libinsighttoolkit3-dev 3.20.1+git20120521-6build1 / usr / include / InsightToolkit / Review / itkFlatStructuringElement.txx

/*=========================================================================

  Program:   Insight Segmentation & Registration Toolkit
  Module:    itkFlatStructuringElement.txx
  Language:  C++
  Date:      $Date$
  Version:   $Revision$

  Copyright (c) Insight Software Consortium. All rights reserved.
  See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even 
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR 
     PURPOSE.  See the above copyright notices for more information.

=========================================================================*/

#ifndef __itkFlatStructuringElement_txx
#define __itkFlatStructuringElement_txx
#include "vnl/vnl_math.h"
#include "itkFlatStructuringElement.h"
#include <math.h>
#include <vector>

#ifndef M_PI
#define M_PI vnl_math::pi
#endif

#include "itkImage.h"
#include "itkImageRegionIterator.h"
#include "itkFloodFilledSpatialFunctionConditionalIterator.h"
#include "itkEllipsoidInteriorExteriorSpatialFunction.h" 

#include "itkVanHerkGilWermanDilateImageFilter.h"


namespace itk
{
template<unsigned int VDimension>
FlatStructuringElement<VDimension> FlatStructuringElement<VDimension>
::Poly(RadiusType radius, unsigned lines)
{
  Self res = Self();
  res = res.PolySub(Dispatch<VDimension>(), radius, lines);
  res.SetRadius( radius );
#if 0
  float theta, phi, step;
  theta = phi = 0;
  step = M_PI/(lines - 1);

  while (theta < M_PI) 
    {

    std::cout << "theta= " << theta << " phi = " << phi << std::endl;
    LType O = res.mkOffset(phi, theta);
    std::cout << O << std::endl;
    if (res.checkParallel(O, res.m_Lines))
      {
      std::cout << "Already have this line" << std::endl;
      }
    else
      {
      res.m_Lines.push_back(O);
      }
    theta += step;
    phi += step;
    }
  std::cout << "---------------" << std::endl;
#endif
  res.ComputeBufferFromLines();
  return(res);

}

template<unsigned int VDimension>
FlatStructuringElement<VDimension> FlatStructuringElement<VDimension>
::PolySub(const Dispatch<2> &, RadiusType radius, unsigned lines) const
{
  // radial decomposition method from "Radial Decomposition of Discs
  // and Spheres" - CVGIP: Graphical Models and Image Processing
  //std::cout << "2 dimensions" << std::endl;
  Self res = Self();
  res.m_Decomposable = true;
  
  unsigned int rr = 0;
  for (unsigned i=0;i<VDimension;i++)
    {
    if (radius[i] > rr) rr = radius[i];
    }
  if (lines == 0)
    {
    // select some default line values
    if (rr <= 3) lines=2;
    else if (rr <= 8) lines=4;
    else lines=6;
    }
  // start with a circle - figure out the length of the structuring
  // element we need -- This method results in a polygon with 2*lines
  // sides, each side with length k, where k is the structuring
  // element length. Therefore the value of k we need to produce the
  // radius we want is: (M_PI * rr * 2)/(2*lines)
  float k1 = (M_PI * (float)radius[0])/((float)lines);
  float k2 = (M_PI * (float)radius[1])/((float)lines);
  //std::cout << "k= " << k << std::endl;
  float theta, step;
  step = M_PI/lines;
  theta = 0;
  // just to ensure that we get the last one
  while (theta <= M_PI/2.0 + 0.0001)
    {
    LType O;
    O[0] = k1 * vcl_cos(theta);
    O[1] = k2 * vcl_sin(theta);
    if (!res.checkParallel(O, res.m_Lines))
      {
      //std::cout << O << std::endl;
      res.m_Lines.push_back(O);
      }
     O[0] = k1 * vcl_cos(-theta);
     O[1] = k2 * vcl_sin(-theta);
     if (!res.checkParallel(O, res.m_Lines))
       {
       //std::cout << O << std::endl;
       res.m_Lines.push_back(O);
       }
     theta += step;
     //std::cout << "theta1 = " << theta << " " << M_PI/2.0 << std::endl;
    }
    
  return(res);
}

//    O[0] = k1 * vcl_cos(phi) * vcl_cos(theta);
//    O[1] = k2 * vcl_cos(phi) * vcl_sin(theta);
//    O[2] = k3 * vcl_sin(theta);

