02 -
           6 MU12 MU03 MU11 MU20^2 + MU03^2 MU20^3

If more than one region is passed the results are stored in tuples, the index of a value in the tuple corresponding to the index of a region in the input.

In case of empty region all parameters have the value 0.0 if no other behavior was set (see set_systemset_systemset_systemSetSystemSetSystem).

Parallelization

• 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 Z is the area of the region the mean runtime complexity is O(sqrt(Z)).

Result

The operator moments_region_centralmoments_region_centralmoments_region_centralMomentsRegionCentralMomentsRegionCentral returns the value 2 (H_MSG_TRUE) if the input is not empty. The behavior in case of empty input (no input regions available) is set via the operator set_system('no_object_result',<Result>)set_system("no_object_result",<Result>)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>). The behavior in case of empty region (the region is the empty set) is set via set_system('empty_region_result',<Result>)set_system("empty_region_result",<Result>)set_system("empty_region_result",<Result>)SetSystem("empty_region_result",<Result>)SetSystem("empty_region_result",<Result>). If necessary an exception is raised.

Possible Predecessors

thresholdthresholdthresholdThresholdThreshold, regiongrowingregiongrowingregiongrowingRegiongrowingRegiongrowing, connectionconnectionconnectionConnectionConnection

Alternatives

moments_region_2ndmoments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2nd

See also

elliptic_axiselliptic_axiselliptic_axisEllipticAxisEllipticAxis

Module

Foundation