Principal Component Based Diffeomorphic Surface Mapping

• Published in: IEEE transactions on medical imaging Vol. 31; no. 2; pp. 302 - 311
• Main Authors: Anqi Qiu, Younes, L., Miller, M. I.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2012; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Brain - anatomy & histology; Computer Simulation; Diffeomorphisms; Hilbert space; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Imaging, Three-Dimensional - methods; initial momentum; Kernel; Magnetic Resonance Imaging - methods; Models, Statistical; Pattern Recognition, Automated - methods; Principal Component Analysis; Reproducibility of Results; Sensitivity and Specificity; Shape; Studies; surface mapping; Surface waves; Vectors
• ISSN: 0278-0062; 1558-254X; 1558-254X
• DOI: 10.1109/TMI.2011.2168567

We present a new diffeomorphic surface mapping algorithm under the framework of large deformation diffeomorphic metric mapping (LDDMM). Unlike existing LDDMM approaches, this new algorithm reduces the complexity of the estimation of diffeomorphic transformations by incorporating a shape prior in which a nonlinear diffeomorphic shape space is represented by a linear space of initial momenta of diffeomorphic geodesic flows from a fixed template. In addition, for the first time, the diffeomorphic mapping is formulated within a decision-theoretic scheme based on Bayesian modeling in which an empirical shape prior is characterized by a low dimensional Gaussian distribution on initial momentum. This is achieved using principal component analysis (PCA) to construct the eigenspace of the initial momentum. A likelihood function is formulated as the conditional probability of observing surfaces given any particular value of the initial momentum, which is modeled as a random field of vector-valued measures characterizing the geometry of surfaces. We define the diffeomorphic mapping as a problem that maximizes a posterior distribution of the initial momentum given observable surfaces over the eigenspace of the initial momentum. We demonstrate the stability of the initial momentum eigenspace when altering training samples using a bootstrapping method. We then validate the mapping accuracy and show robustness to outliers whose shape variation is not incorporated into the shape prior.