Operators

# moments_region_central (Operator)

## Name

moments_region_central — Geometric moments of regions.

## Signature

moments_region_central(Regions : : : I1, I2, I3, I4)

## Description

The operator moments_region_central calculates the central moments (I1, I2, I3, I4).

``` Calculation: Then the moments Ii  are defined by:

I1 = MU20 MU02 - MU11^2
I2 = (MU30 MU03 - MU21  MU12)^2
-4(MU30 MU12 - MU21^2)(MU21  MU03 - MU12^2)
I3 = MU20 (MU21 MU03 - MU12^2) - MU11(MU30 MU03
- MU21  MU12) + MU02 (MU30 MU12 - MU21^2)
I4 = MU30^2 MU02^3 - 6 MU30 MU21 MU11 MU02^2 +
6 MU30 MU12  MU02 (2 MU11^2 - MU20  MU02)
+ MU30 MU03 (6 MU20 MU11 MU02 - 8 MU11^3) +
9{MU21^2} MU20 MU02^2 - 18 MU21 MU12 MU20 MU11 MU02
+ 6 MU21 MU03 MU20 (2 MU11^2 - MU20 MU02)+
9 MU12^2 MU20^2 MU02 -
6 MU12 MU03 MU11 MU20^2 + MU03^2 MU20^3
```

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).

## Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Automatically parallelized on tuple level.

## Parameters

Regions (input_object)  region(-array) object

Regions to be examined.

I1 (output_control)  real(-array) (real)

Moment of 2nd order.

I2 (output_control)  real(-array) (real)

Moment of 2nd order.

I3 (output_control)  real(-array) (real)

Moment of 2nd order.

I4 (output_control)  real(-array) (real)

Moment of 3rd order.

## Complexity

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

## Result

The operator moments_region_central 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.