# moments_region_3rd (Operator)

## Name

`moments_region_3rd` — Geometric moments of regions.

## Signature

`moments_region_3rd(Regions : : : M21, M12, M03, M30)`

## Description

The operator `moments_region_3rd` calculates the translation-invariant central moments (`M21`, `M12`, `M03`, `M30`) of order p+q.

Calculation:

x and y are the coordinates of the center of a region R with the area Z.

Then the moments are defined by:

,

wherein are .

If more than one region is passed the results are stored in tuples, the index of a value in the tuple corresponding to the index of a region in the input.

In case of empty region all parameters have the value 0.0 if no other behavior was set (see `set_system`).

## Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Automatically parallelized on tuple level.

## Parameters

`Regions` (input_object)  region(-array) `→` object

Regions to be examined.

`M21` (output_control)  real(-array) `→` (real)

Moment of 3rd order (line-dependent).

`M12` (output_control)  real(-array) `→` (real)

Moment of 3rd order (column-dependent).

`M03` (output_control)  real(-array) `→` (real)

Moment of 3rd order (column-dependent).

`M30` (output_control)  real(-array) `→` (real)

Moment of 3rd order (line-dependent).

## Complexity

If Z is the area of the region the mean runtime complexity is O(sqrt(Z)).

## Result

The operator `moments_region_3rd` returns the value 2 (H_MSG_TRUE) if the input is not empty. The behavior in case of empty input (no input regions available) is set via the operator `set_system('no_object_result',<Result>)`. The behavior in case of empty region (the region is the empty set) is set via `set_system('empty_region_result',<Result>)`. If necessary an exception is raised.

## Possible Predecessors

`threshold`, `regiongrowing`, `connection`

## Alternatives

`moments_region_2nd`

## See also

`elliptic_axis`

Foundation