+// =========================================================================
+// @author Leonardo Florez Valencia
+// @email florez-l@javeriana.edu.co
+// =========================================================================
+#ifndef __fpa__Common__OriginalRandomWalker__hxx__
+#define __fpa__Common__OriginalRandomWalker__hxx__
+
+#include <cmath>
+#include <map>
+#include <itkImageRegionConstIteratorWithIndex.h>
+#include <Eigen/Sparse>
+
+// -------------------------------------------------------------------------
+template< class _TImage, class _TLabels, class _TScalar >
+void fpa::Common::OriginalRandomWalker< _TImage, _TLabels, _TScalar >::
+AddSeed( const TIndex& seed, const TLabel& label )
+{
+ this->m_Seeds.push_back( seed );
+ this->m_Labels.push_back( label );
+ this->Modified( );
+}
+
+// -------------------------------------------------------------------------
+template< class _TImage, class _TLabels, class _TScalar >
+fpa::Common::OriginalRandomWalker< _TImage, _TLabels, _TScalar >::
+OriginalRandomWalker( )
+ : Superclass( ),
+ m_Beta( TScalar( 90 ) ),
+ m_Epsilon( TScalar( 1e-5 ) ),
+ m_NormalizeWeights( true )
+{
+ fpaFilterOptionalInputConfigureMacro( InputLabels, TLabels );
+ fpaFilterOutputConfigureMacro( OutputProbabilities, TScalarImage );
+}
+
+// -------------------------------------------------------------------------
+template< class _TImage, class _TLabels, class _TScalar >
+fpa::Common::OriginalRandomWalker< _TImage, _TLabels, _TScalar >::
+~OriginalRandomWalker( )
+{
+}
+
+// -------------------------------------------------------------------------
+template< class _TImage, class _TLabels, class _TScalar >
+void fpa::Common::OriginalRandomWalker< _TImage, _TLabels, _TScalar >::
+GenerateData( )
+{
+ typedef Eigen::SparseMatrix< TScalar > _TSparseMatrix;
+ typedef Eigen::SimplicialLDLT< _TSparseMatrix > _TSparseSolver;
+ typedef Eigen::Triplet< TScalar > _TTriplet;
+ typedef std::vector< _TTriplet > _TTriplets;
+ typedef std::map< unsigned long, unsigned long > _TMap;
+ typedef _TMap::value_type _TMapValue;
+
+ // Some input values
+ const TImage* in = this->GetInput( );
+ TRegion region = in->GetRequestedRegion( );
+ unsigned long N = region.GetNumberOfPixels( );
+
+ // Prepare seeds for linear algebra
+ _TMap seeds;
+ for( unsigned int i = 0; i < this->m_Seeds.size( ); ++i )
+ seeds.insert(
+ _TMapValue(
+ Self::_1D( this->m_Seeds[ i ], region ),
+ this->m_Labels[ i ]
+ )
+ );
+
+ // Use input labels
+ /* TODO
+ const TLabels* in_labels = this->GetInputLabels( );
+ if( in_labels != NULL )
+ {
+ itk::ImageRegionConstIteratorWithIndex< TLabels > lIt( in_labels, region );
+ for( lIt.GoToBegin( ); !lIt.IsAtEnd( ); ++lIt )
+ if( lIt.Get( ) != 0 )
+ seeds.insert(
+ _TMapValue( Self::_1D( lIt.GetIndex( ), region ), lIt.Get( ) )
+ );
+
+ } // fi
+ */
+
+ // Prepare label tables
+ _TMap labels, inv_labels, seeds_indexes;
+ _TMap::const_iterator hIt = seeds.begin( );
+ for( ; hIt != seeds.end( ); ++hIt )
+ {
+ seeds_indexes[ hIt->first ] = seeds_indexes.size( ) - 1;
+ if( labels.find( hIt->second ) == labels.end( ) )
+ {