template<unsigned int VDimension>
FlatStructuringElement<VDimension> FlatStructuringElement<VDimension>
::PolySub(const Dispatch<3> &, RadiusType radius, unsigned lines) const
{
  Self res = Self();
  res.m_Decomposable = true;
  // std::cout << "3 dimensions" << std::endl;
  unsigned int rr = 0;
  int iterations = 1;
  int faces = lines * 2;
  for (unsigned i=0;i<VDimension;i++)
    {
    if (radius[i] > rr) rr = radius[i];
    }
  switch (faces)
    {
    case 12:
      {
      // dodecahedron
      float phi = (1.0 + vcl_sqrt(5.0)) / 2.0;
      float b = 1.0/phi;
      float c = 2.0 - phi;
      unsigned facets = 12;
      typedef std::vector<FacetType> FacetArrayType;
      FacetArrayType FacetArray;
      FacetArray.resize( facets );
      // set up vectors normal to the faces - only put in 3 points for
      // each face:
      // face 1
      LType PP(0.0);
      FacetType Fc;
      b /= 2.0;
      c /= 2.0;
  
      PP[0]=c;PP[1]=0;PP[2]=0.5;
      Fc.P1 = PP;
      PP[0]=-c;PP[1]=0;PP[2]=0.5;
      Fc.P2 = PP;
      PP[0]=-b;PP[1]=b;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[0] = Fc;
  
      PP[0]=-c;PP[1]=0;PP[2]=0.5;
      Fc.P1 = PP;
      PP[0]=c;PP[1]=0;PP[2]=0.5;
      Fc.P2 = PP;
      PP[0]=b;PP[1]=-b;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[1] = Fc;
      
      PP[0]=c;PP[1]=0;PP[2]=-0.5;
      Fc.P1 = PP;
      PP[0]=-c;PP[1]=0;PP[2]=-0.5;
      Fc.P2 = PP;
      PP[0]=-b;PP[1]=-b;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[2] = Fc;
  
      PP[0]=-c;PP[1]=0;PP[2]=-0.5;
      Fc.P1 = PP;
      PP[0]=c;PP[1]=0;PP[2]=-0.5;
      Fc.P2 = PP;
      PP[0]=b;PP[1]=b;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[3] = Fc;
  
      PP[0]=0;PP[1]=0.5;PP[2]=-c;
      Fc.P1 = PP;
      PP[0]=0;PP[1]=0.5;PP[2]=c;
      Fc.P2 = PP;
      PP[0]=b;PP[1]=b;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[4] = Fc;
  
      PP[0]=0;PP[1]=0.5;PP[2]=c;
      Fc.P1 = PP;
      PP[0]=0;PP[1]=0.5;PP[2]=-c;
      Fc.P2 = PP;
      PP[0]=-b;PP[1]=b;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[5] = Fc;
  
      PP[0]=0;PP[1]=-0.5;PP[2]=-c;
      Fc.P1 = PP;
      PP[0]=0;PP[1]=-0.5;PP[2]=c;
      Fc.P2 = PP;
      PP[0]=-b;PP[1]=-b;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[6] = Fc;
  
      PP[0]=0;PP[1]=-0.5;PP[2]=c;
      Fc.P1 = PP;
      PP[0]=0;PP[1]=-0.5;PP[2]=-c;
      Fc.P2 = PP;
      PP[0]=b;PP[1]=-b;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[7] = Fc;
  
      PP[0]=0.5;PP[1]=c;PP[2]=0;
      Fc.P1 = PP;
      PP[0]=0.5;PP[1]=-c;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=b;PP[1]=-b;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[8] = Fc;
  
      PP[0]=0.5;PP[1]=-c;PP[2]=0;
      Fc.P1 = PP;
      PP[0]=0.5;PP[1]=c;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=b;PP[1]=b;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[9] = Fc;
  
      PP[0]=-0.5;PP[1]=c;PP[2]=0;
      Fc.P1 = PP;
      PP[0]=-0.5;PP[1]=-c;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=-b;PP[1]=-b;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[10] = Fc;
  
