moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd (Operator)

Name

moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd — Calculate the geometric moments of regions.

Signature

Description

moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd calculates the geometric moments M11M11M11M11m11m11, M20M20M20M20m20m20 and M02M02M02M02m02m02 of the input regions in RegionsRegionsRegionsRegionsregionsregions. Furthermore the major and minor axis of the input regions are calculated and returned in IaIaIaIaiaia and IbIbIbIbibib.

The covariance matrix is given by:

The row-dependent moment of 2nd order is returned in M20M20M20M20m20m20 and the column-dependent moment of 2nd order is returned in M02M02M02M02m02m02. The moment M11M11M11M11m11m11 represents the covariance between the row and column coordinates of the region points.

Calculation:

and are the coordinates of the center of gravity of a region R. Then the moments are defined by:

wherein r and c run over all pixels of the region R.

Furthermore the length of the major and minor axes are defined by:

wherein is defined by:

The equation for the major and minor axes can be derived from the definition of the moments by diagonalizing the covariance matrix and reforming the resulting formula.

If more than one region is passed, the results are returned in tuples. The index of a tuple element corresponds to the index of the respective input region.

If an empty region is passed, 0.0 is returned for all parameters, if no other behavior was set (see set_systemset_systemSetSystemSetSystemSetSystemset_system).

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

Result

The operator moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd 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>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)set_system("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>)SetSystem("empty_region_result",<Result>)SetSystem("empty_region_result",<Result>)SetSystem("empty_region_result",<Result>)set_system("empty_region_result",<Result>). If necessary an exception is raised.

Possible Predecessors

thresholdthresholdThresholdThresholdThresholdthreshold, regiongrowingregiongrowingRegiongrowingRegiongrowingRegiongrowingregiongrowing, connectionconnectionConnectionConnectionConnectionconnection

Alternatives

moments_region_2nd_invarmoments_region_2nd_invarMomentsRegion2ndInvarMomentsRegion2ndInvarMomentsRegion2ndInvarmoments_region_2nd_invar

See also

elliptic_axiselliptic_axisEllipticAxisEllipticAxisEllipticAxiselliptic_axis

References

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

Module

Foundation