#include <FMMPointFunctors.h>

Public Types
typedef TImage	Image
typedef Image::Point	Point
typedef Image::Value	Value
typedef TSet	Set

Public Member Functions
	BOOST_CONCEPT_ASSERT ((CImage< TImage >))
	BOOST_CONCEPT_ASSERT ((CDigitalSet< TSet >))
	BOOST_STATIC_ASSERT ((boost::is_same< Point, typename TSet::Point >::value))
	L2FirstOrderLocalDistance (Image &aImg, TSet &aSet)
	L2FirstOrderLocalDistance (const L2FirstOrderLocalDistance &other)
L2FirstOrderLocalDistance &	operator= (const L2FirstOrderLocalDistance &other)
	~L2FirstOrderLocalDistance ()
Value	operator() (const Point &aPoint)
void	selfDisplay (std::ostream &out) const

Data Fields
Image *	myImgPtr
Set *	mySetPtr

Private Types
typedef std::vector< Value >	Values

Private Member Functions
Value	compute (Values &aValueList) const
Value	gradientNorm (const Value &aValue, const Values &aValueList) const

Detailed Description

template<typename TImage, typename TSet>
class DGtal::L2FirstOrderLocalDistance< TImage, TSet >

Aim: Class for the computation of the Euclidean distance at some point p, from the available distance values of some points lying in the 1-neighborhood of p (ie. points at a L1-distance to p equal to 1).

Description of template class 'L2FirstOrderLocalDistance' <p>
The computed value is such that the upwind gradient of the 
distance map is one, ie. it is the minimum solution \form#156 
over all quadrants, verifying the following quadratic equation:

\( \sum_{i = 1 \ldots d } ( \Phi - \Phi_i )^2 \) where \( \Phi_i \) is the distance value of the point preceeding or following p along the \( i \) axis.

Note:: This class deals with positive or negative distance values (0 is arbitrarily considered as a positive value, ie. starting with a seed of null value, you must get positive values). However, the behavior is undefined when there are both positive and negative distance values in the neighborhood of p.

It is a model of CPointFunctor.

Template Parameters:

TImage	model of CImage used for the mapping point-distance value
TSet	model of CDigitalSet for storing points whose distance value is known

See also:: FMM

Definition at line 92 of file FMMPointFunctors.h.

Member Typedef Documentation

template<typename TImage, typename TSet>

typedef TImage DGtal::L2FirstOrderLocalDistance< TImage, TSet >::Image

Definition at line 101 of file FMMPointFunctors.h.

template<typename TImage, typename TSet>

typedef Image::Point DGtal::L2FirstOrderLocalDistance< TImage, TSet >::Point

Definition at line 102 of file FMMPointFunctors.h.

template<typename TImage, typename TSet>

typedef TSet DGtal::L2FirstOrderLocalDistance< TImage, TSet >::Set

Definition at line 107 of file FMMPointFunctors.h.

template<typename TImage, typename TSet>

typedef Image::Value DGtal::L2FirstOrderLocalDistance< TImage, TSet >::Value

Definition at line 103 of file FMMPointFunctors.h.

template<typename TImage, typename TSet>

typedef std::vector<Value> DGtal::L2FirstOrderLocalDistance< TImage, TSet >::Values

private

Definition at line 112 of file FMMPointFunctors.h.

Constructor & Destructor Documentation

template<typename TImage , typename TSet>

DGtal::L2FirstOrderLocalDistance< TImage, TSet >::L2FirstOrderLocalDistance	(	Image &	aImg,
		TSet &	aSet
	)

inline

Constructor from an image and a set. NB: only pointers are stored

Parameters:

aImg	any distance map
aSet	any digital set

Definition at line 67 of file FMMPointFunctors.ih.

                           : myImgPtr(&aImg), mySetPtr(&aSet)
{
      ASSERT( myImgPtr ); 
      ASSERT( mySetPtr ); 
}

template<typename TImage , typename TSet>

DGtal::L2FirstOrderLocalDistance< TImage, TSet >::L2FirstOrderLocalDistance ( const L2FirstOrderLocalDistance< TImage, TSet > & other )

inline

Copy constructor.

Parameters:

other the object to clone.

Definition at line 77 of file FMMPointFunctors.ih.

                                          : myImgPtr(other.myImgPtr), mySetPtr(other.mySetPtr)
{
      ASSERT( myImgPtr ); 
      ASSERT( mySetPtr ); 
}

template<typename TImage , typename TSet >

DGtal::L2FirstOrderLocalDistance< TImage, TSet >::~L2FirstOrderLocalDistance ( )

inline

Destructor. Does nothing.

Definition at line 104 of file FMMPointFunctors.ih.

{

}

Member Function Documentation

template<typename TImage, typename TSet>

DGtal::L2FirstOrderLocalDistance< TImage, TSet >::BOOST_CONCEPT_ASSERT ( (CImage< TImage >) )

image

template<typename TImage, typename TSet>

DGtal::L2FirstOrderLocalDistance< TImage, TSet >::BOOST_CONCEPT_ASSERT ( (CDigitalSet< TSet >) )

set

template<typename TImage, typename TSet>

DGtal::L2FirstOrderLocalDistance< TImage, TSet >::BOOST_STATIC_ASSERT ( (boost::is_same< Point, typename TSet::Point >::value) )

template<typename TImage , typename TSet >

DGtal::L2FirstOrderLocalDistance< TImage, TSet >::Value DGtal::L2FirstOrderLocalDistance< TImage, TSet >::compute ( Values & aValueList ) const

inlineprivate

Returns an approximation of the Euclidean distance at some point, knowing the distance of its neighbors

Parameters:

aValueList the distance of (some of) the neighbors

Returns:: the computed distance.

