DGtal  0.9.4beta
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DGtal::experimental::ChamferNorm2D< TSpace > Class Template Reference

#include <DGtal/geometry/volumes/distance/ChamferNorm2D.h>

Collaboration diagram for DGtal::experimental::ChamferNorm2D< TSpace >:
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Data Structures

struct  LessOrEqThanAngular
 
struct  LessThanAngular
 

Public Types

typedef TSpace Space
 
typedef Space::Vector Vector
 
typedef Space::Point Point
 
typedef std::vector< VectorDirections
 
typedef Directions::const_iterator ConstIterator
 
typedef double Value
 
typedef Space::Integer RawValue
 
typedef Vector::Component Abscissa
 

Public Member Functions

 BOOST_CONCEPT_ASSERT ((concepts::CSpace< TSpace >))
 
 BOOST_STATIC_ASSERT (TSpace::dimension==2)
 
 ChamferNorm2D (const unsigned int aN)
 
 ChamferNorm2D (const Directions &aDirectionSet, const Directions &aNormalDirectionSet, const Value norm=1.0)
 
 ~ChamferNorm2D ()
 
ConstIterator getCone (const Vector &aDirection, ConstIterator aBegin, ConstIterator aEnd) const
 
ConstIterator getCone (const Vector &aDirection) const
 
Vector getNormalFromCone (ConstIterator aCone) const
 
Vector canonicalRay (const Vector &aRay) const
 
Value operator() (const Point &P, const Point &Q) const
 
RawValue rawDistance (const Point &P, const Point &Q) const
 
DGtal::Closest closest (const Point &origin, const Point &first, const Point &second) const
 
 ChamferNorm2D (const ChamferNorm2D &other)
 
ChamferNorm2D< Space > & operator= (const ChamferNorm2D< Space > &other)
 
Abscissa getLowerRayIntersection (const Vector &aP, const Vector &aQ, const Point &Lmin, const Point &Lmax, const Dimension aDimension) const
 
Abscissa getUpperRayIntersection (const Vector &aP, const Vector &aQ, const Point &Lmin, const Point &Lmax, const Dimension aDimension) const
 
ConstIterator shrinkPSubMask (ConstIterator aBegin, ConstIterator aEnd, const Point &aP, const Point &aQ, const Point &Lmin, const Point &Lmax, const Dimension aDimension, Point &midPoint, Point &nextMidPoint) const
 
ConstIterator shrinkP (ConstIterator aBegin, ConstIterator aEnd, const Point &aP, const Point &aQ, const Point &Lmin, const Point &Lmax, const Dimension aDimension, Point &midPoint, Point &nextMidPoint) const
 
Abscissa getLowerVoronoiEdgeAbscissa (const Point &u, const Point &v, const Point &startingPoint, const Point &endPoint, const Dimension dim) const
 
bool hiddenBy (const Point &u, const Point &v, const Point &w, const Point &startingPoint, const Point &endPoint, const Dimension dim) const
 
ConstIterator begin ()
 
ConstIterator end ()
 
unsigned int size () const
 
void selfDisplay (std::ostream &out) const
 
bool isValid () const
 

Protected Member Functions

 ChamferNorm2D ()
 

Private Member Functions

 BOOST_STATIC_CONSTANT (Abscissa, myInfinity=32562)
 

Private Attributes

Directions myDirections
 
Directions myNormals
 
LessThanAngular myLessThanAngular
 
Value myNorm
 

Detailed Description

template<typename TSpace>
class DGtal::experimental::ChamferNorm2D< TSpace >

Aim: implements a model of CSeparableMetric for Chamfer and path based norms.

Description of template class 'ChamferNorm2D'

This is a proof-of-concept which implements a path-based norm (here chamfer mask) in a separable way in dimension 2. Hence, this metric can be used in all separable volumetric tools like DistanceTransformation or VoronoiMap.

The metric is constructed from a set of directions that defines a set of cones, and weights associated with each cone. Alternatively, to check the computational efficiency of the methods, user can specify a number of cones and a fake chamfer mask will be constructed.

Note that the mask must satisfy norm conditions with axis symmetric unit ball.

