Locally Orderless Registration

TL;DR

This paper introduces a unified framework for image registration based on Locally Orderless Images, clarifies the theoretical basis of local histograms, and compares two density estimators, showing that complex similarity measures can be computed efficiently.

Contribution

It rephrases popular similarity measures within a common Locally Orderless Registration framework, extends the theoretical understanding of local histograms, and compares density estimators for improved registration efficiency.

Findings

Complex similarity measures like NMI can be computed as fast as simple ones.

GPV is asymmetric; PW is preferred due to symmetry.

The framework unifies and clarifies the use of local histograms in registration.

Abstract

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.