Definition at line 170 of file FMMPointFunctors.ih.

{
  ASSERT(aValueList.size() > 0); 
  if ( aValueList.size() == 1 )
    {
      Value d = aValueList.back();
      if (d >= 0) return d + 1.0; 
      else return d - 1.0; 
    } 
  else 
    {
      //function computation
      typename Values::iterator itMax = 
        std::max_element( aValueList.begin(), aValueList.end(), absComparator<Value> ); 
      if ( gradientNorm( *itMax, aValueList ) > 1 )
        {
          aValueList.erase( itMax ); 
          return this->compute(aValueList); 
        }
      else 
        { //resolution
          double a = 0; 
          double b = 0; 
          double c = -1; 
          for (typename Values::iterator it = aValueList.begin(); 
               it != aValueList.end(); ++it)
            {
              Value d = *it; 
              a += 1; 
              b -= static_cast<double>(2*d);
              c += static_cast<double>(d*d); 
            }
 
          //discriminant
          double disc = b*b - 4*a*c;
          ASSERT(disc >= 0); 
          if ( b < 0 )
              return static_cast<Value>( ( -b + std::sqrt(disc) ) / (2*a) );
          else 
              return static_cast<Value>( ( -b - std::sqrt(disc) ) / (2*a) ); 
        }
    }
}

template<typename TImage , typename TSet >

DGtal::L2FirstOrderLocalDistance< TImage, TSet >::Value DGtal::L2FirstOrderLocalDistance< TImage, TSet >::gradientNorm	(	const Value &	aValue,
		const Values &	aValueList
	)		const

inlineprivate

Returns the squared euclidean norm of the gradient of the distance map

Parameters:

aValue	the distance value of the point where the gradient is computed
aValueList	the distance value of (some of) the neighbors

Returns:: the computed gradient norm.

Definition at line 224 of file FMMPointFunctors.ih.

{
  Value sum = 0; 
  for (typename Values::const_iterator it = aValueList.begin(); 
       it != aValueList.end(); ++it)
    {
      Value d = (aValue - *it); 
      sum += (d*d); 
    }
  return sum; 
}

template<typename TImage , typename TSet >

DGtal::L2FirstOrderLocalDistance< TImage, TSet >::Value DGtal::L2FirstOrderLocalDistance< TImage, TSet >::operator() ( const Point & aPoint )

inline

Euclidean distance computation at aPoint , from the available distance values of the 1-neighbors of aPoint .

Parameters:

aPoint the point for which the distance is computed

Returns:: the distance value at aPoint.

Definition at line 113 of file FMMPointFunctors.ih.

References DGtal::findAndGetValue().

{
  //distance values
  Values v; 
  v.reserve(Point::dimension); 
  //two 1-neighbors
  Point neighbor1 = aPoint; 
  Point neighbor2 = aPoint;
 
  typename Point::Iterator it1 = neighbor1.begin(); 
  typename Point::Iterator it2 = neighbor2.begin(); 
  typename Point::ConstIterator it = aPoint.begin(); 
  typename Point::ConstIterator itEnd = aPoint.end(); 
  for ( ; it != itEnd; ++it, ++it1, ++it2)
    {//for each dimension
      typename Point::Coordinate c = *it; 
      *it1 = (c+1); 
      *it2 = (c-1);
      //neighboring values
      Value d, d1, d2 = 0; 
      bool flag1 = findAndGetValue( *myImgPtr, *mySetPtr, neighbor1, d1 );
      bool flag2 = findAndGetValue( *myImgPtr, *mySetPtr, neighbor2, d2 );
      if ( flag1 || flag2 ) 
        {
          if ( flag1 && flag2 )
            { //take the minimal value
              if (std::abs(d1) < std::abs(d2))
                d = d1;
              else 
                d = d2; 
            } else 
            {
              if (flag1) d = d1;
              if (flag2) d = d2; 
            }
          v.push_back(d); 
        }
      *it1 = c; 
      *it2 = c;
    } //end for each dimension
  //computation of the new value
    return this->compute(v); 
}

template<typename TImage , typename TSet >

DGtal::L2FirstOrderLocalDistance< TImage, TSet > & DGtal::L2FirstOrderLocalDistance< TImage, TSet >::operator= ( const L2FirstOrderLocalDistance< TImage, TSet > & other )

inline

Assignment.

Parameters:

other the object to copy.

Returns:: a reference on 'this'.

Definition at line 88 of file FMMPointFunctors.ih.

References DGtal::L2FirstOrderLocalDistance< TImage, TSet >::myImgPtr, and DGtal::L2FirstOrderLocalDistance< TImage, TSet >::mySetPtr.

{
  if( this != &other)
  {
    myImgPtr = other.myImgPtr; 
    mySetPtr = other.mySetPtr; 
      ASSERT( myImgPtr ); 
      ASSERT( mySetPtr ); 
  }
  return *this; 
}