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/*========================================================================= |
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Program: Insight Segmentation & Registration Toolkit |
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Module: $RCSfile: itkLevelSetFunction.txx.html,v $ |
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Language: C++ |
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Date: $Date: 2006/01/17 19:15:40 $ |
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Version: $Revision: 1.4 $ |
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Copyright (c) Insight Software Consortium. All rights reserved. |
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See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details. |
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This software is distributed WITHOUT ANY WARRANTY; without even |
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the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
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PURPOSE. See the above copyright notices for more information. |
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=========================================================================*/ |
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DEF |
#ifndef __itkLevelSetFunction_txx_ |
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DEF |
#define __itkLevelSetFunction_txx_ |
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#include "itkLevelSetFunction.h" |
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#include "vnl/algo/vnl_symmetric_eigensystem.h" |
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namespace itk { |
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template <class TImageType> |
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typename LevelSetFunction<TImageType>::ScalarValueType |
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LEN |
LevelSetFunction<TImageType>::ComputeCurvatureTerm(const NeighborhoodType &neighborhood, |
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LEN |
const FloatOffsetType &offset, GlobalDataStruct *gd) |
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{ |
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if ( m_UseMinimalCurvature == false ) |
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{ |
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return this->ComputeMeanCurvature(neighborhood, offset, gd); |
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} |
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else |
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{ |
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if (ImageDimension == 3) |
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{ |
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return this->ComputeMinimalCurvature(neighborhood, offset, gd); |
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} |
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else if (ImageDimension == 2) |
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{ |
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return this->ComputeMeanCurvature(neighborhood, offset, gd); |
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} |
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else |
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{ |
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return this->ComputeMinimalCurvature(neighborhood, offset, gd); |
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} |
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} |
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} |
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template< class TImageType> |
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typename LevelSetFunction< TImageType >::ScalarValueType |
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LevelSetFunction< TImageType > |
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::ComputeMinimalCurvature( |
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const NeighborhoodType &itkNotUsed(neighborhood), |
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**const FloatOffsetType& itkNotUsed(offset), GlobalDataStruct *gd) |
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{ |
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unsigned int i, j, n; |
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ScalarValueType gradMag = vcl_sqrt(gd->m_GradMagSqr); |
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ScalarValueType Pgrad[ImageDimension][ImageDimension]; |
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ScalarValueType tmp_matrix[ImageDimension][ImageDimension]; |
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const ScalarValueType ZERO = NumericTraits<ScalarValueType>::Zero; |
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vnl_matrix_fixed<ScalarValueType, ImageDimension, ImageDimension> Curve; |
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const ScalarValueType MIN_EIG = NumericTraits<ScalarValueType>::min(); |
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ScalarValueType mincurve; |
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for (i = 0; i < ImageDimension; i++) |
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{ |
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Pgrad[i][i] = 1.0 - gd->m_dx[i] * gd->m_dx[i]/gradMag; |
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for (j = i+1; j < ImageDimension; j++) |
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{ |
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Pgrad[i][j]= gd->m_dx[i] * gd->m_dx[j]/gradMag; |
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Pgrad[j][i] = Pgrad[i][j]; |
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} |
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} |
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|
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//Compute Pgrad * Hessian * Pgrad |
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for (i = 0; i < ImageDimension; i++) |
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{ |
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for (j = i; j < ImageDimension; j++) |
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{ |
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tmp_matrix[i][j]= ZERO; |
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for (n = 0 ; n < ImageDimension; n++) |
