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RegionMoment


Module: FoundationBasic

Computes selected second-order moment of a region in regular and normalized ( divided by region area ) variant.

Name Type Description
Input value
inRegion Region Input region
Input value
inMomentType RegionMomentType
Input value
inCentral Bool
Output value
outMoment Real
Output value
outNormMoment Real

Description

The operation computes the mathematical features of a shape called moments. Those are sums computed as follows:

\[ \begin{aligned} Moment_{2,0}(R) &= \sum_{p \in R} p_x^2 \\ Moment_{1,1}(R) &= \sum_{p \in R} p_x p_y \\ Moment_{0,2}(R) &= \sum_{p \in R} p_y^2 \end{aligned} \]

The summing is conducted over region pixels, while \( p_x \) and \( p_y \) denote, accordingly, x and y coordinate of a pixel.

When inCentral parameter is set, the region is shifted before computations, so that its mass center is at location (0,0).

Hints

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

Errors

This filter can throw an exception to report error. Read how to deal with errors in Error Handling.

List of possible exceptions:

Error type Description
DomainError Empty region on input in RegionMoment.
DomainError Not supported moment type in RegionMoment.

Complexity Level

This filter is available on Basic Complexity Level.

See Also

  • PolygonMoment – Computes the selected second-order moment of a polygon in regular and normalized ( divided by polygon area ) variant.
  • ImageMoment – Computes the selected moment of an image in regular and normalized (divided by sum of pixel values) variant.