DGtal: DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted

Aim: implements weighted separable l_p metrics with exact predicates. More...

#include <DGtal/geometry/volumes/distance/ExactPredicateLpPowerSeparableMetric.h>

Public Types
typedef TSpace	Space
	Copy the space type. More...

typedef Space::Point	Point
	Type for points. More...

typedef Point::Coordinate	Abscissa
	Type for points. More...

typedef Space::Vector	Vector
	Type for vectors. More...

typedef TPromoted	Promoted
	Type for internal distance values. More...

typedef TPromoted	Weight
	Type for internal distance values. More...

typedef TPromoted	Value
	Type for Value (alias) More...

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CSpace< TSpace >))

	BOOST_CONCEPT_ASSERT ((concepts::CInteger< Promoted >))

	ExactPredicateLpPowerSeparableMetric ()

	~ExactPredicateLpPowerSeparableMetric ()

	ExactPredicateLpPowerSeparableMetric (const ExactPredicateLpPowerSeparableMetric &)

ExactPredicateLpPowerSeparableMetric &	operator= (const ExactPredicateLpPowerSeparableMetric &)

Weight	powerDistance (const Point &aPoint, const Point &aQ, const Weight &aWq) const

DGtal::Closest	closestPower (const Point &origin, const Point &first, const Weight &wF, const Point &second, const Weight &wS) const

bool	hiddenByPower (const Point &u, const Weight &wu, const Point &v, const Weight &wv, const Point &w, const Weight &ww, const Point &startingPoint, const Point &endPoint, const typename Point::UnsignedComponent dim) const

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Private Member Functions
Promoted	exactDistanceRepresentation (const Point &aP, const Point &aQ) const

Abscissa	binarySearchHidden (const Abscissa &udim, const Abscissa &vdim, const Promoted &nu, const Promoted &nv, const Abscissa &lower, const Abscissa &upper) const

Detailed Description

template<typename TSpace, DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>
class DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >

Aim: implements weighted separable l_p metrics with exact predicates.

Description of template class 'ExactPredicateLpPowerSeparableMetric'

Given a template parameter p, the class implement classical l_p metric as a model of CPowerSeparableMetric. Hence, given two points $ x=(x_0...x_{n-1})$, $ y=(y_0...y_{n-1})$ in the given digital space (see below) and a weight $ w_y$ we define a power metric such that:

$ powerDistance(x,y,w_y)= \sum_{i=0}^{n-1} |x_i-y_i|^p - w_y $

This class is said to be exact in the sense that the power p is computed without approximation (exponentiation by squaring in $ O(log(p))$ per computation, see BasicMathFunctions::power). As a consequence, hiddenByPower and closestPower methods are error free if the capacity of the template type TPromoted allows to store sums of $ |x_i-y_i|^p$ quantities.

Template Parameters

TSpace	the model of CSpace on which the metric is defined.
p	the exponent of the metric (static DGtal::uint32_t)
TPromoted	model of CSignedInteger used to store power p sums (default: DGtal::int64_t)

Definition at line 87 of file ExactPredicateLpPowerSeparableMetric.h.

Member Typedef Documentation

◆ Abscissa

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

typedef Point::Coordinate DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::Abscissa

Type for points.

Definition at line 100 of file ExactPredicateLpPowerSeparableMetric.h.

◆ Point

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

typedef Space::Point DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::Point

Type for points.

Definition at line 98 of file ExactPredicateLpPowerSeparableMetric.h.

◆ Promoted

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

typedef TPromoted DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::Promoted

Type for internal distance values.

Definition at line 105 of file ExactPredicateLpPowerSeparableMetric.h.

◆ Space

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

typedef TSpace DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::Space

Copy the space type.

Definition at line 94 of file ExactPredicateLpPowerSeparableMetric.h.

◆ Value

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

typedef TPromoted DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::Value

Type for Value (alias)

Definition at line 112 of file ExactPredicateLpPowerSeparableMetric.h.

◆ Vector

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

typedef Space::Vector DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::Vector

Type for vectors.

Definition at line 102 of file ExactPredicateLpPowerSeparableMetric.h.

◆ Weight

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

typedef TPromoted DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::Weight

Type for internal distance values.

Definition at line 108 of file ExactPredicateLpPowerSeparableMetric.h.

Constructor & Destructor Documentation

◆ ExactPredicateLpPowerSeparableMetric() [1/2]

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::ExactPredicateLpPowerSeparableMetric ( )

Constructor.

◆ ~ExactPredicateLpPowerSeparableMetric()

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::~ExactPredicateLpPowerSeparableMetric ( )

Destructor.

◆ ExactPredicateLpPowerSeparableMetric() [2/2]

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::ExactPredicateLpPowerSeparableMetric ( const ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted > & )

inline

Copy constructor.

