elliptic_axiselliptic_axiselliptic_axisEllipticAxisEllipticAxis (Operator)

Name

elliptic_axiselliptic_axiselliptic_axisEllipticAxisEllipticAxis — Parameters of the equivalent ellipse.

Signature

Description

The operator elliptic_axiselliptic_axiselliptic_axisEllipticAxisEllipticAxis calculates the radii and the orientation of the ellipse having the “same orientation” and the “same side relation” as the input region. Several input regions can be passed in RegionsRegionsRegionsRegionsregions as tuples. The length of the main radius RaRaRaRara and the secondary radius RbRbRbRbrb as well as the orientation of the main axis with regard to the horizontal (PhiPhiPhiPhiphi) are determined. The angle is indicated in arc measure.

Calculation:

        If the moments M20, M02 and M11 are
        normalized to the area (see moments_region_2ndmoments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2nd),
        the radii RaRaRaRara and RbRbRbRbrb are calculated as:

        RaRaRaRara = sqrt(8.0*(M20+M02+sqrt((M20-M02)^2+4.0*M11^2)))/2.0
        RbRbRbRbrb = sqrt(8.0*(M20+M02-sqrt((M20-M02)^2+4.0*M11^2)))/2.0

        The orientation Phi is defined by:

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

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('no_object_result',<Result>)set_system("no_object_result",<Result>)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("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 RaRaRaRara and RbRbRbRbrb can assume the value 0. In particular, for an empty region and a region containing a single point RaRaRaRara = RbRbRbRbrb = 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), RbRbRbRbrb = 0 is returned.

Parallelization

• 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

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)

read_image(&Image,"fabrik");
open_window(0,0,-1,-1,0,"visible","",&WindowHandle);
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);
set_draw(WindowHandle,"margin");
disp_region(Ellipses,WindowHandle);

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)

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)

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_axiselliptic_axiselliptic_axisEllipticAxisEllipticAxis 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>)set_system("no_object_result",<Result>)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("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>)set_system("empty_region_result",<Result>)set_system("empty_region_result",<Result>)SetSystem("empty_region_result",<Result>)SetSystem("empty_region_result",<Result>). If necessary an exception is raised.

Possible Predecessors

thresholdthresholdthresholdThresholdThreshold, regiongrowingregiongrowingregiongrowingRegiongrowingRegiongrowing, connectionconnectionconnectionConnectionConnection

Possible Successors

gen_ellipsegen_ellipsegen_ellipseGenEllipseGenEllipse

Alternatives

smallest_rectangle2smallest_rectangle2smallest_rectangle2SmallestRectangle2SmallestRectangle2, orientation_regionorientation_regionorientation_regionOrientationRegionOrientationRegion

See also

moments_region_2ndmoments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2nd, select_shapeselect_shapeselect_shapeSelectShapeSelectShape, set_shapeset_shapeset_shapeSetShapeSetShape

References

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

Module

Foundation