      PP[0]=-0.5;PP[1]=-c;PP[2]=0;
      Fc.P1 = PP;
      PP[0]=-0.5;PP[1]=c;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=-b;PP[1]=b;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[11] = Fc;
      for (unsigned j = 0; j < facets; j++)
        {
        // Find a line perpendicular to each face
        LType L, A, B;
        A = FacetArray[j].P2 - FacetArray[j].P1;
        B = FacetArray[j].P3 - FacetArray[j].P1;
        L[0] = A[1]*B[2] - B[1]*A[2];
        L[1] = B[0]*A[2] - A[0]*B[2];
        L[2] = A[0]*B[1] - B[0]*A[1];
        
        L.Normalize();
        // Scale to required length
        L *= rr;
        if (!res.checkParallel(L, res.m_Lines))
          {
          res.m_Lines.push_back(L);
          }
        }
      return(res);
  
      }
    break;
    case 14:
      {
      // cube with the corners cut off
      LType A;
      // The axes
      A[0]=1;A[1]=0;A[2]=0;
      A *= rr;
      res.m_Lines.push_back(A);
      A[0]=0;A[1]=1;A[2]=0;
      A *= rr;
      res.m_Lines.push_back(A);
      A[0]=0;A[1]=0;A[2]=1;
      A *= rr;
      res.m_Lines.push_back(A);
      // Diagonals
      A[0]=1;A[1]=1;A[2]=1;
      A.Normalize();
      A *= rr;
      res.m_Lines.push_back(A);
  
      A[0]=-1;A[1]=1;A[2]=1;
      A.Normalize();
      A *= rr;
      res.m_Lines.push_back(A);
  
      A[0]=1;A[1]=-1;A[2]=1;
      A.Normalize();
      A *= rr;
      res.m_Lines.push_back(A);
  
      A[0]=-1;A[1]=-1;A[2]=1;
      A.Normalize();
      A *= rr;
      res.m_Lines.push_back(A);
      return(res);
      }
    break;
    case 20:
      {
      // Icosahedron
      float phi = (1.0 + vcl_sqrt(5.0)) / 2.0;
      float a = 0.5;
      float b = 1.0/(2.0*phi);
      unsigned facets = 20;
      typedef std::vector<FacetType> FacetArrayType;
      FacetArrayType FacetArray;
      FacetArray.resize( facets );
      // set up vectors normal to the faces - only put in 3 points for
      // each face:
      // face 1
      LType PP(0.0);
      FacetType Fc;
  
      PP[0]=0;PP[1]=b;PP[2]=-a;
      Fc.P1 = PP;
      PP[0]=b;PP[1]=a;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=-b;PP[1]=a;PP[2]=0;
      Fc.P3 = PP;
      FacetArray[0] = Fc;
      
      PP[0]=0;PP[1]=b;PP[2]=a;
      Fc.P1 = PP;
      PP[0]=-b;PP[1]=a;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=b;PP[1]=a;PP[2]=0;
      Fc.P3 = PP;
      FacetArray[1] = Fc;
      
      PP[0]=0;PP[1]=b;PP[2]=a;
      Fc.P1 = PP;
      PP[0]=0;PP[1]=-b;PP[2]=a;
      Fc.P2 = PP;
      PP[0]=-a;PP[1]=0;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[2] = Fc;
      
      PP[0]=0;PP[1]=b;PP[2]=a;
      Fc.P1 = PP;
      PP[0]=a;PP[1]=0;PP[2]=b;
      Fc.P2 = PP;
      PP[0]=0;PP[1]=-b;PP[2]=a;
      Fc.P3 = PP;
      FacetArray[3] = Fc;
      
      PP[0]=0;PP[1]=b;PP[2]=-a;
      Fc.P1 = PP;
      PP[0]=0;PP[1]=-b;PP[2]=-a;
      Fc.P2 = PP;
      PP[0]=a;PP[1]=0;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[4] = Fc;
      
      PP[0]=0;PP[1]=b;PP[2]=-a;
      Fc.P1 = PP;
      PP[0]=-a;PP[1]=0;PP[2]=-b;
      Fc.P2 = PP;
      PP[0]=0;PP[1]=-b;PP[2]=-a;
      Fc.P3 = PP;
      FacetArray[5] = Fc;
      
      PP[0]=0;PP[1]=-b;PP[2]=a;
      Fc.P1 = PP;
      PP[0]=b;PP[1]=-a;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=-b;PP[1]=-a;PP[2]=0;
      Fc.P3 = PP;
      FacetArray[6] = Fc;
      