+ labels[ hIt->second ] = labels.size( ) - 1;
+ inv_labels[ labels[ hIt->second ] ] = hIt->second;
+
+ } // fi
+
+ } // rof
+
+ // Prepare matrix/image index conversion
+ _TMap indexes;
+ unsigned long o = 0;
+ for( unsigned long n = 0; n < N; ++n )
+ {
+ if( seeds.find( n ) == seeds.end( ) )
+ indexes.insert( _TMap::value_type( n, n - o ) );
+ else
+ o++;
+
+ } // rof
+ unsigned long nLabels = labels.size( );
+
+ // Boundary matrix
+ _TTriplets Bt;
+ _TMap::const_iterator mIt = seeds.begin( );
+ for( unsigned long i = 0; mIt != seeds.end( ); ++mIt, ++i )
+ Bt.push_back( _TTriplet( i, labels[ mIt->second ], TScalar( 1 ) ) );
+ _TSparseMatrix B( seeds.size( ), nLabels );
+ B.setFromTriplets( Bt.begin( ), Bt.end( ) );
+ B.makeCompressed( );
+
+ // Laplacian matrix
+ _TTriplets Lt;
+ itk::ImageRegionConstIteratorWithIndex< TImage > it( in, region );
+ TScalar maxV = TScalar( -1 );
+ for( it.GoToBegin( ); !it.IsAtEnd( ); ++it )
+ {
+ TIndex idx = it.GetIndex( );
+ TScalar vidx = TScalar( it.Get( ) );
+ unsigned long iidx = Self::_1D( idx, region );
+
+ // Neighbors
+ TScalar s = TScalar( 0 );
+ for( unsigned int d = 0; d < TImage::ImageDimension; ++d )
+ {
+ TIndex jdx;
+ for( int l = -1; l <= 1; l += 2 )
+ {
+ jdx = idx;
+ jdx[ d ] += l;
+ if( region.IsInside( jdx ) )
+ {
+ TScalar vjdx = TScalar( in->GetPixel( jdx ) );
+ unsigned long ijdx = Self::_1D( jdx, region );
+ TScalar v = std::fabs( vidx - vjdx );
+ Lt.push_back( _TTriplet( iidx, ijdx, v ) );
+ if( maxV < v )
+ maxV = v;
+
+ } // fi
+
+ } // rof
+
+ } // rof
+
+ } // rof
+ std::vector< TScalar > diag( N, TScalar( 0 ) );
+ typename _TTriplets::iterator tIt;
+ TScalar betaV = -this->m_Beta;
+ if( this->m_NormalizeWeights )
+ betaV /= maxV;
+ for( tIt = Lt.begin( ); tIt != Lt.end( ); ++tIt )
+ {
+ TScalar v = std::exp( betaV * tIt->value( ) );
+ if( v < this->m_Epsilon )
+ v = this->m_Epsilon;
+ *tIt = _TTriplet( tIt->row( ), tIt->col( ), -v );
+ diag[ tIt->col( ) ] += v;
+
+ } // rof
+ for( unsigned long i = 0; i < diag.size( ); ++i )
+ Lt.push_back( _TTriplet( i, i, diag[ i ] ) );
+
+ // Compute R and A
+ _TTriplets Rt, At;
+ for( tIt = Lt.begin( ); tIt != Lt.end( ); ++tIt )
+ {
+ _TMap::const_iterator cIt, rIt;
+ cIt = seeds.find( tIt->col( ) );
+ rIt = seeds.find( tIt->row( ) );
+ if( cIt != seeds.end( ) )
+ {
+ if( rIt == seeds.end( ) )
+ {
+ _TMap::const_iterator iIt = indexes.find( tIt->row( ) );
+ _TMap::const_iterator jIt = seeds_indexes.find( cIt->first );
+ Rt.push_back( _TTriplet( iIt->second, jIt->second, -tIt->value( ) ) );
+
+ } // fi
+ }
+ else
+ {
+ if( rIt == seeds.end( ) )
+ {
+ _TMap::const_iterator iIt = indexes.find( tIt->row( ) );
+ _TMap::const_iterator jIt = indexes.find( tIt->col( ) );
+ At.push_back( _TTriplet( iIt->second, jIt->second, tIt->value( ) ) );
+
+ } // fi
+
+ } // fi
+
+ } // rof
+
+ _TSparseMatrix R( N - seeds.size( ), seeds.size( ) );
+ R.setFromTriplets( Rt.begin( ), Rt.end( ) );
+ R.makeCompressed( );
+
+ _TSparseMatrix A( N - seeds.size( ), N - seeds.size( ) );
+ A.setFromTriplets( At.begin( ), At.end( ) );
+ A.makeCompressed( );
+
