Equivalence of histogram equalization, histogram matching and the Nyul algorithm for intensity standardization in MRI

Abstract

Intensity standardization is an important preprocessing step in automatedanalysis of MRI. A popular method by Nyul et al. uses apiece-wise linear approximation of histogram matching. We showthat this method is a non-uniform trapezoidal Riemann approximationof the ideal histogram matching operation, and suggest thathistogram matching is no better than histogram equalization for intensitystandardization in MRI. Experimental results are derived usingsynthetic data.