libinsighttoolkit4-dev 4.5.0-3 / usr / include / ITK-4.5 / itkOtsuMultipleThresholdsCalculator.hxx

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 *  Copyright Insight Software Consortium
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
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 *         http://www.apache.org/licenses/LICENSE-2.0.txt
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 *  See the License for the specific language governing permissions and
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#ifndef __itkOtsuMultipleThresholdsCalculator_hxx
#define __itkOtsuMultipleThresholdsCalculator_hxx

#include "itkOtsuMultipleThresholdsCalculator.h"

namespace itk
{
template< typename TInputHistogram >
OtsuMultipleThresholdsCalculator< TInputHistogram >
::OtsuMultipleThresholdsCalculator()
{
  m_NumberOfThresholds = 1;
  m_Output.resize(m_NumberOfThresholds);
  m_ValleyEmphasis = false;
  std::fill(m_Output.begin(), m_Output.end(), NumericTraits< MeasurementType >::Zero);
}

template< typename TInputHistogram >
const typename OtsuMultipleThresholdsCalculator< TInputHistogram >::OutputType &
OtsuMultipleThresholdsCalculator< TInputHistogram >
::GetOutput()
{
  return m_Output;
}

/**
 * Increment the thresholds of one position along the histogram
 */
template< typename TInputHistogram >
bool
OtsuMultipleThresholdsCalculator< TInputHistogram >
::IncrementThresholds(InstanceIdentifierVectorType & thresholdIndexes,
                      MeanType globalMean,
                      MeanVectorType & classMean,
                      FrequencyVectorType & classFrequency)
{
  typename TInputHistogram::ConstPointer histogram = this->GetInputHistogram();

  SizeValueType numberOfHistogramBins = histogram->Size();
  SizeValueType numberOfClasses = classMean.size();

  MeanType      meanOld;
  FrequencyType freqOld;

  unsigned int k;
  int          j;

  // from the upper threshold down
  for ( j = static_cast< int >( m_NumberOfThresholds - 1 ); j >= 0; j-- )
    {
    // if this threshold can be incremented (i.e. we're not at the end of the
    // histogram)
    if ( thresholdIndexes[j] < numberOfHistogramBins - 2 - ( m_NumberOfThresholds - 1 - j ) )
      {
      // increment it and update mean and frequency of the class bounded by the
      // threshold
      ++thresholdIndexes[j];

      meanOld = classMean[j];
      freqOld = classFrequency[j];

      classFrequency[j] += histogram->GetFrequency(thresholdIndexes[j]);

      if ( NumericTraits< FrequencyType >::IsPositive(classFrequency[j]) )
        {
        classMean[j] = ( meanOld * static_cast< MeanType >( freqOld )
                         + static_cast< MeanType >( histogram->GetMeasurementVector(thresholdIndexes[j])[0] )
                         * static_cast< MeanType >( histogram->GetFrequency(thresholdIndexes[j]) ) )
                       / static_cast< MeanType >( classFrequency[j] );
        }
      else
        {
        classMean[j] = NumericTraits< MeanType >::Zero;
        }

      // set higher thresholds adjacent to their previous ones, and update mean
      // and frequency of the respective classes
      for ( k = j + 1; k < m_NumberOfThresholds; k++ )
        {
        thresholdIndexes[k] = thresholdIndexes[k - 1] + 1;
        classFrequency[k] = histogram->GetFrequency(thresholdIndexes[k]);
        if ( NumericTraits< FrequencyType >::IsPositive(classFrequency[k]) )
          {
          classMean[k] = static_cast< MeanType >( histogram->GetMeasurementVector(thresholdIndexes[k])[0] );
          }
        else
          {
          classMean[k] = NumericTraits< MeanType >::Zero;
          }
        }

