Analysis of Compactly Supported Transformations for Landmark-based Image Registration

Abstract

Abstract:In this paper we consider landmark-based image registration using radial basis function interpolation schemes. More precisely, we analyze some landmark-based image transformations using compactly supported radial basis functions such as Wendland's, Wu's, and Gneiting's functions. Comparisons of interpolation techniques are performed and numerical experiments show differences in accuracy and smoothness of them in some test cases. Finally, a real-life case with medical images is considered.

Local interpolation schemes for landmark-based image registration: A comparison

“…, m, and the parameters c j (or d j ) in (15) are to be obtained by solving m systems of linear equations. Since we are mainly interested in the bivariate transformation L n : R 2 → R 2 , we take m = 2 in (15), requiring that L n solves Problem 2.1. Therefore, we have to consider…”

“…A more specific application which involves registration and includes imaging techniques, such as computer tomography and magnetic resonance imaging, can be found in [37,38]. Since using globally supported RBFs, as for example the Gaussians, a single landmark pair change may influence the whole registration result, in the last two decades several methods have been presented to circumvent this disadvantage, such as weighted least squares and weighted mean methods (WLSM and WMM, respectively) [24], compactly supported radial basis functions (CSRBFs), especially Wendland's and Gneiting's functions [14,15,23], and elastic body splines (EBSs) [29].…”

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

“…This important property allows the use of RBFs in interpolation problems, such as image registration. RBFs can be classified in two groups: (i) globally supported such as thin-plate spline (TPS) and Gaussian, and (ii) compactly supported such as Gneiting's, Wendland's and Wu's functions, see [1,10,11,12,14], respectively.…”

“…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.…”

Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration

“…Otherwise, the Compactly Supported RBFs (CSRBFs), such as Wendland's and Wu's transformations, can circumvent this disadvantage (see [1,3]), but usually they cannot guarantee that the bending energy is small. Papers [4] and [5] analyse different CSRBF properties for image registration which are based on global deformations.…”