From the NCBC grant 1R01-EB008171-01A1:
The long-term research goal of the proposed project is to develop open-source statistical shape analysis software that will be leveraged by neuroimaging community using the VTK and ITK libraries. In Computational Anatomy (CA) today, all morphometric studies of shape are carried out by metric comparison of anatomical structures via vector field displacements relating the coordinatized structures. Two basic approaches have emerged: Gaussian random field localized statistical shape analysis for understanding connections and interrelations of anatomical substructures and their implicated role in neuropsychiatric illness and metric classifier construction for clustering disease populations via a global image based bio-marker measuring the metric structure of the space of anatomical shapes. Specifically, (a) Localized statistical shape analysis in coordinate systems is carried out via Gaussian Random Field (GRF) models where local shape changes in the form of vector field displacements are encoded as basis functions indexed over the coordinates. The basis functions signal the areas of statistically significant change with respect to shape coordinates. (b) Global image based metric classifiers are constructed by computing metric distances between anatomical structures and performing clustering via multi-dimensional scaling (MDS) and statistical methods based on linear-discriminant analysis (LDA). Classifiers based on morphometric biomarkers from diseased populations are rapidly emerging as part of the Morphometry Biomedical Informatics Research Network (BIRN) via the Semi-Automated SHape Analysis (SASHA) pipeline21. This proposal integrates the GRF approach for localized visualization and detection of anatomical change with the global metric classifier approach depicted in Fig. 1. The vehicles for integration and dissemination are modules for the 3D Slicer application and enhancements to the ITK processing library.
Proposed Laplace-Beltrami filter here:
Principal Components Analysis
The output of Large-Deformation Diffeomorphic Metric Mapping is vector momentum values at each vertex of the template mesh used for matching against a subject population. The dimensions (number of vertices) of these meshes can be large, so we propose to perform our statistical measures on subjects described by a smaller set of basis functions determined via a Kernel PCA calculator.
We use a standard version of Kernel PCA which is described here: http://en.wikipedia.org/wiki/Kernel_principal_component_analysis
The code currently in development is here: