AdaptiveHistogramEqualizationImageFilter- parameter tuning

Courtney_Ambrozic · April 2, 2019, 8:58pm

Hello,

Regarding the AdaptiveHistogramEqualizationImageFilter, is there a way to set the function to completely behave as a classical histogram equalization method? Once alpha is set to 0, does beta represent a range from classical histogram equalization (beta=0) to a pass-through filter (beta=1)? Is there a way to set the window so that it uses the original, full-image histogram for each pixel (without setting the radius to cover the entire image)?

Additionally, I’ve experimented with setting the radius to zero and was surprised to find I had a decent histogram equalization result with one of my 3D images. Wouldn’t setting the radius to zero only use the pixel in question’s histogram for its equalizing process?

Thank you in advance and apologies for the random assortment of questions!

matt.mccormick · April 3, 2019, 4:39pm

Hello Courtney,

Good questions!

While we also have a itk::HistogramMatchingImageFilter; a histogram equalization filter for the entire image is yet to be contributed .

More details on the AdaptiveHistogramEqualizationImageFilter can be found in this example:

https://itk.org/ITKExamples/src/Filtering/ImageStatistics/AdaptiveHistogramEqualizationImageFilter/Documentation.html

And the code:

github.com

InsightSoftwareConsortium/ITK/blob/40c426015c4caabea1e9b75d1f77958596e1bb71/Modules/Filtering/ImageStatistics/include/itkAdaptiveEqualizationHistogram.h#L73-L94


      
          TOutputPixel GetValue(const TInputPixel &pixel)
            {
          
              // Normalize input pixels to [-0.5 0.5] gray level.
              // AdaptiveHistogramEqualization compute kernel components with
              // float, but use double for accumulate and temporaries.
              const double iscale = (double)m_Maximum - m_Minimum;
          
              double sum = 0.0;
              typename MapType::iterator itMap = m_Map.begin();
              const RealType u = ( (double)pixel - m_Minimum ) / iscale - 0.5;
              while ( itMap != m_Map.end() )
                {
                const RealType v =  ( (double)itMap->first - m_Minimum ) / iscale - 0.5;
                const double ikernel =  m_KernelSize - m_BoundaryCount;
                sum += itMap->second * CumulativeFunction(u,v) / ikernel;
          
                ++itMap;
                }

This file has been truncated. show original

github.com

InsightSoftwareConsortium/ITK/blob/40c426015c4caabea1e9b75d1f77958596e1bb71/Modules/Filtering/ImageStatistics/include/itkAdaptiveEqualizationHistogram.h#L115-L122


      
          RealType CumulativeFunction(RealType u, RealType v)
          {
            // Calculate cumulative function
            const RealType s = itk::Math::sgn(u - v);
            const RealType ad = itk::Math::abs( 2.0 * ( u - v ) );
          
            return 0.5 * s * std::pow(ad, m_Alpha) - m_Beta * 0.5 * s * ad + m_Beta * u;
          }

Once alpha is set to 0, does beta represent a range from classical histogram equalization (beta=0) to a pass-through filter (beta=1)?

When alpha is 0, beta is degree that the local mean is subtracted.

Interesting! It may help to step through the code in a debugger to understand what is happening.

Hope this helps,
Matt

Courtney_Ambrozic · April 3, 2019, 4:46pm

Thank you for your help, Matt!