Definition at line 128 of file ExactPredicateLpPowerSeparableMetric.h.

128 {}

Member Function Documentation

◆ binarySearchHidden()

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

Abscissa DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::binarySearchHidden	(	const Abscissa &	udim,
		const Abscissa &	vdim,
		const Promoted &	nu,
		const Promoted &	nv,
		const Abscissa &	lower,
		const Abscissa &	upper
	)		const

private

Perform a binary search on the interval [lower,upper] to detect the mid-point between u and v according to the weighted l_p distance.

Parameters

udim	coordinate of u along dimension dim
vdim	coordinate of v along dimension dim
nu	partial distance of u (sum of \|xj-x_i\|^p) discarding the term along the dimension dim
nv	partial distance of v (sum of \|xj-x_i\|^p) discarding the term along the dimension dim
lower	interval lower bound
upper	interval upper bound

Returns: the Voronoi boundary point coordinates along dimension dim.

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::BOOST_CONCEPT_ASSERT ( (concepts::CInteger< Promoted >) )

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::BOOST_CONCEPT_ASSERT ( (concepts::CSpace< TSpace >) )

◆ closestPower()

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

DGtal::Closest DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::closestPower	(	const Point &	origin,
		const Point &	first,
		const Weight &	wF,
		const Point &	second,
		const Weight &	wS
	)		const

Given an origin and two points, this method decides which one is closest to the origin. This method should be faster than comparing distance values.

Parameters

origin	the origin
first	the first point
wF	the first point weight
second	the second point
wS	the second point weight $

Returns: a Closest enum: FIRST, SECOND or BOTH.

◆ exactDistanceRepresentation()

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

Promoted DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::exactDistanceRepresentation	(	const Point &	aP,
		const Point &	aQ
	)		const

private

Compute the Lp distance without the computation of the power 1/p. I.e. only $ \sum |p_i- q_i|^p$ is given.

Parameters

aP	a first point
aQ	a second point

Returns: the power p of the l_p distance between aP and aQ.

◆ hiddenByPower()

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

bool DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::hiddenByPower	(	const Point &	u,
		const Weight &	wu,
		const Point &	v,
		const Weight &	wv,
		const Point &	w,
		const Weight &	ww,
		const Point &	startingPoint,
		const Point &	endPoint,
		const typename Point::UnsignedComponent	dim
	)		const

Given three weighted sites (u,v,w) and a straight segment [startingPoint,endPoint] along dimension dim, we detect if the power cells of u and w strictly hide the power cell of v on the straight line.

This method is in $ O(log(n))$ if n is the size of the straight segment. For $ l_2$ metric (p=2), the method is in $ O(1)$.

Precondition: u,v and w must be such that u[dim] < v[dim] < w[dim]

Parameters

u	a site
wu	a weight
v	a site
wv	a weight
w	a site
ww	a weight
startingPoint	starting point of the segment
endPoint	end point of the segment
dim	direction of the straight line

Returns: true if (u,w) hides v.

◆ isValid()

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

bool DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ operator=()

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

ExactPredicateLpPowerSeparableMetric& DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::operator= ( const ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted > & )

inline

Assignment.

Returns: a reference on 'this'.

Definition at line 134 of file ExactPredicateLpPowerSeparableMetric.h.

134 { return *this;}

◆ powerDistance()

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

Weight DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::powerDistance	(	const Point &	aPoint,
		const Point &	aQ,
		const Weight &	aWq
	)		const

Return the power distance of a point aPoint and a weighted point (aQ,aWq)

Parameters

aPoint	a point
aQ	a second point
aWq	weight of the second point

Returns: the power distance between aPoint and (Q,WQ)

◆ selfDisplay()

template<typename TSpace , DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>

void DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

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

ExactPredicateLpPowerSeparableMetric.h

Public Types

Public Member Functions

Private Member Functions

Detailed Description

template<typename TSpace, DGtal::uint32_t p, typename TPromoted = DGtal::int64_t> class DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >

Member Typedef Documentation

◆ Abscissa

◆ Point

◆ Promoted

◆ Space

◆ Value

◆ Vector

◆ Weight

Constructor & Destructor Documentation

◆ ExactPredicateLpPowerSeparableMetric() [1/2]

◆ ~ExactPredicateLpPowerSeparableMetric()

◆ ExactPredicateLpPowerSeparableMetric() [2/2]

Member Function Documentation

◆ binarySearchHidden()

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ closestPower()

◆ exactDistanceRepresentation()

◆ hiddenByPower()

◆ isValid()

◆ operator=()

◆ powerDistance()

◆ selfDisplay()

template<typename TSpace, DGtal::uint32_t p, typename TPromoted = DGtal::int64_t>
class DGtal::ExactPredicateLpPowerSeparableMetric< TSpace, p, TPromoted >