ClassesClasses | | Operators

elliptic_axiselliptic_axisEllipticAxisEllipticAxis (Operator)

Name

elliptic_axiselliptic_axisEllipticAxisEllipticAxis — Calculate the parameters of the equivalent ellipse.

Signature

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

Herror elliptic_axis(const Hobject Regions, double* Ra, double* Rb, double* Phi)

Herror T_elliptic_axis(const Hobject Regions, Htuple* Ra, Htuple* Rb, Htuple* Phi)

void EllipticAxis(const HObject& Regions, HTuple* Ra, HTuple* Rb, HTuple* Phi)

HTuple HRegion::EllipticAxis(HTuple* Rb, HTuple* Phi) const

double HRegion::EllipticAxis(double* Rb, double* Phi) const

static void HOperatorSet.EllipticAxis(HObject regions, out HTuple ra, out HTuple rb, out HTuple phi)

HTuple HRegion.EllipticAxis(out HTuple rb, out HTuple phi)

double HRegion.EllipticAxis(out double rb, out double phi)

Description

The operator elliptic_axiselliptic_axisEllipticAxisEllipticAxisEllipticAxis calculates the radii RaRaRaRara and RbRbRbRbrb and the orientation PhiPhiPhiPhiphi of the ellipse having the same orientation and the same aspect ratio as the input region in RegionsRegionsRegionsRegionsregions. Several input regions can be passed as tuples. RaRaRaRara represents the main radius of the ellipse whereas the radius RbRbRbRbrb represents the secondary radius of the ellipse. The orientation of the main axis with regard to the x-axis is returned in PhiPhiPhiPhiphi 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_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2nd), the radii RaRaRaRara and RbRbRbRbrb are calculated as:

The orientation PhiPhiPhiPhiphi 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>)).

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.

Execution Information

Parameters

RegionsRegionsRegionsRegionsregions (input_object)  region(-array) objectHRegionHRegionHobject

Input regions.

RaRaRaRara (output_control)  real(-array) HTupleHTupleHtuple (real) (double) (double) (double)

Main radius (normalized to the area).

Assertion: Ra >= 0.0

RbRbRbRbrb (output_control)  real(-array) HTupleHTupleHtuple (real) (double) (double) (double)

Secondary radius (normalized to the area).

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

PhiPhiPhiPhiphi (output_control)  real(-array) HTupleHTupleHtuple (real) (double) (double) (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)

Example (C)

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);

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)

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)

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)

Complexity

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

Result

The operator elliptic_axiselliptic_axisEllipticAxisEllipticAxisEllipticAxis 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>)SetSystem("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>)SetSystem("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_ellipseGenEllipseGenEllipseGenEllipse

Alternatives

smallest_rectangle2smallest_rectangle2SmallestRectangle2SmallestRectangle2SmallestRectangle2, orientation_regionorientation_regionOrientationRegionOrientationRegionOrientationRegion

See also

moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2nd, select_shapeselect_shapeSelectShapeSelectShapeSelectShape, set_shapeset_shapeSetShapeSetShapeSetShape

References

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

Module

Foundation


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