Operators

# elliptic_axis (Operator)

## Name

elliptic_axis — Parameters of the equivalent ellipse.

## Signature

elliptic_axis(Regions : : : Ra, Rb, Phi)

## Description

The operator elliptic_axis calculates the radii Ra and Rb and the orientation Phi of the ellipse having the same orientation and the same aspect ratio as the input region in Regions. Several input regions can be passed as tuples. Ra represents the main radius of the ellipse whereas the radius Rb represents the secondary radius of the ellipse. The orientation of the main axis with regard to the x-axis is returned in Phi which is represented in radians. The principle axis of the ellipse is equivalent to the principle axis of the inertia moment of the input region.

Calculation:

If the moments M20, M02 and M11 are normalized and passed to the area (see moments_region_2nd), the radii Ra and Rb are calculated as:

```
Ra = sqrt(8.0*(M20+M02+sqrt((M20-M02)^2+4.0*M11^2)))/2.0
Rb = sqrt(8.0*(M20+M02-sqrt((M20-M02)^2+4.0*M11^2)))/2.0

```

The orientation Phi is defined by:

```        Phi = -0.5 * atan2(2.0 * M11,M02 - M20)
```

If more than one region is passed, the results are stored in tuples. The index of an resulting tuple element corresponds to the index of the respective input region.

If an empty region is passed, all parameters have the value 0.0 if no other behavior was set (see set_system('no_object_result',<Result>)).

## Attention

It should be noted that, like for all region-moments-based operators, the region's pixels are regarded as mathematical, infinitely small points that are represented by the center of the pixels. This means that Ra and Rb can assume the value 0. In particular, for an empty region and a region containing a single point Ra = Rb = 0 is returned. Furthermore, for regions whose points lie exactly on a straight line (e.g., one pixel high horizontal regions or one pixel wide vertical regions), Rb = 0 is returned.

## Parallelization

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

## Parameters

Regions (input_object)  region(-array) object

Input region(s).

Ra (output_control)  real(-array) (real)

Main radius (normalized to the area).

Assertion: Ra >= 0.0

Rb (output_control)  real(-array) (real)

Secondary radius (normalized to the area).

Assertion: Rb >= 0.0 && Rb <= Ra

Phi (output_control)  real(-array) (real)

Assertion: - pi / 2 < Phi && Phi <= pi / 2

## Example (HDevelop)

```read_image(Image,'fabrik')
open_window(0,0,-1,-1,'root','visible','',WindowHandle)
regiongrowing(Image,Seg,5,5,6,100)
elliptic_axis(Seg,Ra,Rb,Phi)
area_center(Seg,_,Row,Column)
gen_ellipse(Ellipses,Row,Column,Phi,Ra,Rb)
set_draw(WindowHandle,'margin')
disp_region(Ellipses,WindowHandle)
```

## Complexity

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

## Result

The operator elliptic_axis 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.