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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

Description

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.

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 Black image on input in ImageMoment.
DomainError Empty region on input in ImageMoment.

Complexity Level

This filter is available on Advanced Complexity Level.