# moments_region_2nd_invar (Operator)

## Name

`moments_region_2nd_invar` — Geometric moments of regions.

## Signature

`moments_region_2nd_invar(Regions : : : M11, M20, M02)`

## Description

The operator `moments_region_2nd_invar` calculates the scaled moments (`M20`, `M02`) and the procut of inertia of the axes through the center parallel to the coordinate axes (`M11`).

Calculation:

and are the coordinates of the center of a region R with the area F. Then the moments are defined by:

,

wherein Z and S run through all pixels of the region R.

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).
• Automatically parallelized on tuple level.

## Parameters

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

Regions to be examined.

`M11` (output_control)  real(-array) `→` (real)

Product of inertia of the axes through the center parallel to the coordinate axes.

`M20` (output_control)  real(-array) `→` (real)

Moment of 2nd order (line-dependent).

`M02` (output_control)  real(-array) `→` (real)

Moment of 2nd order (column-dependent).

## Complexity

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

## Result

The operator `moments_region_2nd_invar` 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`

`elliptic_axis`