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/*=========================================================================
Program: Insight Segmentation & Registration Toolkit
Module: $RCSfile: itkGaussianOperator.txx,v $
Language: C++
Date: $Date: 2006-03-19 04:36:58 $
Version: $Revision: 1.21 $
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 _itkGaussianOperator_txx
#define _itkGaussianOperator_txx
#include "itkGaussianOperator.h"
#include "itkOutputWindow.h"
#include "itkMacro.h"
namespace itk
{
template<class TPixel,unsigned int VDimension, class TAllocator>
typename GaussianOperator<TPixel,VDimension, TAllocator>
::CoefficientVector
GaussianOperator<TPixel,VDimension, TAllocator>
::GenerateCoefficients()
{
CoefficientVector coeff;
double sum;
int i;
int j;
typename CoefficientVector::iterator it;
const double et = ::exp(-m_Variance);
const double cap = 1.0 - m_MaximumError;
// Create the kernel coefficients as a std::vector
sum = 0.0;
coeff.push_back(et * ModifiedBesselI0(m_Variance));
sum += coeff[0];
coeff.push_back(et * ModifiedBesselI1(m_Variance));
sum += coeff[1]* 2.0;
for (i=2; sum < cap; i++)
{
coeff.push_back(et* ModifiedBesselI(i, m_Variance));
sum += coeff[i] *2.0;
if (coeff[i] <= 0.0) break; // failsafe
if (coeff.size() > m_MaximumKernelWidth )
{
itkWarningMacro("Kernel size has exceeded the specified maximum width of " << m_MaximumKernelWidth << " and has been truncated to " << static_cast<unsigned long>( coeff.size() ) << " elements. You can raise the maximum width using the SetMaximumKernelWidth method.");
break;
}
}
// Normalize the coefficients so that their sum is one.
for (it = coeff.begin(); it < coeff.end(); ++it)
{
*it /= sum;
}
// Make symmetric
j = static_cast<int>( coeff.size() ) - 1;
coeff.insert(coeff.begin(), j, 0);
for (i=0, it = coeff.end()-1; i < j; --it, ++i)
{
coeff[i] = *it;
}
return coeff;
}
template<class TPixel,unsigned int VDimension, class TAllocator>
double
GaussianOperator<TPixel,VDimension, TAllocator>
::ModifiedBesselI0(double y)
{
double d, accumulator;
double m;
if ((d=vcl_fabs(y)) < 3.75)
{
m=y/3.75;
m*=m;
accumulator = 1.0 + m *(3.5156229+m*(3.0899424+m*(1.2067492
+ m*(0.2659732+m*(0.360768e-1 +m*0.45813e-2)))));
}
else
{
m=3.5/d;
accumulator =(::exp(d)/::sqrt(d))*(0.39894228+m*(0.1328592e-1
+m*(0.225319e-2+m*(-0.157565e-2+m*(0.916281e-2
+m*(-0.2057706e-1+m*(0.2635537e-1+m*(-0.1647633e-1
+m*0.392377e-2))))))));
}
return accumulator;
}
template<class TPixel,unsigned int VDimension, class TAllocator>
double
GaussianOperator<TPixel,VDimension, TAllocator>
::ModifiedBesselI1(double y)
{
double d, accumulator;
double m;
if ((d=vcl_fabs(y)) < 3.75)
{
m=y/3.75;
m*=m;
accumulator = d*(0.5+m*(0.87890594+m*(0.51498869+m*(0.15084934
+m*(0.2658733e-1+m*(0.301532e-2+m*0.32411e-3))))));
}
else
{
m=3.75/d;
accumulator = 0.2282967e-1+m*(-0.2895312e-1+m*(0.1787654e-1
-m*0.420059e-2));
accumulator = 0.39894228+m*(-0.3988024e-1+m*(-0.362018e-2
+m*(0.163801e-2+m*(-0.1031555e-1+m*accumulator))));
accumulator *= (::exp(d)/::sqrt(d));
}
if (y<0.0) return -accumulator;
else return accumulator;
}
template<class TPixel,unsigned int VDimension, class TAllocator>
double
GaussianOperator<TPixel,VDimension, TAllocator>
::ModifiedBesselI(int n, double y)
{
const double ACCURACY = 40.0;
int j;
double qim, qi, qip, toy;
double accumulator;
if (n<2)
{
throw ExceptionObject(__FILE__, __LINE__, "Order of modified bessel is > 2.", ITK_LOCATION); // placeholder
}
if (y==0.0) return 0.0;
else
{
toy=2.0/vcl_fabs(y);
qip=accumulator=0.0;
qi=1.0;
for (j=2*(n+(int)::sqrt(ACCURACY*n)); j>0 ; j--)
{
qim=qip+j*toy*qi;
qip=qi;
qi=qim;
if (fabs(qi) > 1.0e10)
{
accumulator*=1.0e-10;
qi *=1.0e-10;
qip*=1.0e-10;
}
if (j==n) accumulator=qip;
}
accumulator *= ModifiedBesselI0(y)/qi;
if (y<0.0 && (n&1)) return -accumulator;
else return accumulator;
}
}
}// end namespace itk
#endif
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