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{ |
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tmp_matrix[i][j] += Pgrad[i][n] * gd->m_dxy[n][j]; |
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} |
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tmp_matrix[j][i]=tmp_matrix[i][j]; |
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} |
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} |
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for (i = 0; i < ImageDimension; i++) |
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{ |
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for (j = i; j < ImageDimension; j++) |
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{ |
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Curve(i,j) = ZERO; |
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for (n = 0 ; n < ImageDimension; n++) |
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{ |
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Curve(i,j) += tmp_matrix[i][n] * Pgrad[n][j]; |
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} |
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Curve(j,i) = Curve(i,j); |
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} |
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} |
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|
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//Eigensystem |
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vnl_symmetric_eigensystem<ScalarValueType> eig(Curve); |
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mincurve=vnl_math_abs(eig.get_eigenvalue(ImageDimension-1)); |
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for (i = 0; i < ImageDimension; i++) |
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{ |
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if(vnl_math_abs(eig.get_eigenvalue(i)) < mincurve && |
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vnl_math_abs(eig.get_eigenvalue(i)) > MIN_EIG) |
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{ |
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mincurve = vnl_math_abs(eig.get_eigenvalue(i)); |
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} |
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} |
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return ( mincurve / gradMag ); |
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} |
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template< class TImageType> |
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typename LevelSetFunction< TImageType >::ScalarValueType |
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LevelSetFunction< TImageType > |
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::Compute3DMinimalCurvature(const NeighborhoodType &neighborhood, |
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const FloatOffsetType& offset, GlobalDataStruct *gd) |
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{ |
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ScalarValueType mean_curve = this->ComputeMeanCurvature(neighborhood, offset, gd); |
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int i0 = 0, i1 = 1, i2 = 2; |
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ScalarValueType gauss_curve = |
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****(2*(gd->m_dx[i0]*gd->m_dx[i1]*(gd->m_dxy[i2][i0] |
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*gd->m_dxy[i1][i2]-gd->m_dxy[i0][i1]*gd->m_dxy[i2][i2]) + |
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********gd->m_dx[i1]*gd->m_dx[i2]*(gd->m_dxy[i2][i0] |
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*gd->m_dxy[i0][i1]-gd->m_dxy[i1][i2]*gd->m_dxy[i0][i0]) + |
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********gd->m_dx[i0]*gd->m_dx[i2]*(gd->m_dxy[i1][i2] |
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*gd->m_dxy[i0][i1]-gd->m_dxy[i2][i0]*gd->m_dxy[i1][i1])) + |
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*****gd->m_dx[i0]*gd->m_dx[i0]*(gd->m_dxy[i1][i1] |
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*gd->m_dxy[i2][i2]-gd->m_dxy[i1][i2]*gd->m_dxy[i1][i2]) + |
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*****gd->m_dx[i1]*gd->m_dx[i1]*(gd->m_dxy[i0][i0] |
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*gd->m_dxy[i2][i2]-gd->m_dxy[i2][i0]*gd->m_dxy[i2][i0]) + |
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*****gd->m_dx[i2]*gd->m_dx[i2]*(gd->m_dxy[i1][i1] |
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*gd->m_dxy[i0][i0]-gd->m_dxy[i0][i1]*gd->m_dxy[i0][i1]))/ |
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****(gd->m_dx[i0]*gd->m_dx[i0] + gd->m_dx[i1]*gd->m_dx[i1] + gd->m_dx[i2]*gd->m_dx[i2]); |
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|
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ScalarValueType discriminant = mean_curve * mean_curve-gauss_curve; |
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if (discriminant < 0.0) |
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{ |
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discriminant = 0.0; |
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} |
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discriminant = sqrt(discriminant); |
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return (mean_curve - discriminant); |
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} |
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template <class TImageType> |
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typename LevelSetFunction<TImageType>::ScalarValueType |
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LevelSetFunction<TImageType>::ComputeMeanCurvature( |
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const NeighborhoodType &itkNotUsed(neighborhood), |
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IND |
**const FloatOffsetType &itkNotUsed(offset), GlobalDataStruct *gd) |
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{ |
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// Calculate the mean curvature |
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ScalarValueType curvature_term = NumericTraits<ScalarValueType>::Zero; |
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unsigned int i, j; |
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for (i = 0; i < ImageDimension; i++) |
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{ |
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for(j = 0; j < ImageDimension; j++) |
