moments_region_2ndmoments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2nd (Operator)

Name

moments_region_2ndmoments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2nd — Geometric moments of regions.

Signature

Description

The operator moments_region_2ndmoments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2nd calculates the moments (M20M20M20M20m20, M02M02M02M02m02) and the product of inertia of the axes through the center parallel to the coordinate axes (M11M11M11M11m11). Furthermore the main axes of inertia (IaIaIaIaia, IbIbIbIbib) are calculated.

Calculation:

Z0 and S0 are the coordinates of the center of a region R with the area F. Then the moments Mij are defined by:

Mij = SUM ( (Z0 - Z)^i (S0 - S)^j )

wherein Z and S run through all pixels of the region R.

Furthermore,

h = (M20 + M02) / 2.

then IaIaIaIaia and IbIbIbIbib are defined by:

IaIaIaIaia = h + sqrt ( h^2 - M20 x M02 + M11^2)

IbIbIbIbib = h - sqrt ( h^2 - M20 x M02 + M11^2)

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

Result

The operator moments_region_2ndmoments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2nd 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 (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_2nd_invarmoments_region_2nd_invarmoments_region_2nd_invarMomentsRegion2ndInvarMomentsRegion2ndInvar

See also

elliptic_axiselliptic_axiselliptic_axisEllipticAxisEllipticAxis

Module

Foundation