We propose a generic method for the statistical analysis of collections

We propose a generic method for the statistical analysis of collections of anatomical shape complexes, namely sets of surfaces that were previously segmented and labeled in a group of subjects. such meshes may include small holes, show irregular sampling or split objects into different parts. More important, such methods analyze the intrinsic shape of each structure independently, therefore neglecting the fact that brain anatomy consist of an intricate arrangement of various structures with strong interrelationships. 114590-20-4 IC50 By contrast, we aim at measuring differences between shape complexes in a way that can account for both the differences in shape of the individual components and the relative position of the components within the complex. This goal cannot be achieved by concatenating the shape parameters of each component or by finding correlations between such parameters (Tsai et al., 2003; Gorczowski et al., 2010), as such approaches do not take into account the fact that the organization of the shape complex would not change, and in particular, that different structures must not intersect. One way to address this problem is to consider surfaces as embedded in 3D space and to measure shape variations induced by deformations of the underlying 3D space. This idea stems from Grenanders group theory for modeling objects (Grenander, 1994), which revisits morphometry by the use of 3D space deformations. The similarity between shape complexes is then quantified by the amount of deformation needed to warp one shape complex to another. Only smooth and invertible 3D deformations (i.e., diffeomorphisms) are used, so that the internal organization of the shape complex is preserved during deformation since neither surface intersection nor shearing may occur. The approach determines point correspondences over the whole 3D volume by using the fact that surfaces should match as a soft constraint. The method is therefore robust to segmentation errors in that exact correspondences among points lying on surfaces are not enforced. In this context, a diffeomorphism could be seen as a low-pass filter to smooth shape differences. In this paper, it is our goal to show that the deformation 114590-20-4 IC50 parameters capture the most relevant parts of the shape variations, namely the ones that would distinguish between normal and disease. Here, we propose a method that builds on the implementation of Grenanders theory in the LDDMM framework (Miller et al., 2006; Vaillant et al., 2007; McLachlan and Marsland, 2007). The method has 3 components: (i) estimation of an average model of the shape complex, called the template complex, which is representative of the population under study; (ii) estimation of the 3D deformations that map the template complex to the complex of each subject; and (iii) statistical analysis of the deformation parameters and their interpretation in terms of variations of the template complex. 114590-20-4 IC50 The first two steps are estimated simultaneously in a combined optimization framework. The resulting template complex and set of deformations are now referred to as an are of the form +in the ambient 3D space, which is assumed to be the sum of radial basis functions located at control point positions {for instance. It is beneficial to assume that is a positive definite symmetric kernel, namely that is continuous and that for any finite set of distinct points {and vectors {vanish. Translation invariant kernels are of particular interest. According to Bochners theorem, functions of the form C is a kernel allows us to define the pre-Hilbert space as the set of any finite sums Gata3 of terms for vector weights and satisfies the reproducing property: and weight.

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