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{ |
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if(j != i) |
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{ |
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curvature_term -= gd->m_dx[i] * gd->m_dx[j] * gd->m_dxy[i][j]; |
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curvature_term += gd->m_dxy[j][j] * gd->m_dx[i] * gd->m_dx[i]; |
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} |
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} |
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} |
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return (curvature_term / gd->m_GradMagSqr ); |
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} |
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template <class TImageType> |
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typename LevelSetFunction<TImageType>::VectorType |
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LevelSetFunction<TImageType>::InitializeZeroVectorConstant() |
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{ |
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VectorType ans; |
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for (unsigned int i = 0; i < ImageDimension; ++i) |
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{ |
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ans[i] = NumericTraits<ScalarValueType>::Zero; |
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} |
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return ans; |
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} |
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template <class TImageType> |
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typename LevelSetFunction<TImageType>::VectorType |
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LevelSetFunction<TImageType>::m_ZeroVectorConstant = |
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LevelSetFunction<TImageType>::InitializeZeroVectorConstant(); |
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template <class TImageType> |
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void |
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LevelSetFunction<TImageType>:: |
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PrintSelf(std::ostream& os, Indent indent) const |
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{ |
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Superclass::PrintSelf(os, indent); |
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os << indent << "WaveDT: " << m_WaveDT << std::endl; |
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os << indent << "DT: " << m_DT << std::endl; |
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os << indent << "UseMinimalCurvature " << m_UseMinimalCurvature << std::endl; |
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os << indent << "EpsilonMagnitude: " << m_EpsilonMagnitude << std::endl; |
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os << indent << "AdvectionWeight: " << m_AdvectionWeight << std::endl; |
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os << indent << "PropagationWeight: " << m_PropagationWeight << std::endl; |
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os << indent << "CurvatureWeight: " << m_CurvatureWeight << std::endl; |
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LEN |
os << indent << "LaplacianSmoothingWeight: " << m_LaplacianSmoothingWeight << std::endl; |
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} |
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template< class TImageType > |
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double LevelSetFunction<TImageType>::m_WaveDT = 1.0/(2.0 * ImageDimension); |
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template < class TImageType > |
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double LevelSetFunction<TImageType>::m_DT = 1.0/(2.0 * ImageDimension); |
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template< class TImageType > |
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typename LevelSetFunction< TImageType >::TimeStepType |
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LevelSetFunction<TImageType> |
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::ComputeGlobalTimeStep(void *GlobalData) const |
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{ |
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TimeStepType dt; |
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GlobalDataStruct *d = (GlobalDataStruct *)GlobalData; |
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d->m_MaxAdvectionChange += d->m_MaxPropagationChange; |
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if (vnl_math_abs(d->m_MaxCurvatureChange) > 0.0) |
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{ |
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if (d->m_MaxAdvectionChange > 0.0) |
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{ |
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dt = vnl_math_min((m_WaveDT / d->m_MaxAdvectionChange), |
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IND |
************************( m_DT / d->m_MaxCurvatureChange )); |
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} |
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else |
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{ |
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dt = m_DT / d->m_MaxCurvatureChange; |
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} |
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} |
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else |
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{ |
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if (d->m_MaxAdvectionChange > 0.0) |
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{ |
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dt = m_WaveDT / d->m_MaxAdvectionChange; |
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} |
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else |
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{ |
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dt = 0.0; |
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} |
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} |
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// reset the values |
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d->m_MaxAdvectionChange = NumericTraits<ScalarValueType>::Zero; |
