First Order Locally Orderless Registration

TL;DR

This paper introduces an extension of the Locally Orderless Registration framework to incorporate first-order information for image density estimation, enhancing image similarity measures for registration tasks.

Contribution

It extends the Locally Orderless Registration framework to include first-order information, allowing for more advanced similarity measures in image registration.

Findings

Extended the framework to include first-order information

Demonstrated how standard similarity measures fit into the new framework

Discussed potential for incorporating higher-order information

Abstract

First Order Locally Orderless Registration (FLOR) is a scale-space framework for image density estimation used for defining image similarity, mainly for Image Registration. The Locally Orderless Registration framework was designed in principle to use zeroth-order information, providing image density estimates over three scales: image scale, intensity scale, and integration scale. We extend it to take first-order information into account and hint at higher-order information. We show how standard similarity measures extend into the framework. We study especially Sum of Squared Differences (SSD) and Normalized Cross-Correlation (NCC) but present the theory of how Normalised Mutual Information (NMI) can be included.