Aim: This class precomputes the Voronoi Covariance Measure of a set of points. It can compute the covariance measure of an arbitrary function with given support. More...

#include <DGtal/geometry/volumes/estimation/VoronoiCovarianceMeasure.h>

Data Structures
struct	CharacteristicSetPredicate

Public Types
typedef TSpace	Space
	the type of digital space More...

typedef TSeparableMetric	Metric
	the type of metric More...

typedef Space::Point	Point
	the type of digital point More...

typedef Space::Size	Size
	the type for counting elements More...

typedef Space::Integer	Integer
	the type of each digital point coordinate, some integral type More...

typedef DGtal::HyperRectDomain< Space >	Domain
	the type of rectangular domain of the VCM. More...

typedef DGtal::ImageContainerBySTLVector< Domain, bool >	CharacteristicSet
	the type of a binary image that is the characteristic function of K. More...

typedef DGtal::SpatialCubicalSubdivision< Space >	ProximityStructure
	the structure used for proximity queries. More...

typedef DGtal::functors::NotPointPredicate< CharacteristicSetPredicate >	NotPredicate
	the type of the point predicate used by the voronoi map. More...

typedef DGtal::VoronoiMap< Space, NotPredicate, Metric >	Voronoi
	the type of the Voronoi map. More...

typedef double	Scalar
	the type for "real" numbers. More...

typedef DGtal::SimpleMatrix< Scalar, Space::dimension, Space::dimension >	MatrixNN
	the type for nxn matrix of real numbers. More...

typedef MatrixNN::RowVector	VectorN
	the type for N-vector of real numbers More...

typedef std::vector< Point >	PointContainer
	the list of points More...

typedef std::map< Point, MatrixNN >	Point2MatrixNN
	Associates a matrix to points. More...

Public Member Functions
	VoronoiCovarianceMeasure (double _R, double _r, Metric aMetric=Metric(), bool verbose=false)

	~VoronoiCovarianceMeasure ()

Scalar	R () const

Scalar	r () const

void	clean ()

template<typename PointInputIterator >
void	init (PointInputIterator itb, PointInputIterator ite)

const Domain &	domain () const

const Voronoi &	voronoiMap () const

const Point2MatrixNN &	vcmMap () const

template<typename Point2ScalarFunction >
MatrixNN	measure (Point2ScalarFunction chi_r, Point p) const

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Protected Member Functions
	VoronoiCovarianceMeasure ()

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

	BOOST_CONCEPT_ASSERT ((concepts::CSeparableMetric< TSeparableMetric >))

	VoronoiCovarianceMeasure (const VoronoiCovarianceMeasure &other)

VoronoiCovarianceMeasure &	operator= (const VoronoiCovarianceMeasure &other)

Private Attributes
double	myBigR
	The parameter R in the VCM, i.e. the offset radius for the compact set K. More...

double	mySmallR

Metric	myMetric
	The metric chosen for the Voronoi map. More...

bool	myVerbose
	Tells if it is verbose mode. More...

Domain	myDomain
	The domain in which all computations are done. More...

CharacteristicSet *	myCharSet
	A binary image that defines the characteristic set of K. More...

Voronoi *	myVoronoi
	Stores the voronoi map. More...

Point2MatrixNN	myVCM
	The map point -> VCM. More...

ProximityStructure *	myProximityStructure
	The structure used for proximity queries. More...

Detailed Description

template<typename TSpace, typename TSeparableMetric>
class DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >

Aim: This class precomputes the Voronoi Covariance Measure of a set of points. It can compute the covariance measure of an arbitrary function with given support.

Description of template class 'VoronoiCovarianceMeasure'

You may obtain the whole sequence (Point,VCM) by accessing the map vcmMap.

Note: Documentation in Computing the Voronoi Covariance Measure of a point set.