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d->m_MaxPropagationChange = NumericTraits<ScalarValueType>::Zero; |
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d->m_MaxCurvatureChange = NumericTraits<ScalarValueType>::Zero; |
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return dt; |
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} |
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template< class TImageType > |
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void |
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LevelSetFunction< TImageType> |
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::Initialize(const RadiusType &r) |
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{ |
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this->SetRadius(r); |
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// Dummy neighborhood. |
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NeighborhoodType it; |
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it.SetRadius( r ); |
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// Find the center index of the neighborhood. |
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m_Center = it.Size() / 2; |
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// Get the stride length for each axis. |
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for(unsigned int i = 0; i < ImageDimension; i++) |
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{ m_xStride[i] = it.GetStride(i); } |
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} |
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template< class TImageType > |
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typename LevelSetFunction< TImageType >::PixelType |
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LevelSetFunction< TImageType > |
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::ComputeUpdate(const NeighborhoodType &it, void *globalData, |
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const FloatOffsetType& offset) |
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{ |
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unsigned int i, j; |
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const ScalarValueType ZERO = NumericTraits<ScalarValueType>::Zero; |
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const ScalarValueType center_value = it.GetCenterPixel(); |
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|
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ScalarValueType laplacian, x_energy, laplacian_term, propagation_term, |
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IND |
****curvature_term, advection_term, propagation_gradient; |
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VectorType advection_field; |
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// Global data structure |
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GlobalDataStruct *gd = (GlobalDataStruct *)globalData; |
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// Compute the Hessian matrix and various other derivatives. Some of these |
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// derivatives may be used by overloaded virtual functions. |
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gd->m_GradMagSqr = 1.0e-6; |
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SEM |
for( i = 0 ; i < ImageDimension; i++) |
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{ |
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const unsigned int positionA = |
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static_cast<unsigned int>( m_Center + m_xStride[i]); |
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const unsigned int positionB = |
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IND |
******static_cast<unsigned int>( m_Center - m_xStride[i]); |
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|
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gd->m_dx[i] = 0.5 * (it.GetPixel( positionA ) - |
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IND |
*********************it.GetPixel( positionB ) ); |
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|
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gd->m_dxy[i][i] = it.GetPixel( positionA ) |
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IND |
******+ it.GetPixel( positionB ) - 2.0 * center_value; |
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|
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gd->m_dx_forward[i] = it.GetPixel( positionA ) - center_value; |
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gd->m_dx_backward[i] = center_value - it.GetPixel( positionB ); |
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gd->m_GradMagSqr += gd->m_dx[i] * gd->m_dx[i]; |
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|
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for( j = i+1; j < ImageDimension; j++ ) |
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{ |
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const unsigned int positionAa = static_cast<unsigned int>( |
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m_Center - m_xStride[i] - m_xStride[j] ); |
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const unsigned int positionBa = static_cast<unsigned int>( |
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m_Center - m_xStride[i] + m_xStride[j] ); |
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const unsigned int positionCa = static_cast<unsigned int>( |
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m_Center + m_xStride[i] - m_xStride[j] ); |
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const unsigned int positionDa = static_cast<unsigned int>( |
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m_Center + m_xStride[i] + m_xStride[j] ); |
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|
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gd->m_dxy[i][j] = gd->m_dxy[j][i] = 0.25 *( it.GetPixel( positionAa ) |
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IND |
******************************************- it.GetPixel( positionBa ) |
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IND |
******************************************- it.GetPixel( positionCa ) |
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IND |
******************************************+ it.GetPixel( positionDa ) |
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IND |
********); |
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|
} |
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} |
