elliptic_axiselliptic_axisEllipticAxisEllipticAxiselliptic_axis (Operator)

Name

elliptic_axiselliptic_axisEllipticAxisEllipticAxiselliptic_axis — Calculate the parameters of the equivalent ellipse.

Signature

Description

The operator elliptic_axiselliptic_axisEllipticAxisEllipticAxisEllipticAxiselliptic_axis calculates the radii RaRaRaRarara and RbRbRbRbrbrb and the orientation PhiPhiPhiPhiphiphi of the ellipse having the same orientation and the same aspect ratio as the input region in RegionsRegionsRegionsRegionsregionsregions. Several input regions can be passed as tuples. RaRaRaRarara represents the main radius of the ellipse whereas the radius RbRbRbRbrbrb represents the secondary radius of the ellipse. The orientation of the main axis with regard to the x-axis is returned in PhiPhiPhiPhiphiphi 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 , and are normalized and passed to the area (see moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd), the radii RaRaRaRarara and RbRbRbRbrbrb are calculated as:

The orientation PhiPhiPhiPhiphiphi is defined by:

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

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

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)

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);

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)

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)

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)

Complexity

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

Result

The operator elliptic_axiselliptic_axisEllipticAxisEllipticAxisEllipticAxiselliptic_axis returns the value 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>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)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>)set_system("empty_region_result",<Result>)SetSystem("empty_region_result",<Result>)SetSystem("empty_region_result",<Result>)SetSystem("empty_region_result",<Result>)set_system("empty_region_result",<Result>). If necessary an exception is raised.

Possible Predecessors

thresholdthresholdThresholdThresholdThresholdthreshold, regiongrowingregiongrowingRegiongrowingRegiongrowingRegiongrowingregiongrowing, connectionconnectionConnectionConnectionConnectionconnection

Possible Successors

gen_ellipsegen_ellipseGenEllipseGenEllipseGenEllipsegen_ellipse

Alternatives

smallest_rectangle2smallest_rectangle2SmallestRectangle2SmallestRectangle2SmallestRectangle2smallest_rectangle2, orientation_regionorientation_regionOrientationRegionOrientationRegionOrientationRegionorientation_region

See also

moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd, select_shapeselect_shapeSelectShapeSelectShapeSelectShapeselect_shape, set_shapeset_shapeSetShapeSetShapeSetShapeset_shape

References

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

Module

Foundation