Line Equation structure. More...

#include <HoughLine.h>

Public Member Functions
	HoughLine ()
	empty constructor (all line values are set to 0) More...

	HoughLine (const utils::Point32f &offs, const utils::Point32f &dir)
	create a line by given parameters More...

	HoughLine (icl32f distance, icl32f angle)
	create a line by given distance and angle More...

void	sample (core::ImgBase *image, icl32f r, icl32f g, icl32f b, icl32f alpha=255) const
	draws the line into an image More...

float	rho () const
	convenence function for transf. into IppPointPolar More...

float	theta () const
	convenence function for transf. into IppPointPolar More...

Static Public Member Functions
static utils::Point32f	getIntersection (const HoughLine &a, const HoughLine &b)
	Computes the intersection between two lines. More...

static std::vector< utils::Point32f >	getPairwiseIntersections (const std::vector< HoughLine > &lines)
	calculates all pairwise intersection within a set of lines More...

Static Public Attributes
static const utils::Point32f	NO_INTERSECTION
	indicator for no found intersection (lines intersect in infinity – max-float) More...

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

◆ HoughLine() [1/3]

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

empty constructor (all line values are set to 0)

◆ HoughLine() [2/3]

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

◆ HoughLine() [3/3]

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

◆ getIntersection()

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.

◆ getPairwiseIntersections()

static std::vector<utils::Point32f> icl::cv::HoughLine::getPairwiseIntersections ( const std::vector< HoughLine > & lines )

static

calculates all pairwise intersection within a set of lines

◆ rho()

float icl::cv::HoughLine::rho ( ) const

inline

convenence function for transf. into IppPointPolar

◆ sample()

void icl::cv::HoughLine::sample	(	core::ImgBase *	image,
		icl32f	r,
		icl32f	g,
		icl32f	b,
		icl32f	alpha = `255`
	)		const

draws the line into an image

◆ theta()

float icl::cv::HoughLine::theta ( ) const

inline

convenence function for transf. into IppPointPolar

Member Data Documentation

◆ m_angle

float icl::cv::HoughLine::m_angle

private

◆ m_direction

utils::Point32f icl::cv::HoughLine::m_direction

private

◆ m_distance

float icl::cv::HoughLine::m_distance

private

◆ m_offset

utils::Point32f icl::cv::HoughLine::m_offset

private

◆ NO_INTERSECTION

const utils::Point32f icl::cv::HoughLine::NO_INTERSECTION

static

indicator for no found intersection (lines intersect in infinity – max-float)

The documentation for this struct was generated from the following file:

/Users/alneuman/vm/icl/ICLCV/src/ICLCV/HoughLine.h

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ HoughLine() [1/3]

◆ HoughLine() [2/3]

◆ HoughLine() [3/3]

Member Function Documentation

◆ getIntersection()

◆ getPairwiseIntersections()

◆ rho()

◆ sample()

◆ theta()

Member Data Documentation

◆ m_angle

◆ m_direction

◆ m_distance

◆ m_offset

◆ NO_INTERSECTION