Template Parameters

TSpace	type of Digital Space (model of CSpace).
TSeparableMetric	a model of CSeparableMetric used for computing the Voronoi map (e.g. Euclidean metric is DGtal::ExactPredicateLpSeparableMetric<TSpace, 2> )

Examples: geometry/volumes/dvcm-2d.cpp.

Definition at line 79 of file VoronoiCovarianceMeasure.h.

Member Typedef Documentation

◆ CharacteristicSet

template<typename TSpace , typename TSeparableMetric >

typedef DGtal::ImageContainerBySTLVector<Domain,bool> DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::CharacteristicSet

the type of a binary image that is the characteristic function of K.

Definition at line 91 of file VoronoiCovarianceMeasure.h.

◆ Domain

template<typename TSpace , typename TSeparableMetric >

typedef DGtal::HyperRectDomain<Space> DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::Domain

the type of rectangular domain of the VCM.

Definition at line 90 of file VoronoiCovarianceMeasure.h.

◆ Integer

template<typename TSpace , typename TSeparableMetric >

typedef Space::Integer DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::Integer

the type of each digital point coordinate, some integral type

Definition at line 89 of file VoronoiCovarianceMeasure.h.

◆ MatrixNN

template<typename TSpace , typename TSeparableMetric >

typedef DGtal::SimpleMatrix< Scalar, Space::dimension, Space::dimension > DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::MatrixNN

the type for nxn matrix of real numbers.

Definition at line 120 of file VoronoiCovarianceMeasure.h.

◆ Metric

template<typename TSpace , typename TSeparableMetric >

typedef TSeparableMetric DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::Metric

the type of metric

Definition at line 86 of file VoronoiCovarianceMeasure.h.

◆ NotPredicate

template<typename TSpace , typename TSeparableMetric >

typedef DGtal::functors::NotPointPredicate<CharacteristicSetPredicate> DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::NotPredicate

the type of the point predicate used by the voronoi map.

Definition at line 114 of file VoronoiCovarianceMeasure.h.

◆ Point

template<typename TSpace , typename TSeparableMetric >

typedef Space::Point DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::Point

the type of digital point

Definition at line 87 of file VoronoiCovarianceMeasure.h.

◆ Point2MatrixNN

template<typename TSpace , typename TSeparableMetric >

typedef std::map<Point,MatrixNN> DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::Point2MatrixNN

Associates a matrix to points.

Definition at line 123 of file VoronoiCovarianceMeasure.h.

◆ PointContainer

template<typename TSpace , typename TSeparableMetric >

typedef std::vector<Point> DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::PointContainer

the list of points

Definition at line 122 of file VoronoiCovarianceMeasure.h.

◆ ProximityStructure

template<typename TSpace , typename TSeparableMetric >

typedef DGtal::SpatialCubicalSubdivision<Space> DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::ProximityStructure

the structure used for proximity queries.

Definition at line 92 of file VoronoiCovarianceMeasure.h.

◆ Scalar

template<typename TSpace , typename TSeparableMetric >

typedef double DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::Scalar

the type for "real" numbers.

Definition at line 117 of file VoronoiCovarianceMeasure.h.

◆ Size

template<typename TSpace , typename TSeparableMetric >

typedef Space::Size DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::Size

the type for counting elements

Definition at line 88 of file VoronoiCovarianceMeasure.h.

◆ Space

template<typename TSpace , typename TSeparableMetric >

typedef TSpace DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::Space

the type of digital space

Definition at line 85 of file VoronoiCovarianceMeasure.h.

◆ VectorN

template<typename TSpace , typename TSeparableMetric >

typedef MatrixNN::RowVector DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::VectorN

the type for N-vector of real numbers

Definition at line 121 of file VoronoiCovarianceMeasure.h.

◆ Voronoi

template<typename TSpace , typename TSeparableMetric >

typedef DGtal::VoronoiMap<Space, NotPredicate, Metric > DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::Voronoi

the type of the Voronoi map.

Definition at line 115 of file VoronoiCovarianceMeasure.h.