As discussed in [25] and in nD Volumetric Analysis using Separable Processes, we have the following properties:

Template Parameters
TSpacea model CSpace of dimension 2.

Definition at line 86 of file ChamferNorm2D.h.

Member Typedef Documentation

template<typename TSpace>
typedef Vector::Component DGtal::experimental::ChamferNorm2D< TSpace >::Abscissa

Vector components type.

Definition at line 112 of file ChamferNorm2D.h.

template<typename TSpace>
typedef Directions::const_iterator DGtal::experimental::ChamferNorm2D< TSpace >::ConstIterator

Definition at line 104 of file ChamferNorm2D.h.

template<typename TSpace>
typedef std::vector< Vector > DGtal::experimental::ChamferNorm2D< TSpace >::Directions

Container for set of directions.

Definition at line 103 of file ChamferNorm2D.h.

template<typename TSpace>
typedef Space::Point DGtal::experimental::ChamferNorm2D< TSpace >::Point

Type for points.

Definition at line 100 of file ChamferNorm2D.h.

template<typename TSpace>
typedef Space::Integer DGtal::experimental::ChamferNorm2D< TSpace >::RawValue

Value type for exact distance evaluation.

Definition at line 109 of file ChamferNorm2D.h.

template<typename TSpace>
typedef TSpace DGtal::experimental::ChamferNorm2D< TSpace >::Space

Underlying Space.

Definition at line 95 of file ChamferNorm2D.h.

template<typename TSpace>
typedef double DGtal::experimental::ChamferNorm2D< TSpace >::Value

Value type for embedded distance evaluation.

Definition at line 107 of file ChamferNorm2D.h.

template<typename TSpace>
typedef Space::Vector DGtal::experimental::ChamferNorm2D< TSpace >::Vector

Type for vectors.

Definition at line 98 of file ChamferNorm2D.h.

Constructor & Destructor Documentation

template<typename TSpace>
DGtal::experimental::ChamferNorm2D< TSpace >::ChamferNorm2D ( const unsigned int  aN)

Constructor from a number N. Will generate a partial mask with aN directions (from Farey fractions). Weights are set to sattisfy the norm condition using the 3-4-mask wieghts. Hence, increasing aN does not improve the metric. This constructor is just used to compute efficiency statistics when aN increases.

template<typename TSpace>
DGtal::experimental::ChamferNorm2D< TSpace >::ChamferNorm2D ( const Directions aDirectionSet,
const Directions aNormalDirectionSet,
const Value  norm = 1.0 
)

Constructor from direction and noraml vector sets.

Parameters
aDirectionSetthe set of vectors of the chamfer norm mask. This set should correspond to the vectors of the chamfer mask with positive abscissa. Internally, this set will be symmetrized w.r.t. y-axis to make it complete.
aNormalDirectionSetfor each cone, the associated normal vector.
[in]normthe normalization factor associated with th mask (default is 1.0)
template<typename TSpace>
DGtal::experimental::ChamferNorm2D< TSpace >::~ChamferNorm2D ( )

Destructor.

template<typename TSpace>
DGtal::experimental::ChamferNorm2D< TSpace >::ChamferNorm2D ( const ChamferNorm2D< TSpace > &  other)
inline

Copy constructor.

Parameters
otherthe object to clone.

Definition at line 290 of file ChamferNorm2D.h.

References DGtal::experimental::ChamferNorm2D< TSpace >::myDirections, and DGtal::experimental::ChamferNorm2D< TSpace >::myNormals.

291  {
292  this->myDirections = other.myDirections;
293  this->myNormals = other.myNormals;
294  }
Directions myNormals
Normal to cone container.
Directions myDirections
Mask container.
template<typename TSpace>
DGtal::experimental::ChamferNorm2D< TSpace >::ChamferNorm2D ( )
protected

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

Member Function Documentation

template<typename TSpace>
ConstIterator DGtal::experimental::ChamferNorm2D< TSpace >::begin ( )
inline
Returns
the begin iterator to the mask direction set

Definition at line 466 of file ChamferNorm2D.h.

