Simple Geodesic Regression for Image Time-Series

TitleSimple Geodesic Regression for Image Time-Series
Publication TypeConference Paper
Year of Publication2012
AuthorsHong Y, Sanchez M, Styner M, Niethammer M
Conference NameWorkshop on Biomedical Image Registration (WBIR)

Geodesic regression generalizes linear regression to general Riemannian manifolds. Applied to images, it allows for a compact approximation of an image time-series through an initial image and an initial momentum. Geodesic regression requires the definition of a squared residual (squared distance) between the regression geodesic and the measurement images. In principle, this squared distance should also be defined through a geodesic connecting an image on the regression geodesicto its respective measurement. However, in practice only standard registration distances (such as sum of squared distances) are used, to reduce computation time. This paper describes a simplified geodesic regression method which approximates the registration-based distances with respect to a fixed initial image. This results in dramatically simplified computations. In particular, the method becomes straightforward to implement using readily available large displacement diffeomorphic metric mapping (LDDMM) shooting algorithms and decouples the problem into pairwise image registrations allowing parallel computations. We evaluate the approach using 2D synthetic images and real 3D brain images.