[Insight-developers] OtsuThresholdCalculator versus OtsuMultipleThresholdsCalculator

[Padfield, Dirk R (GE Global Research)]

Hi ITK Developers,

I was just looking through the OtsuThresholdCalculator and OtsuMultipleThresholdsCalculator to see whether I could refactor them so that the Otsu inherits from the OtsuMultiple since the latter is a more general case of the former.  Currently, the code for these two filters is totally different resulting in significant code duplication and a need to keep both filters in sync.

As a first step, I wrote a CMake test to check that the output of the OtsuMultiple with 1 threshold is the same as the output of the Otsu.  Unfortunately, they are not!  The two filters output thresholds that are different by 1 histogram bin!  This can be a quite extreme difference when the numberOfHistogramBins is low, and it leads to different thresholds even when the numberOfHistogramBins is reasonably high (say 256).  I tracked it down to this code in the Calculators:

The relevant code from Otsu:
    const double tolerance = 0.00001;
    if ( (varBetween - tolerance) > maxVarBetween )
      {
      maxVarBetween = varBetween;
      maxBinNumber = j;
      }
    }
  this->GetOutput()->Set( static_cast<OutputType>( histogram->GetMeasurement( maxBinNumber + 1, 0 ) ) );

The relevant code from MultipleOtsu:
    if ( varBetween > maxVarBetween )
      {
      maxVarBetween = varBetween;
      maxVarThresholdIndexes = thresholdIndexes;
      }
    }
  for ( j = 0; j < m_NumberOfThresholds; j++ )
    {
    m_Output[j] = histogram->GetBinMax(0, maxVarThresholdIndexes[j]);
    }

The difference is that the Otsu adds one to the computed threshold whereas the MultipleOtsu does not.  This is problematic because users would expect them to give the same result.

My question is: how should we proceed?  If we change one or the other, people's code that use the changed one will give slightly different answers.  If we don't change them, the two filters will give different outputs for the same input, and it will not be possible to refactor them to share code.

What are your thoughts?

Thanks,
Dirk