[ITK-users] OtsuMultipleThresholdsImageFilter creates asymmetric classes for symmetric a distribution

[hellman]

Hi all,

I am planning to use OtsuMultipleThresholdsImageFilter to segment an image
into a number of classes. I started by testing it for a small image with
only a single threshold to see that I understand how it works. The results
surprise me though.

I create a 1D-image with four pixels: 1000, 2000, 3000 and 4000. Computing a
threshold to split this distribution into two classes of maximum
between-class variance should give a threshold between 2000 and 3000.
However, OtsuMultipleThresholdsImageFilter gives me a value 1996.17, which
puts 1000 in one class and 2000, 3000, 4000 in the other class. This does
not give the smallest between-class variance.

The code that I tried can be found below. Do I misunderstand how this filter
should work or is there a bug in its implementation?

Running the following code with ITK 4.12.0 and ITK 4.12.2 prints 1996.17:

#include <itkOtsuMultipleThresholdsImageFilter.h>

typedef itk::Image<float, 1> ImageType;
typedef itk::Image<int, 1> LabelImageType;

int main(int argc, char *argv[])
{
  typename ImageType::Pointer input = ImageType::New();

  ImageType::RegionType region;
  region.GetModifiableSize()[0] = 4;
  input->SetRegions(region);
  input->Allocate();
  
  ImageType::IndexType index;
  index[0] = 0;
  input->SetPixel(index, 1000);
  index[0] = 1;
  input->SetPixel(index, 2000);
  index[0] = 2;
  input->SetPixel(index, 3000);
  index[0] = 3;
  input->SetPixel(index, 4000);

  auto otsuFilter = itk::OtsuMultipleThresholdsImageFilter<ImageType,
LabelImageType>::New();
  otsuFilter->SetInput(input);
  otsuFilter->SetNumberOfHistogramBins(128);
  otsuFilter->SetNumberOfThresholds(1);
  otsuFilter->Update();

  std::cout << otsuFilter->GetThresholds()[0] << std::endl;

  return 0;
}

Best wishes,
Fredrik Hellman



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