      PP[0]=0;PP[1]=-b;PP[2]=-a;
      Fc.P1 = PP;
      PP[0]=-b;PP[1]=-a;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=b;PP[1]=-a;PP[2]=0;
      Fc.P3 = PP;
      FacetArray[7] = Fc;
      
      PP[0]=-b;PP[1]=a;PP[2]=0;
      Fc.P1 = PP;
      PP[0]=-a;PP[1]=0;PP[2]=b;
      Fc.P2 = PP;
      PP[0]=-a;PP[1]=0;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[8] = Fc;
      
      PP[0]=-b;PP[1]=-a;PP[2]=0;
      Fc.P1 = PP;
      PP[0]=-a;PP[1]=0;PP[2]=-b;
      Fc.P2 = PP;
      PP[0]=-a;PP[1]=0;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[9] = Fc;
       
      PP[0]=b;PP[1]=a;PP[2]=0;
      Fc.P1 = PP;
      PP[0]=a;PP[1]=0;PP[2]=-b;
      Fc.P2 = PP;
      PP[0]=a;PP[1]=0;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[10] = Fc;
       
      PP[0]=b;PP[1]=-a;PP[2]=0;
      Fc.P1 = PP;
      PP[0]=a;PP[1]=0;PP[2]=b;
      Fc.P2 = PP;
      PP[0]=a;PP[1]=0;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[11] = Fc;
       
      PP[0]=0;PP[1]=b;PP[2]=a;
      Fc.P1 = PP;
      PP[0]=-a;PP[1]=0;PP[2]=b;
      Fc.P2 = PP;
      PP[0]=-b;PP[1]=a;PP[2]=0;
      Fc.P3 = PP;
      FacetArray[12] = Fc;
       
      PP[0]=0;PP[1]=b;PP[2]=a;
      Fc.P1 = PP;
      PP[0]=b;PP[1]=a;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=a;PP[1]=0;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[13] = Fc;
       
      PP[0]=0;PP[1]=b;PP[2]=-a;
      Fc.P1 = PP;
      PP[0]=-b;PP[1]=a;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=-a;PP[1]=0;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[14] = Fc;
       
      PP[0]=0;PP[1]=b;PP[2]=-a;
      Fc.P1 = PP;
      PP[0]=a;PP[1]=0;PP[2]=-b;
      Fc.P2 = PP;
      PP[0]=b;PP[1]=a;PP[2]=0;
      Fc.P3 = PP;
      FacetArray[15] = Fc;
       
      PP[0]=0;PP[1]=-b;PP[2]=-a;
      Fc.P1 = PP;
      PP[0]=-a;PP[1]=0;PP[2]=-b;
      Fc.P2 = PP;
      PP[0]=-b;PP[1]=-a;PP[2]=0;
      Fc.P3 = PP;
      FacetArray[16] = Fc;
        
      PP[0]=0;PP[1]=-b;PP[2]=-a;
      Fc.P1 = PP;
      PP[0]=b;PP[1]=-a;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=a;PP[1]=0;PP[2]=-b;
      Fc.P3 = PP;
      FacetArray[17] = Fc;
         
      PP[0]=0;PP[1]=-b;PP[2]=a;
      Fc.P1 = PP;
      PP[0]=-b;PP[1]=-a;PP[2]=0;
      Fc.P2 = PP;
      PP[0]=-a;PP[1]=0;PP[2]=b;
      Fc.P3 = PP;
      FacetArray[18] = Fc;
         
      PP[0]=0;PP[1]=-b;PP[2]=a;
      Fc.P1 = PP;
      PP[0]=a;PP[1]=0;PP[2]=b;
      Fc.P2 = PP;
      PP[0]=b;PP[1]=-a;PP[2]=0;
      Fc.P3 = PP;
      FacetArray[19] = Fc;
   
      for (unsigned j = 0; j < facets; j++)
        {
        // Find a line perpendicular to each face
        LType L, A, B;
        A = FacetArray[j].P2 - FacetArray[j].P1;
        B = FacetArray[j].P3 - FacetArray[j].P1;
        L[0] = A[1]*B[2] - B[1]*A[2];
        L[1] = B[0]*A[2] - A[0]*B[2];
        L[2] = A[0]*B[1] - B[0]*A[1];
        