Constructor & Destructor Documentation

◆ VoronoiCovarianceMeasure() [1/3]

template<typename TSpace , typename TSeparableMetric >

DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::VoronoiCovarianceMeasure	(	double	_R,
		double	_r,
		Metric	aMetric = `Metric()`,
		bool	verbose = `false`
	)

Constructor.

Parameters

_R	the offset radius for the set of points. Voronoi cells are intersected with this offset. The unit corresponds to a step in the digital space.
_r	(an upper bound of) the radius of the support of forthcoming kernel functions ( \( \chi_r \)). The unit corresponds to a step in the digital space. This parameter is used for preparing the data structure that answers to proximity queries.
aMetric	an instance of the metric.
verbose	if 'true' displays information on ongoing computation.

◆ ~VoronoiCovarianceMeasure()

template<typename TSpace , typename TSeparableMetric >

DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::~VoronoiCovarianceMeasure ( )

Destructor.

◆ VoronoiCovarianceMeasure() [2/3]

template<typename TSpace , typename TSeparableMetric >

DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::VoronoiCovarianceMeasure ( )

protected

Constructor. Forbidden by default (protected to avoid g++ warnings).

◆ VoronoiCovarianceMeasure() [3/3]

template<typename TSpace , typename TSeparableMetric >

DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::VoronoiCovarianceMeasure ( const VoronoiCovarianceMeasure< TSpace, TSeparableMetric > & other )

private

Copy constructor.

Parameters

other the object to clone. Forbidden by default.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<typename TSpace , typename TSeparableMetric >

DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::BOOST_CONCEPT_ASSERT ( (concepts::CSeparableMetric< TSeparableMetric >) )

private

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<typename TSpace , typename TSeparableMetric >

DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::BOOST_CONCEPT_ASSERT ( (concepts::CSpace< TSpace >) )

private

◆ clean()

template<typename TSpace , typename TSeparableMetric >

void DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::clean ( )

Cleans intermediate data structure likes the characteristic set and the voronoi map.

Note: Further calls to voronoiMap are no more valid.

◆ domain()

template<typename TSpace , typename TSeparableMetric >

const Domain & DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::domain ( ) const

Returns: the domain of computation

◆ init()

template<typename TSpace , typename TSeparableMetric >

template<typename PointInputIterator >

void DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::init	(	PointInputIterator	itb,
		PointInputIterator	ite
	)

Computes the Voronoi Covariance Measure for the set of points given by range [itb,ite)

Template Parameters

PointInputIterator an input iterator on digital points.

Parameters

itb	the start of the range
ite	the end of the range.

Precondition: itb != ite.; [itb,ite) is a valid range (ite can be reached from itb).

◆ isValid()

template<typename TSpace , typename TSeparableMetric >

bool DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::isValid ( ) const

Checks the validity/consistency of the object.

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

◆ measure()

template<typename TSpace , typename TSeparableMetric >

template<typename Point2ScalarFunction >

MatrixNN DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::measure	(	Point2ScalarFunction	chi_r,
		Point	p
	)		const

Computes the Voronoi Covariance Measure of the function chi_r.

Template Parameters

Point2ScalarFunction the type of a functor Point->Scalar. For instance functors::HatPointFunction and functors::BallConstantPointFunction are models of this type.

Parameters

chi_r	the kernel function whose support is included in the cube centered on the origin with edge size 2r (see VoronoiCovarianceMeasure).
p	the point where the kernel function is moved. It must lie within domain.

◆ operator=()

template<typename TSpace , typename TSeparableMetric >

VoronoiCovarianceMeasure & DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::operator= ( const VoronoiCovarianceMeasure< TSpace, TSeparableMetric > & other )

private

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'. Forbidden by default.

◆ R()

template<typename TSpace , typename TSeparableMetric >

Scalar DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::R ( ) const

Returns: the parameter R in the VCM, i.e. the offset radius for the compact set K.