      // update mean and frequency of the highest class
      classFrequency[numberOfClasses - 1] = histogram->GetTotalFrequency();
      classMean[numberOfClasses - 1] = globalMean * histogram->GetTotalFrequency();

      for ( k = 0; k < numberOfClasses - 1; k++ )
        {
        classFrequency[numberOfClasses - 1] -= classFrequency[k];
        classMean[numberOfClasses - 1] -= classMean[k] * static_cast< MeanType >( classFrequency[k] );
        }

      if ( NumericTraits< FrequencyType >::IsPositive(classFrequency[numberOfClasses - 1]) )
        {
        classMean[numberOfClasses - 1] /= static_cast< MeanType >( classFrequency[numberOfClasses - 1] );
        }
      else
        {
        classMean[numberOfClasses - 1] = NumericTraits< MeanType >::Zero;
        }

      // exit the for loop if a threshold has been incremented
      break;
      }
    else  // if this threshold can't be incremented
      {
      // if it's the lowest threshold
      if ( j == 0 )
        {
        // we couldn't increment because we're done
        return false;
        }
      }
    }
  // we incremented
  return true;
}

/**
 * Compute Otsu's thresholds
 */
template< typename TInputHistogram >
void
OtsuMultipleThresholdsCalculator< TInputHistogram >
::Compute()
{
  typename TInputHistogram::ConstPointer histogram = this->GetInputHistogram();

  // TODO: as an improvement, the class could accept multi-dimensional
  // histograms
  // and the user could specify the dimension to apply the algorithm to.
  if ( histogram->GetSize().Size() != 1 )
    {
    itkExceptionMacro(<< "Histogram must be 1-dimensional.");
    }

  // compute global mean
  typename TInputHistogram::ConstIterator iter = histogram->Begin();
  typename TInputHistogram::ConstIterator end = histogram->End();

  MeanType      globalMean = NumericTraits< MeanType >::Zero;
  FrequencyType globalFrequency = histogram->GetTotalFrequency();
  while ( iter != end )
    {
    globalMean += static_cast< MeanType >( iter.GetMeasurementVector()[0] )
                  * static_cast< MeanType >( iter.GetFrequency() );
    ++iter;
    }
  globalMean /= static_cast< MeanType >( globalFrequency );

  SizeValueType numberOfClasses = m_NumberOfThresholds + 1;

  // initialize thresholds
  InstanceIdentifierVectorType thresholdIndexes(m_NumberOfThresholds);

  SizeValueType j;
  for ( j = 0; j < m_NumberOfThresholds; j++ )
    {
    thresholdIndexes[j] = j;
    }

  InstanceIdentifierVectorType maxVarThresholdIndexes = thresholdIndexes;

  // compute frequency and mean of initial classes
  FrequencyType       freqSum = NumericTraits< FrequencyType >::Zero;
  FrequencyVectorType classFrequency(numberOfClasses);
  for ( j = 0; j < numberOfClasses - 1; j++ )
    {
    classFrequency[j] = histogram->GetFrequency(thresholdIndexes[j]);
    freqSum += classFrequency[j];
    }
  classFrequency[numberOfClasses - 1] = globalFrequency - freqSum;

  // Convert the frequencies to probabilities (i.e. normalize the histogram).
  SizeValueType histSize = histogram->GetSize()[0];
  WeightVectorType imgPDF(histSize);
  for ( j = 0; j < histSize; j++ )
    {
      imgPDF[j] = (WeightType)histogram->GetFrequency(j) / (WeightType)globalFrequency;
    }

  MeanType       meanSum = NumericTraits< MeanType >::Zero;
  MeanVectorType classMean(numberOfClasses);
  for ( j = 0; j < numberOfClasses - 1; j++ )
    {
    if ( NumericTraits< FrequencyType >::IsPositive(classFrequency[j]) )
      {
      classMean[j] = static_cast< MeanType >( histogram->GetMeasurementVector(j)[0] );
      }
    else
      {
      classMean[j] = NumericTraits< MeanType >::Zero;
      }
    meanSum += classMean[j] * static_cast< MeanType >( classFrequency[j] );
    }

  if ( NumericTraits< FrequencyType >::IsPositive(classFrequency[numberOfClasses - 1]) )
    {
    classMean[numberOfClasses
              - 1] =
      ( globalMean * static_cast< MeanType >( globalFrequency )
       - meanSum ) / static_cast< MeanType >( classFrequency[numberOfClasses - 1] );
    }
  else
    {
    classMean[numberOfClasses - 1] = NumericTraits< MeanType >::Zero;
    }

