rectangularityrectangularityRectangularityRectangularity (Operator)


rectangularityrectangularityRectangularityRectangularity — Shape factor for the rectangularity of a region.


rectangularity(Regions : : : Rectangularity)

Herror rectangularity(const Hobject Regions, double* Rectangularity)

Herror T_rectangularity(const Hobject Regions, Htuple* Rectangularity)

void Rectangularity(const HObject& Regions, HTuple* Rectangularity)

HTuple HRegion::Rectangularity() const

static void HOperatorSet.Rectangularity(HObject regions, out HTuple rectangularity)

HTuple HRegion.Rectangularity()


The operator rectangularityrectangularityRectangularityRectangularityRectangularity calculates the rectangularity of the input regions.

To determine the rectangularity, first a rectangle is computed that has the same first and second order moments as the input region. The computation of the rectangularity measure is finally based on the area of the difference between the computed rectangle and the input region normalized with respect to the area of the rectangle.

In the documentation of this chapter (Regions / Features), you can find an image illustrating regions which vary in their rectangularity.

For rectangles rectangularityrectangularityRectangularityRectangularityRectangularity returns the value 1. The more the input region deviates from a perfect rectangle, the less the returned value for RectangularityRectangularityRectangularityRectangularityrectangularity will be.

In case of an empty region the operator rectangularityrectangularityRectangularityRectangularityRectangularity returns the value 0 (if no other behavior was set (see set_systemset_systemSetSystemSetSystemSetSystem)). If more than one region is passed the numerical values of the rectangularity are stored in a tuple, the position of a value in the tuple corresponding to the position of the region in the input tuple.


For input regions which orientation cannot be computed by using second order moments (as it is the case for square regions, for example), the returned RectangularityRectangularityRectangularityRectangularityrectangularity is underestimated by up to 10% depending on the orientation of the input region.

Execution Information


RegionsRegionsRegionsRegionsregions (input_object)  region(-array) objectHRegionHRegionHobject

Region(s) to be examined.

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

Rectangularity of the input region(s).

Assertion: 0 <= Rectangularity && Rectangularity <= 1.0


The operator rectangularityrectangularityRectangularityRectangularityRectangularity 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 (the 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


circularitycircularityCircularityCircularityCircularity, compactnesscompactnessCompactnessCompactnessCompactness, convexityconvexityConvexityConvexityConvexity, eccentricityeccentricityEccentricityEccentricityEccentricity

See also

contlengthcontlengthContlengthContlengthContlength, area_centerarea_centerAreaCenterAreaCenterAreaCenter, select_shapeselect_shapeSelectShapeSelectShapeSelectShape


P. L. Rosin: “Measuring rectangularity”; Machine Vision and Applications; vol. 11; pp. 191-196; Springer-Verlag, 1999.