◆ r()

template<typename TSpace , typename TSeparableMetric >

Scalar DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::r ( ) const

Returns: the parameter r in VCM(chi_r), i.e. an upper bound for the diameter of the support of kernel functions.

◆ selfDisplay()

template<typename TSpace , typename TSeparableMetric >

void DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ vcmMap()

template<typename TSpace , typename TSeparableMetric >

const Point2MatrixNN & DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::vcmMap ( ) const

Returns: the Voronoi Covariance Matrix of each Voronoi cell as a map Point -> Matrix

Note: empty if init has not been called.

◆ voronoiMap()

template<typename TSpace , typename TSeparableMetric >

const Voronoi & DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::voronoiMap ( ) const

Returns: the current Voronoi map

Precondition: init must have been called before.

Field Documentation

◆ myBigR

template<typename TSpace , typename TSeparableMetric >

double DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::myBigR

private

The parameter R in the VCM, i.e. the offset radius for the compact set K.

Definition at line 224 of file VoronoiCovarianceMeasure.h.

◆ myCharSet

template<typename TSpace , typename TSeparableMetric >

CharacteristicSet* DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::myCharSet

private

A binary image that defines the characteristic set of K.

Definition at line 235 of file VoronoiCovarianceMeasure.h.

◆ myDomain

template<typename TSpace , typename TSeparableMetric >

Domain DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::myDomain

private

The domain in which all computations are done.

Definition at line 233 of file VoronoiCovarianceMeasure.h.

◆ myMetric

template<typename TSpace , typename TSeparableMetric >

Metric DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::myMetric

private

The metric chosen for the Voronoi map.

Definition at line 229 of file VoronoiCovarianceMeasure.h.

◆ myProximityStructure

template<typename TSpace , typename TSeparableMetric >

ProximityStructure* DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::myProximityStructure

private

The structure used for proximity queries.

Definition at line 241 of file VoronoiCovarianceMeasure.h.

◆ mySmallR

template<typename TSpace , typename TSeparableMetric >

double DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::mySmallR

private

The parameter r in VCM(chi_r), i.e. an upper bound for the diameter of the support of kernel functions.

Definition at line 227 of file VoronoiCovarianceMeasure.h.

◆ myVCM

template<typename TSpace , typename TSeparableMetric >

Point2MatrixNN DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::myVCM

private

The map point -> VCM.

Definition at line 239 of file VoronoiCovarianceMeasure.h.

◆ myVerbose

template<typename TSpace , typename TSeparableMetric >

bool DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::myVerbose

private

Tells if it is verbose mode.

Definition at line 231 of file VoronoiCovarianceMeasure.h.

◆ myVoronoi

template<typename TSpace , typename TSeparableMetric >

Voronoi* DGtal::VoronoiCovarianceMeasure< TSpace, TSeparableMetric >::myVoronoi

private

Stores the voronoi map.

Definition at line 237 of file VoronoiCovarianceMeasure.h.

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

VoronoiCovarianceMeasure.h

Data Structures

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ CharacteristicSet

◆ Domain

◆ Integer

◆ MatrixNN

◆ Metric

◆ NotPredicate

◆ Point

◆ Point2MatrixNN

◆ PointContainer

◆ ProximityStructure

◆ Scalar

◆ Size

◆ Space

◆ VectorN

◆ Voronoi

Constructor & Destructor Documentation

◆ VoronoiCovarianceMeasure() [1/3]

◆ ~VoronoiCovarianceMeasure()

◆ VoronoiCovarianceMeasure() [2/3]

◆ VoronoiCovarianceMeasure() [3/3]

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ clean()

◆ domain()

◆ init()

◆ isValid()

◆ measure()

◆ operator=()

◆ R()

◆ r()

◆ selfDisplay()

◆ vcmMap()

◆ voronoiMap()

Field Documentation

◆ myBigR

◆ myCharSet

◆ myDomain

◆ myMetric

◆ myProximityStructure

◆ mySmallR

◆ myVCM

◆ myVerbose

◆ myVoronoi