moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2nd (Operator)


moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2nd — Calculate the geometric moments of regions.


moments_region_2nd(Regions : : : M11, M20, M02, Ia, Ib)

Herror moments_region_2nd(const Hobject Regions, double* M11, double* M20, double* M02, double* Ia, double* Ib)

Herror T_moments_region_2nd(const Hobject Regions, Htuple* M11, Htuple* M20, Htuple* M02, Htuple* Ia, Htuple* Ib)

void MomentsRegion2nd(const HObject& Regions, HTuple* M11, HTuple* M20, HTuple* M02, HTuple* Ia, HTuple* Ib)

HTuple HRegion::MomentsRegion2nd(HTuple* M20, HTuple* M02, HTuple* Ia, HTuple* Ib) const

double HRegion::MomentsRegion2nd(double* M20, double* M02, double* Ia, double* Ib) const

static void HOperatorSet.MomentsRegion2nd(HObject regions, out HTuple m11, out HTuple m20, out HTuple m02, out HTuple ia, out HTuple ib)

HTuple HRegion.MomentsRegion2nd(out HTuple m20, out HTuple m02, out HTuple ia, out HTuple ib)

double HRegion.MomentsRegion2nd(out double m20, out double m02, out double ia, out double ib)


moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2nd calculates the geometric moments M11M11M11M11m11, M20M20M20M20m20 and M02M02M02M02m02 of the input regions in RegionsRegionsRegionsRegionsregions. Furthermore the major and minor axis of the input regions are calculated and returned in IaIaIaIaia and IbIbIbIbib.

The covariance matrix is given by:

The row-dependent moment of 2nd order is returned in M20M20M20M20m20 and the column-dependent moment of 2nd order is returned in M02M02M02M02m02. The moment M11M11M11M11m11 represents the covariance between the row and column coordinates of the region points.


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_systemSetSystemSetSystemSetSystem).

Execution Information


RegionsRegionsRegionsRegionsregions (input_object)  region(-array) objectHRegionHRegionHobject

Input regions.

M11M11M11M11m11 (output_control)  real(-array) HTupleHTupleHtuple (real) (double) (double) (double)

Product of inertia of the axes through the center parallel to the coordinate axes.

M20M20M20M20m20 (output_control)  real(-array) HTupleHTupleHtuple (real) (double) (double) (double)

Moment of 2nd order (row-dependent).

M02M02M02M02m02 (output_control)  real(-array) HTupleHTupleHtuple (real) (double) (double) (double)

Moment of 2nd order (column-dependent).

IaIaIaIaia (output_control)  real(-array) HTupleHTupleHtuple (real) (double) (double) (double)

Length of the major axis of the input region.

IbIbIbIbib (output_control)  real(-array) HTupleHTupleHtuple (real) (double) (double) (double)

Length of the minor axis of the input region.


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


The operator moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2nd 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>). 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>). If necessary an exception is raised.

Possible Predecessors

thresholdthresholdThresholdThresholdThreshold, regiongrowingregiongrowingRegiongrowingRegiongrowingRegiongrowing, connectionconnectionConnectionConnectionConnection



See also



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