        L.Normalize();
        // Scale to required length
        L *= rr;
        if (!res.checkParallel(L, res.m_Lines))
          {
          res.m_Lines.push_back(L);
          }
        }
      return(res);
      }
    break;
    case 32:
      {
      iterations = 1;
      // 2 iterations leads to 128 faces, which is too many
      // subdivision of octahedron
      // create triangular facet approximation to a sphere - begin with
      // unit sphere
      // total number of facets is 8 * (4^iterations)
      unsigned int facets = 8 * (int)vcl_pow((double)4, iterations);
      float sqrt2 = vcl_sqrt(2.0);
      // std::cout << facets << " facets" << std::endl;
      typedef std::vector<FacetType> FacetArrayType;
      FacetArrayType FacetArray;
      FacetArray.resize( facets );
      
      // original corners of octahedron
      LType P0(0.0), P1(0.0), P2(0.0), P3(0.0), P4(0.0), P5(0.0); 
      P0[0]=0;         P0[1]=0;       P0[2]=1;
      P1[0]=0;         P1[1]=0;       P1[2]=-1;
      P2[0]=-1.0/sqrt2;P2[1]=-1/sqrt2;P2[2]=0;
      P3[0]=1/sqrt2;   P3[1]=-1/sqrt2;P3[2]=0;
      P4[0]=1/sqrt2;   P4[1]=1/sqrt2; P4[2]=0;
      P5[0]=-1/sqrt2;  P5[1]=1/sqrt2; P5[2]=0;
      
      FacetType F0, F1, F2, F3, F4, F5, F6, F7;
      F0.P1 = P0; F0.P2 = P3; F0.P3 = P4;
      F1.P1 = P0; F1.P2 = P4; F1.P3 = P5;
      F2.P1 = P0; F2.P2 = P5; F2.P3 = P2;
      F3.P1 = P0; F3.P2 = P2; F3.P3 = P3;
      F4.P1 = P1; F4.P2 = P4; F4.P3 = P3;
      F5.P1 = P1; F5.P2 = P5; F5.P3 = P4;
      F6.P1 = P1; F6.P2 = P2; F6.P3 = P5;
      F7.P1 = P1; F7.P2 = P3; F7.P3 = P2;
      
      FacetArray[0] = F0;
      FacetArray[1] = F1;
      FacetArray[2] = F2;
      FacetArray[3] = F3;
      FacetArray[4] = F4;
      FacetArray[5] = F5;
      FacetArray[6] = F6;
      FacetArray[7] = F7;
      int pos = 8;
      // now subdivide the octahedron
      for (unsigned it = 0; it<(unsigned)iterations; it++)
        {
        // Bisect edges and move to sphere
        unsigned ntold = pos;
        for (unsigned i = 0; i < ntold; i++)
          {
          LType Pa, Pb, Pc;
          for (unsigned d = 0; d<  VDimension;d++)
            {
            Pa[d] = (FacetArray[i].P1[d] + FacetArray[i].P2[d])/2;
            Pb[d] = (FacetArray[i].P2[d] + FacetArray[i].P3[d])/2;
            Pc[d] = (FacetArray[i].P3[d] + FacetArray[i].P1[d])/2;
            }
          Pa.Normalize();
          Pb.Normalize();
          Pc.Normalize();
          FacetArray[pos].P1 = FacetArray[i].P1; 
          FacetArray[pos].P2 = Pa; 
          FacetArray[pos].P3 = Pc;
          pos++;
          FacetArray[pos].P1 = Pa;
          FacetArray[pos].P2 = FacetArray[i].P2;  
          FacetArray[pos].P3 = Pb;
          pos++;
          FacetArray[pos].P1 = Pb;
          FacetArray[pos].P2 = FacetArray[i].P3;  
          FacetArray[pos].P3 = Pc;
          pos++;
          FacetArray[i].P1 = Pa;
          FacetArray[i].P2 = Pb;
          FacetArray[i].P3 = Pc;
          }
        }
      
        
      for (unsigned j = 0; j < facets; j++)
        {
        // Find a line perpendicular to each face
        LType L, A, B;
        A = FacetArray[j].P2 - FacetArray[j].P1;
        B = FacetArray[j].P3 - FacetArray[j].P1;
        L[0] = A[1]*B[2] - B[1]*A[2];
        L[1] = B[0]*A[2] - A[0]*B[2];
        L[2] = A[0]*B[1] - B[0]*A[1];
        