References DGtal::experimental::ChamferNorm2D< TSpace >::myDirections.

467  {
468  return myDirections.begin();
469  }
Directions myDirections
Mask container.
template<typename TSpace>
DGtal::experimental::ChamferNorm2D< TSpace >::BOOST_CONCEPT_ASSERT ( (concepts::CSpace< TSpace >)  )
template<typename TSpace>
DGtal::experimental::ChamferNorm2D< TSpace >::BOOST_STATIC_ASSERT ( TSpace::dimension  = =2)
template<typename TSpace>
DGtal::experimental::ChamferNorm2D< TSpace >::BOOST_STATIC_CONSTANT ( Abscissa  ,
myInfinity  = 32562 
)
private

Static constant.

template<typename TSpace>
Vector DGtal::experimental::ChamferNorm2D< TSpace >::canonicalRay ( const Vector aRay) const

Return the canonical ray for a given ray.

This method construct a vector in the first quadrant corresponding to aRay.

Returns
Vector |aRay[i]|
template<typename TSpace>
DGtal::Closest DGtal::experimental::ChamferNorm2D< TSpace >::closest ( const Point origin,
const Point first,
const Point second 
) const
inline

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
originthe origin
firstthe first point
secondthe second point
Returns
a Closest enum: FIRST, SECOND or BOTH.

Definition at line 271 of file ChamferNorm2D.h.

References DGtal::ClosestBOTH, DGtal::ClosestFIRST, DGtal::ClosestSECOND, and DGtal::experimental::ChamferNorm2D< TSpace >::operator()().

274  {
275  Value a = this->operator()(origin,first),
276  b = this->operator()(origin,second);
277  if (a<b)
278  return ClosestFIRST;
279  else
280  if (a>b)
281  return ClosestSECOND;
282  else
283  return ClosestBOTH;
284  }
Value operator()(const Point &P, const Point &Q) const
template<typename TSpace>
ConstIterator DGtal::experimental::ChamferNorm2D< TSpace >::end ( )
inline
Returns
the end iterator to the mask direction set

Definition at line 474 of file ChamferNorm2D.h.

References DGtal::experimental::ChamferNorm2D< TSpace >::myDirections.

475  {
476  return myDirections.end();
477  }
Directions myDirections
Mask container.
template<typename TSpace>
ConstIterator DGtal::experimental::ChamferNorm2D< TSpace >::getCone ( const Vector aDirection,
ConstIterator  aBegin,
ConstIterator  aEnd 
) const

Returns the cone associated to a direction (iterator it) in the range [aBegin, eEnd).

The cone is given by [it, it+1):

(*it) <= aDirection < (*(it+1)) (For the angular comparator).

Precondition
We have *aBegin <= aDirection < *aEnd
Parameters
[in]aDirectionthe direction to probe
[in]aBeginthe begin of the range in which the search is performed.
[in]aEndthe end of the range in which the search is performed.
Returns
a ConstIterator to the cone the direction belongs to.

Referenced by DGtal::experimental::ChamferNorm2D< TSpace >::getCone().

template<typename TSpace>
ConstIterator DGtal::experimental::ChamferNorm2D< TSpace >::getCone ( const Vector aDirection) const
inline

Returns the cone associated to a direction (iterator it) in the whole mask.

The cone is given by [it, it+1):

(*it) <= aDirection < (*(it+1)) (For the angular comparator).

Precondition
We have *aBegin <= aDirection < *aEnd
Parameters
aDirectionthe direction to probe
Returns
a const iterator to the cone the direction belongs to.

Definition at line 213 of file ChamferNorm2D.h.

References DGtal::experimental::ChamferNorm2D< TSpace >::getCone(), and DGtal::experimental::ChamferNorm2D< TSpace >::myDirections.

