Abstract
Abstract. Statistical shape models (SSM) capture the variation of shape across a population, in order to allow further analysis. Previous work demonstrates that deformation fields contain global transformation components, even if global pre- registration is performed. It is crucial to construction of SSMs to remove these global transformation components from the local deformations - thus obtaining minimal deformations - prior to using these as input for SSM construction. In medical image processing, parameterized SSMs based on control points of free-form deformations (FFD) are a popular choice, since they offer several advantages compared to SSMs based on dense deformation fields. In this work, we extend the previous approach by presenting a framework for construction of both, unparameterized and FFD-based SSMs from minimal deformations. The core of the method is computation of minimal deformations by extraction of the linear part from the original dense deformations. For FFD-based SSMs, the FFD-parameterization of the minimal deformations is performed by projection onto the space of FFDs. Both steps are computed by close-form solutions optimally in the least-square sense. The proposed method is evaluated on a data set of 62 MR images of the corpus callosum. The results show a significant improvement achieved by the proposed method for SSMs built on dense fields, as well as on FFD-based SSMs.
Highlights
In this paper we consider the construction of statistical shape models (SSM) from deformation fields which are computed by a non-linear registration method.4 This approach is discussed for example in [1] and [2], while the advantages of this approach for medical applications are discussed in [1].Previous work [3, 4] demonstrates that in general, computed deformations contain a substantial amount of global linear transformation, even if global pre-registration is performed, please compare Fig. 1
The only component of the framework which includes an approximation is the projection of minimal deformations onto the free-form deformations (FFD) model
The basic ideas underlying the proposed methods are the interpretation of displacement fields as corresponding point sets and the ability to switch between representations of deformations
Summary
In this paper we consider the construction of statistical shape models (SSM) from deformation fields which are computed by a non-linear registration method. This approach is discussed for example in [1] and [2], while the advantages of this approach for medical applications are discussed in [1].Previous work [3, 4] demonstrates that in general, computed deformations contain a substantial amount of global linear transformation, even if global pre-registration is performed, please compare Fig. 1. Since SSMs should only describe variations in shape (a) original deformation Tlocal (b) extracted similarity Tlin (c) minimal deformation Tnl and not e.g. in position, it is intuitive that they should be constructed on minimal deformations, rather than on deformations which still contain global linear transformation components such as similarity. It is shown in [4] that it is not a minor effect, but crucial to build SSMs on minimal deformation fields, in order to obtain correct shape models. If similarity transformation components are not removed from deformation fields prior to SSM construction, this will in general lead to shape models in which the first modes do not necessarily describe the largest variations in shape [4], see Fig. 3
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