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Computes the selected moment of an image in regular and normalized (divided by sum of pixel values) variant.

Name Type Description
inImage Image Input image
inRoi Region* Range of pixels to be processed
inMomentType ImageMomentType
inCentral Bool
outMoment Real
outNormMoment Real


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

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

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

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

Hardware Acceleration

This operation supports automatic parallelization for multicore and multiprocessor systems.


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 Black image on input in ImageMoment.
DomainError Empty region on input in ImageMoment.
DomainError Region exceeds an input image in ImageMoment.

Complexity Level

This filter is available on Advanced Complexity Level.

See Also

  • RegionMoment – Computes selected second-order moment of a region in regular and normalized ( divided by region area ) variant.
  • ShapeMoment – Computes the selected second-order moment of a shape in regular and normalized ( divided by shape area ) variant.