214  {
215  return getCone(aDirection, myDirections.begin(), myDirections.end());
216  }
ConstIterator getCone(const Vector &aDirection, ConstIterator aBegin, ConstIterator aEnd) const
Directions myDirections
Mask container.
template<typename TSpace>
Abscissa DGtal::experimental::ChamferNorm2D< TSpace >::getLowerRayIntersection ( const Vector aP,
const Vector aQ,
const Point Lmin,
const Point Lmax,
const Dimension  aDimension 
) const

Compute the intersection between (aP,aQ) and (Lmin, Lmax). More precisely, if we suppose that

Precondition
We have \( Lmin[aDimension] < Lmax[aDimension]\)
We have \( Lmin[(aDimension+1)%2] == Lmax[(aDimension+1)%2]\)
We have \( (aP,aQ) \cap (Lmin,Lmax) \)

this method returns the lower rounding abscissa of the rational intersection point.

Parameters
aPfirst extremity point
aQsecond extremity point
Lminfirst extremity point of the L segment
Lmaxsecond extremity point of the L segment
aDimensiona dimension
Returns
the lowest rounding intersection point.
template<typename TSpace>
Abscissa DGtal::experimental::ChamferNorm2D< TSpace >::getLowerVoronoiEdgeAbscissa ( const Point u,
const Point v,
const Point startingPoint,
const Point endPoint,
const Dimension  dim 
) const

Returns the lower abscissa of the Voronoi edge between u and v along the span (startingPoint,endPoint).

Parameters
ua site
va site
startingPointstarting point of the segment
endPointend point of the segment
dimdirection of the straight line
Returns
the abscissa on (startingPoint,endPoint) of the Voronoi cell.
template<typename TSpace>
Vector DGtal::experimental::ChamferNorm2D< TSpace >::getNormalFromCone ( ConstIterator  aCone) const
Parameters
aConethe input cone
Returns
the normal associated with a cone (aCone, aCone+1)
template<typename TSpace>
Abscissa DGtal::experimental::ChamferNorm2D< TSpace >::getUpperRayIntersection ( const Vector aP,
const Vector aQ,
const Point Lmin,
const Point Lmax,
const Dimension  aDimension 
) const

Compute the intersection between (aP,aQ) and (Lmin, Lmax). More precisely, if we suppose that

Precondition
We have \( Lmin[aDimension] < Lmax[aDimension]\)
We have \( Lmin[(aDimension+1)%2] == Lmax[(aDimension+1)%2]\)
We have \( (aP,aQ) \cap (Lmin,Lmax) \)

this method returns the upper rounding abscissa of the rational intersection point.

Parameters
aPfirst extremity point
aQsecond extremity point
Lminfirst extremity point of the L segment
Lmaxsecond extremity point of the L segment
aDimensiona dimension
Returns
the lowest rounding intersection point.
template<typename TSpace>
bool DGtal::experimental::ChamferNorm2D< TSpace >::hiddenBy ( const Point u,
const Point v,
const Point w,
const Point startingPoint,
const Point endPoint,
const Dimension  dim 
) const

The main hiddenBy predicate. (in \( O(log^2(n))\)).

Parameters
ua site
va site
wa site
startingPointstarting point of the segment
endPointend point of the segment
dimdirection of the straight line
Returns
true if (u,w) hides v (strictly).
template<typename TSpace>
bool DGtal::experimental::ChamferNorm2D< TSpace >::isValid ( ) const

Checks the validity/consistency of the object.

Returns
'true' if the object is valid, 'false' otherwise.
template<typename TSpace>
Value DGtal::experimental::ChamferNorm2D< TSpace >::operator() ( const Point P,
const Point Q 
) const

Returns the distance for the chamfer norm between P and Q.

Parameters
Pa point
Qa point
Returns
the distance between P and Q.

Referenced by DGtal::experimental::ChamferNorm2D< TSpace >::closest().

template<typename TSpace>
ChamferNorm2D<Space>& DGtal::experimental::ChamferNorm2D< TSpace >::operator= ( const ChamferNorm2D< Space > &  other)
inline

Assignment.

Parameters
otherthe object to copy.
Returns
a reference on 'this'.

Definition at line 302 of file ChamferNorm2D.h.

References DGtal::experimental::ChamferNorm2D< TSpace >::myDirections, and DGtal::experimental::ChamferNorm2D< TSpace >::myNormals.