        L.Normalize();
        // Scale to required length
        L *= rr;
        if (!res.checkParallel(L, res.m_Lines))
          {
          res.m_Lines.push_back(L);
          }
        }
      return(res);
      }
    break;
    default:
      std::cout << "Unsupported number of lines" << std::endl;
      return(res);
    }
}

template<unsigned int VDimension>
FlatStructuringElement<VDimension> FlatStructuringElement<VDimension>
::PolySub(const DispatchBase &, RadiusType , unsigned) const
{
  Self res = Self();
  res.m_Decomposable = true;
  std::cout << "Don't know how to deal with this many dimensions" << std::endl;
  return(res);
}


template<unsigned int VDimension>
FlatStructuringElement<VDimension> FlatStructuringElement<VDimension>
::Box(RadiusType radius)
{
  // this should work for any number of dimensions
  Self res = Self();
  res.m_Decomposable = true;
  res.SetRadius( radius );
  for (unsigned i = 0;i<VDimension;i++)
    {
    if (radius[i] != 0)
      {
      LType L;
      L.Fill(0);
      L[i] = radius[i]*2+1;
      res.m_Lines.push_back(L);
      }
    }
  // this doesn't work if one of the dimensions is zero. Suspect an
  //"inconsistency" in the way 
//  res.ComputeBufferFromLines();
   Iterator kernel_it;
   for( kernel_it=res.Begin(); kernel_it != res.End(); ++kernel_it )
     {
     *kernel_it= true;
     }

  return(res);
}


template<unsigned int VDimension>
FlatStructuringElement<VDimension> FlatStructuringElement<VDimension>
::Cross(RadiusType radius)
{
  // this should work for any number of dimensions
  Self res = Self();
  res.m_Decomposable = false;
  res.SetRadius( radius );
  Iterator kernel_it;
  for( kernel_it=res.Begin(); kernel_it != res.End(); ++kernel_it )
    {
    *kernel_it= false;
    }
  for( int d = 0; d<(int)VDimension; d++ )
    {
    OffsetType o;
    o.Fill( 0 );
    for( int i=-(int)radius[d]; i<=(int)radius[d]; i++ )
      {
      o[d] = i;
      res[o] = true;
      }
    }

  return(res);
}


template<unsigned int VDimension>
FlatStructuringElement<VDimension> FlatStructuringElement<VDimension>
::Ball(RadiusType radius)
{
  Self res = Self();
  res.SetRadius( radius );
  res.m_Decomposable = false;

  unsigned int i;
  
  // Image typedef
  typedef Image<bool, VDimension> ImageType;

  // Create an image to hold the ellipsoid
  //
  typename ImageType::Pointer sourceImage = ImageType::New();
  typename ImageType::RegionType region;
  RadiusType size = radius;
  for( i=0; i<(int)VDimension; i++ )
    {
    size[i] = 2*size[i] + 1;
    }
  region.SetSize( size );

  sourceImage->SetRegions( region );
  sourceImage->Allocate();
  // sourceImage->Print( std::cout );

  // Set the background to be zero
  //
  ImageRegionIterator<ImageType> it(sourceImage, region);

  for(it.GoToBegin(); !it.IsAtEnd(); ++it)
    {
    it.Set(false);
    }

  
  // Create the ellipsoid
  //

  // Ellipsoid spatial function typedef
  typedef EllipsoidInteriorExteriorSpatialFunction<VDimension> EllipsoidType;
  
  // Create an ellipsoid spatial function for the source image
  typename EllipsoidType::Pointer spatialFunction = EllipsoidType::New();

  // Define and set the axes lengths for the ellipsoid
  typename EllipsoidType::InputType axes;
  for (i=0; i < VDimension; i++)
    {
    axes[i] = res.GetSize(i);
    }
  spatialFunction->SetAxes( axes );

  // Define and set the center of the ellipsoid in physical space
  typename EllipsoidType::InputType center;
  for (i=0; i < VDimension; i++)
    {
    // put the center of ellipse in the middle of the center pixel
    center[i] = res.GetRadius(i) + 0.5; 
    }
  spatialFunction->SetCenter( center );

