Operators

# 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).

## 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.

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.