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Header: AVL.h
Namespace: avl
Module: FoundationBasic

Computes the area of a region divided by the area of a circular region having the same feature.


void avl::RegionCircularity
	const avl::Region& inRegion,
	const avl::CircularityMeasure::Type inCircularityMeasure,
	float& outCircularity,
	avl::Circle2D& diagCircle


Name Type Default Description
Input value
inRegion const Region& Input region
Input value
inCircularityMeasure const CircularityMeasure::Type RadiusPreserving Which algorithm should be used to compute a circle
Output value
outCircularity float&
Diagnostic input
diagCircle Circle2D& Computed circle which area was compared.


Circularity is a measure of similarity of a region shape to the perfect circle. Circular regions have circularity close to 1.0, while the more elongated the region is (or contains more holes), the closer to 0.0 is its circularity.

Mathematically, the circularity is calculated as follows: Where c denotes a circular region having the same feature as input region r. The feature being considered depends on the inCircularityMeasure chosen and it is:

  • the minimal bounding circle in case of BoundingCirclePreserving
  • the perimeter in case of PerimeterPreserving
  • the radius (maximal distance from mass center to any of the region pixels) in case of RadiusPreserving


  • If the input region is not guaranteed to be non-empty, precede this filter with SkipEmptyRegion.


Circularity with RadiusPreserving of the sample region equals to 0.667.

Circularity with PerimeterPreserving of the sample region equals to 1.000.


List of possible exceptions:

Error type Description
DomainError Empty region on input in RegionCircularity.
DomainError Not supported circularity measure in RegionCircularity.

See Also

  • RegionConvexity – Computes the area of a region divided by area of its convex hull.
  • RegionElongation – Computes the elongation factor of a region ( perfect circle has minimal elongation equal 1.0 ).
  • PolygonCircularity – Computes the area of a polygon divided by the area of a circle having the same feature.