Line Equation structure. More...

#include <HoughLine.h>

Public Member Functions
	HoughLine ()
	empty constructor (all line values are set to 0)
	HoughLine (const utils::Point32f &offs, const utils::Point32f &dir)
	create a line by given parameters
	HoughLine (icl32f distance, icl32f angle)
	create a line by given distance and angle
void	sample (core::ImgBase *image, icl32f r, icl32f g, icl32f b, icl32f alpha=255) const
	draws the line into an image
float	rho () const
	convenence function for transf. into IppPointPolar
float	theta () const
	convenence function for transf. into IppPointPolar
Static Public Member Functions
static utils::Point32f	getIntersection (const HoughLine &a, const HoughLine &b)
	Computes the intersection between two lines.
static std::vector < utils::Point32f >	getPairwiseIntersections (const std::vector< HoughLine > &lines)
	calculates all pairwise intersection within a set of lines
Static Public Attributes
static const utils::Point32f	NO_INTERSECTION
	indicator for no found intersection (lines intersect in infinity -- max-float)
Private Attributes
float	m_distance
float	m_angle
utils::Point32f	m_offset
utils::Point32f	m_direction

Detailed Description

Line Equation structure.

Lines can (among others) be represented in parameter form:

$l: \vec{o}+\lambda \vec{d}$

,or by given radius $r$ and angle $\alpha$ .

$x \cos(\alpha) + y \sin(\alpha) - r = 0$

This class provides both information.

Constructor & Destructor Documentation

icl::cv::HoughLine::HoughLine ( )

empty constructor (all line values are set to 0)

icl::cv::HoughLine::HoughLine	(	const utils::Point32f &	offs,
		const utils::Point32f &	dir
	)

create a line by given parameters

Parameters:

offs	offset vector
dir	direction vector

icl::cv::HoughLine::HoughLine	(	icl32f	distance,
		icl32f	angle
	)

create a line by given distance and angle

Parameters:

distance	distance from the origin
angle	angle of vector perpendicular to the line

Member Function Documentation

static utils::Point32f icl::cv::HoughLine::getIntersection	(	const HoughLine &	a,
		const HoughLine &	b
	)		`[static]`

Computes the intersection between two lines.

Assuming two lines given in polar coordinates

$x \cos(\alpha) + y \sin(\alpha) - r = 0$

,

which can be seen geometrically, as a line that is perpendicular to the vector $(\cos(\alpha), \sin(\alpha) )^{\tau}$ with distance r to the origin, we can calculate the intersection as follows:

Firstly, we have to transform the line equations into parameter form

$l: \vec{o}+\lambda \vec{d}$

(offset- and direction vector) using the following rules

$\vec{o} = r * ( \cos(\alpha) \sin(\alpha) )^{\tau}$

$\vec{d} = ( -\sin(\alpha) \cos(\alpha) ]^{\tau}$

This results in:

$g_1: \vec{o}_1+ \lambda_1 * \vec{d}_1$

(using angle $\alpha$ and distance $r$ ) and

$g_2: \vec{o}_2+ \lambda_2 * \vec{d}_2$

(using angle $\beta$ and distance $s$ ) and

The intersection can be calculated by solving the equation system

$g1 = g2$

, or in other words:

$\lambda_1\cdot -\sin(\alpha) + \lambda_2 \cdot \sin(\beta) = s\cos(\beta) - r\cos(\alpha)$

$\lambda_1\cdot \cos(\alpha) + \lambda_2 \cdot -\cos(\beta) = s\sin(\beta) - r\sin(\alpha)$

This is equal to

$Mx = b$

With

$M = \left( \begin{array}{cc} -\sin(\alpha) & \sin(\beta) \\ \cos(\alpha) & -\cos(\beta) \\ \end{array} \right)$

$B = \left( \begin{array}{c} s\cos(\beta) - r\cos(\alpha) \\ s\sin(\beta) - r\sin(\alpha) \\ \end{array} \right)$

and

$x = (\lambda_1, \lambda_2)^{\tau}$

Of course $ Mx=b $ can be solved by $x=M^{-1}b$

If the lines do not intersect ( $\alpha$ and $\beta$ are very similar), $M$ becomes singular and it's inverse cannot be calculated. This function returns NO_INTERSECTION in this case.