  VarianceType maxVarBetween = NumericTraits< VarianceType >::Zero;
  for ( j = 0; j < numberOfClasses; j++ )
    {
    maxVarBetween += (static_cast< VarianceType >( classFrequency[j] ) / static_cast< VarianceType >( globalFrequency ))
      * static_cast< VarianceType >( ( classMean[j] ) * ( classMean[j] ) );
    }

  // Sum the relevant weights for valley emphasis
  WeightType valleyEmphasisFactor = NumericTraits< WeightType >::Zero;
  if (m_ValleyEmphasis)
    {
    for ( j = 0; j < numberOfClasses - 1; j++ )
      {
      valleyEmphasisFactor = imgPDF[thresholdIndexes[j]];
      }
    valleyEmphasisFactor = 1.0 - valleyEmphasisFactor;
    maxVarBetween = maxVarBetween * valleyEmphasisFactor;
    }

  // explore all possible threshold configurations and choose the one that
  // yields maximum between-class variance
  while ( Self::IncrementThresholds(thresholdIndexes, globalMean, classMean, classFrequency) )
    {
    VarianceType varBetween = NumericTraits< VarianceType >::Zero;
    for ( j = 0; j < numberOfClasses; j++ )
      {
      // The true between-class variance \sigma_B^2 for any number of classes is defined as:
      // \sigma_B^2 = \sum_{k=1}^{M} \omega_k (\mu_k - \mu_T)^2
      // where \omega_k = classFrequency[j]/globalFrequency is the probability of the class,
      // \mu_k = classMean[j] is the mean of the class,
      // \mu_T = globalMean is the overall mean,
      // and M is the number of classes.
      // However, in the paper "A Fast Algorithm for Multilevel Thresholding" by Liao, Chen, and Chung,
      // it was shown that this can be simplified to
      // (\sum_{k=1}^{M} \omega_k \mu_k^2) - \mu_T^2
      // Since we are looking for the argmax, the second term can be ignored because it is a constant, leading to the simpler
      // (\sum_{k=1}^{M} \omega_k \mu_k^2), which is what is implemented here.
      // Although this is no longer truly a "between class variance", we keep that name since it is only different by a constant.
      varBetween += (static_cast< VarianceType >( classFrequency[j] ) / static_cast< VarianceType >( globalFrequency ))
              * static_cast< VarianceType >( ( classMean[j] ) * ( classMean[j] ) );
      }

    if (m_ValleyEmphasis)
    {
      // Sum relevant weights to get valley emphasis factor
      valleyEmphasisFactor = NumericTraits< WeightType >::Zero;
      for ( j = 0; j < numberOfClasses - 1; j++ )
      {
        valleyEmphasisFactor += imgPDF[thresholdIndexes[j]];
      }
      valleyEmphasisFactor = 1.0 - valleyEmphasisFactor;
      varBetween = varBetween * valleyEmphasisFactor;
    }

    if ( varBetween > maxVarBetween )
      {
      maxVarBetween = varBetween;
      maxVarThresholdIndexes = thresholdIndexes;
      }
    }

  // copy corresponding bin max to threshold vector
  m_Output.resize(m_NumberOfThresholds);

  for ( j = 0; j < m_NumberOfThresholds; j++ )
    {
    m_Output[j] = histogram->GetMeasurement(maxVarThresholdIndexes[j],0);
    }
}

template< typename TInputHistogram >
void
OtsuMultipleThresholdsCalculator< TInputHistogram >
::PrintSelf(std::ostream & os, Indent indent) const
{
  Superclass::PrintSelf(os, indent);

  os << indent << "NumberOfThresholds: " << m_NumberOfThresholds;

  os << indent << "Output: ";
  for ( SizeValueType j = 0; j < m_NumberOfThresholds; j++ )
    {
    os << m_Output[j] << " ";
    }
  os << std::endl;
}
} // end namespace itk

#endif