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|
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if ( m_CurvatureWeight != ZERO ) |
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{ |
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LEN |
curvature_term = this->ComputeCurvatureTerm(it, offset, gd) * m_CurvatureWeight |
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IND |
******* this->CurvatureSpeed(it, offset); |
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|
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gd->m_MaxCurvatureChange = vnl_math_max(gd->m_MaxCurvatureChange, |
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vnl_math_abs(curvature_term)); |
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} |
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else |
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{ |
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curvature_term = ZERO; |
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} |
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|
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// Calculate the advection term. |
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// $\alpha \stackrel{\rightharpoonup}{F}(\mathbf{x})\cdot\nabla\phi $ |
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// |
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// Here we can use a simple upwinding scheme since we know the |
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// sign of each directional component of the advective force. |
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// |
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if (m_AdvectionWeight != ZERO) |
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{ |
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|
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advection_field = this->AdvectionField(it, offset, gd); |
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advection_term = ZERO; |
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|
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for(i = 0; i < ImageDimension; i++) |
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{ |
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|
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x_energy = m_AdvectionWeight * advection_field[i]; |
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|
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if (x_energy > ZERO) |
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{ |
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advection_term += advection_field[i] * gd->m_dx_backward[i]; |
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} |
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else |
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{ |
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advection_term += advection_field[i] * gd->m_dx_forward[i]; |
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} |
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|
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gd->m_MaxAdvectionChange |
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IND |
********= vnl_math_max(gd->m_MaxAdvectionChange, vnl_math_abs(x_energy)); |
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} |
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advection_term *= m_AdvectionWeight; |
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|
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} |
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else |
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{ |
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advection_term = ZERO; |
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} |
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|
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if (m_PropagationWeight != ZERO) |
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{ |
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// Get the propagation speed |
| 395 |
LEN |
propagation_term = m_PropagationWeight * this->PropagationSpeed(it, offset, gd); |
| 396 |
|
|
| 397 |
|
// |
| 398 |
|
// Construct upwind gradient values for use in the propagation speed term: |
| 399 |
|
// $\beta G(\mathbf{x})\mid\nabla\phi\mid$ |
| 400 |
|
// |
| 401 |
|
// The following scheme for ``upwinding'' in the normal direction is taken |
| 402 |
|
// from Sethian, Ch. 6 as referenced above. |
| 403 |
|
// |
| 404 |
|
propagation_gradient = ZERO; |
| 405 |
|
|
| 406 |
|
if ( propagation_term > ZERO ) |
| 407 |
|
{ |
| 408 |
|
for(i = 0; i< ImageDimension; i++) |
| 409 |
|
{ |
| 410 |
LEN |
propagation_gradient += vnl_math_sqr( vnl_math_max(gd->m_dx_backward[i], ZERO) ) |
| 411 |
IND |
**********+ vnl_math_sqr( vnl_math_min(gd->m_dx_forward[i], ZERO) ); |
| 412 |
|
} |
| 413 |
|
} |
| 414 |
|
else |
| 415 |
|
{ |
| 416 |
|
for(i = 0; i< ImageDimension; i++) |
| 417 |
|
{ |
| 418 |
LEN |
propagation_gradient += vnl_math_sqr( vnl_math_min(gd->m_dx_backward[i], ZERO) ) |
| 419 |
IND |
**********+ vnl_math_sqr( vnl_math_max(gd->m_dx_forward[i], ZERO) ); |
| 420 |
|
} |
| 421 |
|
} |
| 422 |
|
|
| 423 |
|
// Collect energy change from propagation term. This will be used in |
| 424 |
|
// calculating the maximum time step that can be taken for this iteration. |
| 425 |
|
gd->m_MaxPropagationChange = |
| 426 |
IND |
******vnl_math_max(gd->m_MaxPropagationChange, |
| 427 |
|
vnl_math_abs(propagation_term)); |
| 428 |
|
|
| 429 |
|
propagation_term *= vcl_sqrt( propagation_gradient ); |
| 430 |
|
} |
| 431 |
|
else propagation_term = ZERO; |
| 432 |
|
|
| 433 |
|
if(m_LaplacianSmoothingWeight != ZERO) |
| 434 |
|
{ |
| 435 |
|
laplacian = ZERO; |
| 436 |
|
|
| 437 |
|
// Compute the laplacian using the existing second derivative values |
| 438 |
|
for(i = 0;i < ImageDimension; i++) |
| 439 |
|
{ |
| 440 |
|
laplacian += gd->m_dxy[i][i]; |
| 441 |
|
} |
| 442 |
|
|
| 443 |
|
// Scale the laplacian by its speed and weight |
| 444 |
|
laplacian_term = |
| 445 |
LEN,IND |
******laplacian * m_LaplacianSmoothingWeight * LaplacianSmoothingSpeed(it,offset, gd); |
| 446 |
|
} |
| 447 |
|
else |
| 448 |
IND |
****laplacian_term = ZERO; |
| 449 |
|
|
| 450 |
|
// Return the combination of all the terms. |
| 451 |
|
return ( PixelType ) ( curvature_term - propagation_term |
| 452 |
|
- advection_term - laplacian_term ); |
| 453 |
|
} |
| 454 |
|
|
| 455 |
|
} // end namespace itk |
| 456 |
|
|
| 457 |
|
#endif |
| 458 |
|
|
