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

Name | Type | Description | |
---|---|---|---|

inRegion | Region | Input region | |

inMomentType | RegionMomentType | ||

inCentral | Bool | ||

outMoment | Real | ||

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

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

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