  // Define the orientations of the ellipsoid axes, for now, we'll use
  // the identify matrix
  typename EllipsoidType::OrientationType orientations;
  orientations.fill( 0.0 );
  orientations.fill_diagonal( 1.0 );
  spatialFunction->SetOrientations(orientations);

  typename ImageType::IndexType seed;
  for (i=0; i < VDimension; i++)
    {
    seed[i] = res.GetRadius(i);
    }
  FloodFilledSpatialFunctionConditionalIterator<ImageType, EllipsoidType> 
    sfi = FloodFilledSpatialFunctionConditionalIterator<ImageType,
    EllipsoidType>(sourceImage, spatialFunction, seed);
  sfi.SetCenterInclusionStrategy();
  
  // Iterate through the entire image and set interior pixels to 1
  for(; !sfi.IsAtEnd(); ++sfi)
    {
    sfi.Set(true);
    }

  
  // Copy the ellipsoid into the kernel
  //
  Iterator kernel_it;
  for (it.GoToBegin(), kernel_it=res.Begin();!it.IsAtEnd();++it,++kernel_it)
    {
    *kernel_it = it.Get();
    }

  // Clean up
  //   ...temporary image should be cleaned up by SmartPointers automatically

  return res;
}


template<unsigned int NDimension>
FlatStructuringElement<NDimension> 
FlatStructuringElement<NDimension>
::Annulus(RadiusType radius,
          unsigned int thickness,
          bool includeCenter)
{
  Self result = Self();
  result.SetRadius( radius );
  result.m_Decomposable = false;
  
  // Image typedef
  typedef Image<bool,NDimension> ImageType;

  // Create an image to hold the ellipsoid
  //
  typename ImageType::Pointer kernelImage = ImageType::New();
  typename ImageType::RegionType region;
  RadiusType size = radius;
  for(unsigned int i=0; i<NDimension; i++ )
    {
    size[i] = 2*size[i] + 1;
    }
  region.SetSize( size );

  kernelImage->SetRegions( region );
  kernelImage->Allocate();

  // Set the background to be zero
  //
  ImageRegionIterator<ImageType> it(kernelImage, region);

  for(it.GoToBegin(); !it.IsAtEnd(); ++it)
    {
    it.Set(false);
    }

  // Create two ellipsoids
  //

  // Ellipsoid spatial function typedef
  typedef EllipsoidInteriorExteriorSpatialFunction<NDimension> EllipsoidType;
  
  // Create an ellipsoid spatial function for the source image
  typename EllipsoidType::Pointer ellipsoidOuter = EllipsoidType::New();
  typename EllipsoidType::Pointer ellipsoidInner = EllipsoidType::New();

  // Define and set the axes lengths for the ellipsoid
  typename EllipsoidType::InputType axesOuter;
  typename EllipsoidType::InputType axesInner;
  for (unsigned int i=0; i < NDimension; i++)
    {
    axesOuter[i] = result.GetSize(i);
    axesInner[i] = std::max( 2*(long)radius[i] + 1 - 2*(long)thickness, (long)1 );
    }
  ellipsoidOuter->SetAxes( axesOuter );
  ellipsoidInner->SetAxes( axesInner );

  // Define and set the center of the ellipsoid in physical space
  typename EllipsoidType::InputType center;
  for (unsigned int i=0; i < NDimension; i++)
    {
    // put the center of ellipse in the middle of the center pixel
    center[i] = result.GetRadius(i) + 0.5; 
    }
  ellipsoidOuter->SetCenter( center );
  ellipsoidInner->SetCenter( center );

  // Define the orientations of the ellipsoid axes, for now, we'll use
  // the identity matrix
  typename EllipsoidType::OrientationType orientations;
  orientations.fill( 0.0 );
  orientations.fill_diagonal( 1.0 );
  ellipsoidOuter->SetOrientations( orientations );
  ellipsoidInner->SetOrientations( orientations );

  // Create the starting seed
  typename ImageType::IndexType seed;
  for (unsigned int i=0; i < NDimension; i++)
    {
    seed[i] = result.GetRadius(i);
    }

