  Image registration is an important tool for medical image analysis and is
used to bring images into the same reference frame by warping the coordinate
field of one image, such that some similarity measure is minimized. We study
similarity in image registration in the context of Locally Orderless Images
(LOI), which is the natural way to study density estimates and reveals the 3
fundamental scales: the measurement scale, the intensity scale, and the
integration scale.
  This paper has three main contributions: Firstly, we rephrase a large set of
popular similarity measures into a common framework, which we refer to as
Locally Orderless Registration, and which makes full use of the features of
local histograms. Secondly, we extend the theoretical understanding of the
local histograms. Thirdly, we use our framework to compare two state-of-the-art
intensity density estimators for image registration: The Parzen Window (PW) and
the Generalized Partial Volume (GPV), and we demonstrate their differences on a
popular similarity measure, Normalized Mutual Information (NMI).
  We conclude, that complicated similarity measures such as NMI may be
evaluated almost as fast as simple measures such as Sum of Squared Distances
(SSD) regardless of the choice of PW and GPV. Also, GPV is an asymmetric
measure, and PW is our preferred choice.
