Statistical methods in computational anatomy

Abstract

This paper reviews recent developments by the Washington/Brown groups for the study of anatomical shape in the emerging new discipline of computational anatomy. Parametric representations of anatomical variation for computational anatomy are reviewed, restricted to the assumption of small deformations. The generation of covariance operators for probabilistic measures of anatomical variation on coordinatized submanifolds is formulated as an empirical procedure. Populations of brains are mapped to common coordinate systems, from which template coordinate systems are constructed which are closest to the population of anatomies in a minimum distance sense. Variation of several one-, two- and three-dimensional manifolds, i.e. sulci, surfaces and brain volumes are examined via Gaussian measures with mean and covariances estimated directly from maps of templates to targets. Methods are presented for estimating the covariances of vector fields from a family of empirically generated maps, posed as generalized spectrum estimation indexed over the submanifolds. Covariance estimation is made parametric, analogous to autoregressive modelling, by introducing small deformation linear operators for constraining the spectrum of the fields.

Population Shape Regression from Random Design Data

“…This approach is common within the shape analysis literature (Grenander and Miller 1998;Miller et al 1997). Because we are interested in capturing the large, natural geometric variability evident in the brain (cf.…”

Towards accurate, automatic segmentation of the hippocampus and amygdala from MRI by augmenting ANIMAL with a template library and label fusion

“…Once this transformation is found, its inverse can be used to map labels, defined in the atlas, onto the subject's MRI, thus achieving structure segmentation in a potentially automatic fashion. This approach was pioneered by Bajcsy et al (1983) and Miller et al (1997). In one of the first atlas-based applications of the hippocampus, Haller et al developed a two step registration procedure for segmentation of the hippocampus (Haller et al, 1997).…”

Evaluation of fiber bundles across subjects through brain mapping and registration of diffusion tensor data

“…An accurate depiction of normal anatomical variability in specific regions across subjects depends on the homology between them. In recent years, various brain mapping algorithms have been developed (Miller et al, 1997;Styner and Gerig, 2001;Thompson et al, 2001) to address this dependency and to allow an accurate statistical analysis. Mapping algorithms can be classified into two categories: implicit image intensity-based technique; and explicit computational geometrybased technique.…”

“…Statistical analysis (Miller et al, 1997;Styner et al, 2003;Thompson and Toga, 2002) in brain abnormality studies are typically population-based comparisons that reveal significant differences between healthy volunteers and patients. The results can help achieve important objectives in many neuroscience studies, for instance, delineating the anatomical region affected by disease facilitates future course of treatment and surgical planning.…”