+ // Solve dirichlet problem
+ _TSparseSolver solver;
+ solver.compute( A );
+ if( solver.info( ) != Eigen::Success )
+ {
+ std::cerr << "Error computing." << std::endl;
+ } // fi
+ _TSparseMatrix x = solver.solve( R * B );
+ if( solver.info( ) != Eigen::Success )
+ {
+ std::cerr << "Error solving." << std::endl;
+ } // fi
+
+ // Fill outputs
+ TLabels* out_labels = this->GetOutput( );
+ out_labels->SetLargestPossibleRegion( in->GetLargestPossibleRegion( ) );
+ out_labels->SetRequestedRegion( in->GetRequestedRegion( ) );
+ out_labels->SetBufferedRegion( in->GetBufferedRegion( ) );
+ out_labels->SetSpacing( in->GetSpacing( ) );
+ out_labels->SetOrigin( in->GetOrigin( ) );
+ out_labels->SetDirection( in->GetDirection( ) );
+ out_labels->Allocate( );
+
+ TScalarImage* out_probs = this->GetOutputProbabilities( );
+ out_probs->SetLargestPossibleRegion( in->GetLargestPossibleRegion( ) );
+ out_probs->SetRequestedRegion( in->GetRequestedRegion( ) );
+ out_probs->SetBufferedRegion( in->GetBufferedRegion( ) );
+ out_probs->SetSpacing( in->GetSpacing( ) );
+ out_probs->SetOrigin( in->GetOrigin( ) );
+ out_probs->SetDirection( in->GetDirection( ) );
+ out_probs->Allocate( );
+
+ mIt = seeds.begin( );
+ o = 0;
+ unsigned long j = 0;
+ for( unsigned long j = 0; j < N; ++j )
+ {
+ TIndex idx;
+ TLabel lbl;
+ TScalar p;
+ if( mIt->first != j )
+ {
+ idx = Self::_ND( j, region );
+ TScalar maxP = x.coeffRef( j - o, 0 );
+ unsigned long maxL = 0;
+ for( unsigned long l = 1; l < nLabels; ++l )
+ {
+ TScalar vp = x.coeffRef( j - o, l );
+ if( maxP < vp )
+ {
+ maxP = vp;
+ maxL = l;
+
+ } // fi
+
+ } // rof
+ lbl = inv_labels[ maxL ];
+ p = maxP;
+ }
+ else
+ {
+ idx = Self::_ND( mIt->first, region );
+ lbl = mIt->second;
+ p = TScalar( 1 );
+ mIt++;
+ o++;
+
+ } // fi
+ out_labels->SetPixel( idx, lbl );
+ out_probs->SetPixel( idx, p );
+
+ } // rof
+}
+
+// -------------------------------------------------------------------------
+template< class _TImage, class _TLabels, class _TScalar >
+unsigned long
+fpa::Common::OriginalRandomWalker< _TImage, _TLabels, _TScalar >::
+_1D( const TIndex& idx, const TRegion& region )
+{
+ unsigned long i = idx[ 0 ];
+ unsigned long off = 1;
+ typename TRegion::SizeType size = region.GetSize( );
+ for( unsigned int d = 1; d < TIndex::Dimension; ++d )
+ {
+ off *= size[ d - 1 ];
+ i += idx[ d ] * off;
+
+ } // rof
+ return( i );
+}
+
+// -------------------------------------------------------------------------
+template< class _TImage, class _TLabels, class _TScalar >
+typename fpa::Common::OriginalRandomWalker< _TImage, _TLabels, _TScalar >::
+TIndex fpa::Common::OriginalRandomWalker< _TImage, _TLabels, _TScalar >::
+_ND( const unsigned long& i, const TRegion& region )
+{
+ typename TRegion::SizeType size = region.GetSize( );
+
+ unsigned long j = i;
+ TIndex idx;
+ if( TIndex::Dimension == 3 )
+ {
+ unsigned long z = size[ 0 ] * size[ 1 ];
+ idx[ 2 ] = j / z;
+ j -= idx[ 2 ] * z;
+
+ } // fi
+ idx[ 1 ] = j / size[ 0 ];
+ idx[ 0 ] = j % size[ 0 ];
+ return( idx );
+}
+
+#endif // __fpa__Common__OriginalRandomWalker__hxx__
+// eof - $RCSfile$