Uncertainty Quantification for LDDMM Using a Low-Rank Hessian Approximation

Abstract

This paper presents an approach to estimate the uncertainty of registration parameters for the large displacement diffeomorphic metric mapping (LDDMM) registration framework. Assuming a local multivariate Gaussian distribution as an approximation for the registration energy at the optimal registration parameters, we propose a method to approximate the covariance matrix as the inverse of the Hessian of the registration energy to quantify registration uncertainty. In particular, we make use of a low-rank approximation to the Hessian to accurately and efficiently estimate the covariance matrix using few eigenvalues and eigenvectors. We evaluate the uncertainty of the LDDMM registration results for both synthetic and real imaging data.