A Log-Euclidean Polyaffine Registration for Articulated Structures in Medical Images

Abstract

Abstract. In this paper we generalize the Log-Euclidean polyaffine registration framework of Arsigny et al.[1] to deal with articulated structures. This framework has very useful properties as it guarantees the invertibility of smooth geometric transformations. In articulated registration a skeleton model is defined for rigid structures such as bones. The final transformation is affine for the bones and elastic for other tissues in the image. We extend the Arsigny el al.'s method to deal with locally-affine registration of pairs of wires. This enables the possibility of using this registration framework to deal with articulated structures. In this context, the design of the weighting functions, which merge the affine transformations defined for each pair of wires, has a great impact not only on the final result of the registration algorithm, but also on the invertibility of the global elastic transformation. Several experiments, using both synthetic images and hand radiographs, are also presented.

Capturing the multiscale anatomical shape variability with polyaffine transformation trees

“…An efficient registration algorithm using approximations of polyaffine transformations was presented in Commowick et al (2008). In Martín-Fernández et al (2009) an extension to articulated structures was presented, which considers weights (defining the influence of each region) fixed at landmark positions along a manually defined skeleton.…”

High-resolution temporal reconstruction of ankle joint from dynamic MRI

“…In [6], the authors prove that this type parameterization is well-adapted to the registration of articulated structures such as the hip and knee joint for serial x-ray CT mouse images. In [7], an extension of the Log Euclidean polyrigid registration was presented to deal with human articulated structures from 2D radiographs. In our study, we propose to use the log-euclidean framework to estimate high-resolution temporal MRI data.…”

Hierarchical adaptive local affine registration for fast and robust respiratory motion estimation

“…This approach does not require pre-defined segmentations but is based on a distribution of anchor points, each associated with a rigid or affine registration. Martin-Fernandez et al (2009) extended this work by incorporating rigid body structures into the framework. The registration accuracy of such techniques, however, depends on the choice of location for the anchor points.…”