303  {
304  this->myDirections = other.myDirections;
305  this->myNormals = other.myNormals;
306  return *this;
307  }
Directions myNormals
Normal to cone container.
Directions myDirections
Mask container.
template<typename TSpace>
RawValue DGtal::experimental::ChamferNorm2D< TSpace >::rawDistance ( const Point P,
const Point Q 
) const

Returns the raw distance for the chamfer norm between P and Q. For chamfer norm, it corresponds to un-normalized distance value.

Parameters
Pa point
Qa point
Returns
the distance between P and Q.
template<typename TSpace>
void DGtal::experimental::ChamferNorm2D< TSpace >::selfDisplay ( std::ostream &  out) const

Writes/Displays the object on an output stream.

Parameters
outthe output stream where the object is written.
template<typename TSpace>
ConstIterator DGtal::experimental::ChamferNorm2D< TSpace >::shrinkP ( ConstIterator  aBegin,
ConstIterator  aEnd,
const Point aP,
const Point aQ,
const Point Lmin,
const Point Lmax,
const Dimension  aDimension,
Point midPoint,
Point nextMidPoint 
) const

This method returns the cone (ConstIterator, ConstIterator+1) at P which contains

Parameters
[in]aBeginbegin iterator on the current set of directions at P
[in]aEndend iterator on the current set of directions at P
[in]aPcenter of the ball we are shrinking
[in]aQcenter of the second ball
[in]Lminfirst extremity point of the L segment
[in]Lmaxfirst extremity point of the L segment
[in]aDimensiondirection of the (Lmin,LMax segment)
[out]midPointthe point, on the segment, corresponding to the intersection of the the first cone direction and the segment
[out]nextMidPointthe point, on the segment, corresponding to the intersection of the second cone direction and the segment
Returns
the ConstIterator to the cone direction the Voronoi Edge belongs to
template<typename TSpace>
ConstIterator DGtal::experimental::ChamferNorm2D< TSpace >::shrinkPSubMask ( ConstIterator  aBegin,
ConstIterator  aEnd,
const Point aP,
const Point aQ,
const Point Lmin,
const Point Lmax,
const Dimension  aDimension,
Point midPoint,
Point nextMidPoint 
) const

Considering a vertical configuration (aDimension == 1, P[!dimension]<= Lmin[!dimension]), This method returns the cone (ConstIterator, ConstIterator+1) at P which contains the Voronoi Edge of P and Q.

Precondition
We have aP[aDimension] != aQ[aDimension (no alignement)

This method runs in O(log^2(n)), n being the number of directions in the mask.

Parameters
[in]aBeginbegin iterator on the current set of directions at P
[in]aEndend iterator on the current set of directions at P
[in]aPcenter of the ball we are shrinking
[in]aQcenter of the second ball
[in]Lminfirst extremity point of the L segment
[in]Lmaxfirst extremity point of the L segment
[in]aDimensiondirection of the (Lmin,LMax segment)
[out]midPointthe point, on the segment, corresponding to the intersection of the the first cone direction and the segment
[out]nextMidPointthe point, on the segment, corresponding to the intersection of the second cone direction and the segment
Returns
the ConstIterator to the cone direction the Voronoi Edge belongs to
template<typename TSpace>
unsigned int DGtal::experimental::ChamferNorm2D< TSpace >::size ( ) const
inline
Returns
the mask size

Definition at line 483 of file ChamferNorm2D.h.

References DGtal::experimental::ChamferNorm2D< TSpace >::myDirections.

484  {
485  return myDirections.size();
486  }
Directions myDirections
Mask container.

Field Documentation

template<typename TSpace>
Directions DGtal::experimental::ChamferNorm2D< TSpace >::myDirections
private
template<typename TSpace>
LessThanAngular DGtal::experimental::ChamferNorm2D< TSpace >::myLessThanAngular
private

Instance of comparator functor.

Definition at line 521 of file ChamferNorm2D.h.

template<typename TSpace>
Value DGtal::experimental::ChamferNorm2D< TSpace >::myNorm
private

Normalization factor.

Definition at line 527 of file ChamferNorm2D.h.

template<typename TSpace>
Directions DGtal::experimental::ChamferNorm2D< TSpace >::myNormals
private

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