elliptic_axisEllipticAxisEllipticAxiselliptic_axiselliptic_axis🔗

Short description🔗

elliptic_axisEllipticAxisEllipticAxiselliptic_axiselliptic_axis — Calculate the parameters of the equivalent ellipse.

Signature🔗

elliptic_axis( region Regions, out real Ra, out real Rb, out angle.rad Phi )

Description🔗

The operator elliptic_axisEllipticAxis calculates the radii Rarara and Rbrbrb and the orientation Phiphiphi of the ellipse having the same orientation and the same aspect ratio as the input region in Regionsregionsregions. Several input regions can be passed as tuples. Rarara represents the main radius of the ellipse whereas the radius Rbrbrb represents the secondary radius of the ellipse. The orientation of the main axis with regard to the x-axis is returned in Phiphiphi 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.

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

Calculation:

If the moments \(M_{20}\), \(M_{02}\) and \(M_{11}\) are normalized and passed to the area (see moments_region_2ndMomentsRegion2nd), the radii Rarara and Rbrbrb are calculated as:

\[\begin{eqnarray*} \textrm{Ra} = \frac{\sqrt{8(M_{20}+M_{02}+\sqrt{(M_{20}-M_{02})^2+4M_{11}^2})}}{2} \end{eqnarray*}\]

\[\begin{eqnarray*} \textrm{Rb} = \frac{\sqrt{8(M_{20}+M_{02}-\sqrt{(M_{20}-M_{02})^2+4M_{11}^2})}}{2} \end{eqnarray*}\]

The orientation Phiphiphi is defined by:

\[\begin{eqnarray*} \textrm{Phi} = -0.5 atan2(2 M_{11},M_{02} - M_{20}) \end{eqnarray*}\]

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 Rarara and Rbrbrb can assume the value 00. In particular, for an empty region and a region containing a single point Rarara \(=\) Rbrbrb \(=\) 00 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), Rbrbrb \(=\) 00 is returned.

Execution information🔗

Execution information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Automatically parallelized on tuple level.

Parameters🔗

Regionsregionsregions (input_object) region(-array) → objectHObjectHRegionHObjectHobject

Input regions.

Rarara (output_control) real(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Main radius (normalized to the area).

Assertion: Ra >= 0.0

Rbrbrb (output_control) real(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Secondary radius (normalized to the area).

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

Phiphiphi (output_control) angle.rad(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Angle between main radius and x-axis in radians.

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

Example🔗

(HDevelop)

read_image(Image,'fabrik')
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)
dev_set_draw('margin')
dev_display(Ellipses)

(C)

read_image(&Image,"fabrik")\;
regiongrowing(Image,&Seg,5,5,6.0,100)\;
T_elliptic_axis(Seg,&Ra,&Rb,&Phi)\;
T_area_center(Seg,NULL,&Row,&Column)\;
T_gen_ellipse(&Ellipses,Row,Column,Phi,Ra,Rb)\;

Complexity🔗

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

Result🔗

The operator elliptic_axisEllipticAxis 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.

Combinations with other operators🔗

Combinations

Possible predecessors

thresholdThreshold, regiongrowingRegiongrowing, connectionConnection

Possible successors

gen_ellipseGenEllipse

Alternatives

smallest_rectangle2SmallestRectangle2, orientation_regionOrientationRegion

References🔗

R. Haralick, L. Shapiro “Computer and Robot Vision” Addison-Wesley, 1992, pp. 73-75

Module🔗

Foundation