eccentricityeccentricityeccentricityEccentricityEccentricity (Operator)

Name

eccentricityeccentricityeccentricityEccentricityEccentricity — Shape features derived from the ellipse parameters.

Signature

Description

The operator eccentricityeccentricityeccentricityEccentricityEccentricity calculates three shape features derived from the geometric moments.

Definition: If the ellipse radii Ra, Rb and the area A of the
            region are given (see elliptic_axiselliptic_axiselliptic_axisEllipticAxisEllipticAxis),
            the following applies:

   AnisometryAnisometryAnisometryAnisometryanisometry = Ra / Rb

   BulkinessBulkinessBulkinessBulkinessbulkiness = pi Ra Rb / A

   StructureFactorStructureFactorStructureFactorStructureFactorstructureFactor = AnisometryAnisometryAnisometryAnisometryanisometry * BulkinessBulkinessBulkinessBulkinessbulkiness - 1

 

Attention

It should be noted that, like for all region-moments-based operators, the region's pixels are regarded as mathematical, infinitely small points that are represented by the center of the pixels (see the documentation of elliptic_axiselliptic_axiselliptic_axisEllipticAxisEllipticAxis). This can lead to non-empty regions that have RbRbRbRbrb = 0. In these cases, the output features that require a division by RbRbRbRbrb are set to 0. In particular, regions that contain a single point or regions whose points lie exactly on a straight line (e.g., one pixel high horizontal regions or one pixel wide vertical regions) have an anisometry of 0.

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 eccentricityeccentricityeccentricityEccentricityEccentricity 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

See also

elliptic_axiselliptic_axiselliptic_axisEllipticAxisEllipticAxis, moments_region_2ndmoments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2nd, select_shapeselect_shapeselect_shapeSelectShapeSelectShape, area_centerarea_centerarea_centerAreaCenterAreaCenter

Module

Foundation