On the topology preservation of Gneiting's functions in image registration

TL;DR

This paper investigates the topology preservation properties of Gneiting's radial basis functions in landmark-based image registration, comparing their performance with other functions through analytical and experimental methods.

Contribution

It provides the first detailed analysis of Gneiting's functions' topology preservation in image registration, including both theoretical and experimental comparisons.

Findings

Gneiting's functions exhibit favorable topology preservation properties.

Compared to Wendland's and Wu's functions, Gneiting's functions show comparable or improved accuracy.

Topology preservation impacts the smoothness and reliability of image registration results.

Abstract

The purpose of image registration is to determine a transformation such that the transformed version of the source image is similar to the target one. In this paper we focus on landmark-based image registration using radial basis functions (RBFs) transformations, in particular on the topology preservation of compactly supported radial basis functions (CSRBFs) transformations. In [1] the performances of Gneiting's and Wu's functions are compared with the ones of other well known schemes in image registration, as thin plate spline and Wendland's functions. Several numerical experiments and real-life cases with medical images show differences in accuracy and smoothness of the considered interpolation methods, which can be explained taking into account their topology preservation properties. Here we analyze analytically and experimentally the topology preservation performances of Gneiting's functions, comparing results with the ones obtained in [2], where Wendland's and Wu's functions are considered.