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

Abstract

Intensity standardization is an important preprocessing step in automated
analysis of MRI. A popular method by Nyul et al. uses a
piece-wise linear approximation of histogram matching. We show
that this method is a non-uniform trapezoidal Riemann approximation
of the ideal histogram matching operation, and suggest that
histogram matching is no better than histogram equalization for intensity
standardization in MRI. Experimental results are derived using
synthetic data.