# compactness (Operator)

## Name

`compactness` — Shape factor for the compactness of a region.

## Signature

`compactness(Regions : : : Compactness)`

## Description

The operator `compactness` calculates the compactness of the input regions.

Calculation:

If L is the length of the contour (see `contlength`) and F the area of the region the shape factor C is defined as:

C = max(1,C')

In the documentation of this chapter (Regions / Features), you can find an image illustrating regions which vary in their compactness.

The shape factor C of a circle is 1. If the region is long or has holes C is larger than 1. The operator `compactness` responds to the course of the contour (roughness) and to holes. The value of C is clipped to 1.0, because the pixel area of a region can only be an approximation of a real circle's area. This approximation error is bigger for small regions than for large regions.

In case of an empty region the operator `compactness` returns the value 0 if no other behavior was set (see `set_system`). If more than one region is passed the numerical values of the shape factor are stored in a tuple, the position of a value in the tuple corresponding to the position of the region in the input tuple.

## Execution Information

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

## Parameters

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

Region(s) to be examined.

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

Compactness of the input region(s).

Assertion: `Compactness >= 1.0 || Compactness == 0`

## Result

The operator `compactness` 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

`convexity`, `eccentricity`

`contlength`, `area_center`, `select_shape`