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# RegionMoment

Header: | AVL.h |
---|---|

Namespace: | avl |

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

### Syntax

C++

C#

void avl::RegionMoment ( const avl::Region& inRegion, avl::RegionMomentType::Type inMomentType, bool inCentral, float& outMoment, float& outNormMoment )

### Parameters

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

inRegion | const Region& | Input region | ||

inMomentType | RegionMomentType::Type | |||

inCentral | bool | |||

outMoment | float& | |||

outNormMoment | float& |

### 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

List of possible exceptions:

Error type | Description |
---|---|

DomainError |
Empty region on input in RegionMoment. |

DomainError |
Not supported moment type in RegionMoment. |

### 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.