  // Define the iterators for each ellipsoid
  typedef FloodFilledSpatialFunctionConditionalIterator<ImageType, EllipsoidType>
    FloodIteratorType;
  FloodIteratorType itEllipsoidOuter =
    FloodIteratorType( kernelImage, ellipsoidOuter, seed );
  FloodIteratorType itEllipsoidInner = 
    FloodIteratorType( kernelImage, ellipsoidInner, seed );
  itEllipsoidOuter.SetCenterInclusionStrategy();
  itEllipsoidInner.SetCenterInclusionStrategy();

  // Iterate through the image and set all outer pixels to 'ON'
  for(; !itEllipsoidOuter.IsAtEnd(); ++itEllipsoidOuter)
    {
    itEllipsoidOuter.Set(true);
    }
  // Iterate through the image and set all inner pixels to 'OFF'
  for(; !itEllipsoidInner.IsAtEnd(); ++itEllipsoidInner)
    {
    itEllipsoidInner.Set(false);
    }

  // Set center pixel if included
  kernelImage->SetPixel( seed, includeCenter );

  // Copy the annulus into the kernel
  //
  Iterator kernel_it;
  for (it.GoToBegin(), kernel_it=result.Begin(); !it.IsAtEnd(); ++it,++kernel_it)
    {
    *kernel_it = it.Get();
    }

  // Clean up
  //   ...temporary image should be cleaned up by SmartPointers automatically

  return result;
}
template<unsigned int VDimension>
bool
FlatStructuringElement<VDimension>::
checkParallel(LType NewVec, DecompType Lines)
{
  LType NN = NewVec;
  NN.Normalize();
  for (unsigned i = 0; i < Lines.size(); i++)
    {
    LType LL = Lines[i];
    LL.Normalize();
    float L = NN*LL;
    if ((1.0 - vcl_fabs(L)) < 0.000001) return(true);
    }
  return(false);
}

template<unsigned int VDimension>
void FlatStructuringElement< VDimension >
::PrintSelf(std::ostream &os, Indent indent) const
{
  //Superclass::PrintSelf(os, indent);
  if (m_Decomposable)
    {
    os << indent << "SE decomposition:" << std::endl;
    for (unsigned i = 0;i < m_Lines.size(); i++)
      {
      os << indent << m_Lines[i] << std::endl;
      }
    }
}


template<unsigned int VDimension>
void
FlatStructuringElement<VDimension>::
ComputeBufferFromLines()
{
  if( m_Decomposable )
    {
/*    itkExceptionMacro("Element must be decomposable.");*/
    }

  // create an image with a single pixel in the center which will be dilated
  // by the structuring lines (with AnchorDilateImageFilter) so the content
  // of the buffer will reflect the shape of the structuring element

  // Image typedef
  typedef Image<bool, VDimension> ImageType;

  // Create an image to hold the ellipsoid
  //
  typename ImageType::Pointer sourceImage = ImageType::New();
  typename ImageType::RegionType region;
  RadiusType size = this->GetRadius();
  for( int i=0; i<(int)VDimension; i++ )
    {
    size[i] = 2*size[i] + 1;
    }
  region.SetSize( size );
  sourceImage->SetRegions( region );
  sourceImage->Allocate();

  // sourceImage->Print(std::cout);

  // Set the background to be zero
  //
  ImageRegionIterator<ImageType> it( sourceImage, region );

  for( it.GoToBegin(); !it.IsAtEnd(); ++it )
    {
    it.Set( false );
    }

  // set the center pixel to 1
  typename ImageType::IndexType center;
  for( int i=0; i<(int)VDimension; i++)
    {
    center[i] = this->GetRadius()[i];
    }
  sourceImage->SetPixel( center, true );

  // initialize the kernel with everything to false, to avoid warnings in
  // valgrind in the SetKernel() method
  for( Iterator kernel_it=this->Begin(); kernel_it != this->End(); ++kernel_it )
    {
    *kernel_it = false;
    }

  // dilate the pixel
  typedef VanHerkGilWermanDilateImageFilter<ImageType, Self> DilateType;
  typename DilateType::Pointer dilate = DilateType::New();
  dilate->SetInput( sourceImage );
  dilate->SetKernel( *this );
  dilate->Update();

  // copy back the image to the kernel
  ImageRegionIterator<ImageType> oit( dilate->GetOutput(), region );
  Iterator kernel_it;
  for( oit.GoToBegin(), kernel_it=this->Begin(); !oit.IsAtEnd(); ++oit,++kernel_it )
    {
    *kernel_it = oit.Get();
    }

}


}

#endif