Metamorphic geodesic regression

Abstract

We propose a metamorphic geodesic regression approach approximating spatial transformations for image time-series while simultaneously accounting for intensity changes. Such changes occur for example in magnetic resonance imaging (MRI) studies of the developing brain due to myelination. To simplify computations we propose an approximate metamorphic geodesic regression formulation that only requires pairwise computations of image metamorphoses. The approximated solution is an appropriately weighted average of initial momenta. To obtain initial momenta reliably, we develop a shooting method for image metamorphosis.

Fig 1

Bull’s eye metamorphic regression experiment. Measurement images (top row). Metamorphic regression result (middle row) and momenta (bottom row). The first image is chosen as base image. Momenta images: left: time-weighted average of the initial momenta; right: momenta of the measurement images with respect to the base image.

Fig 2

Square metamorphic regression experiment. (a) moving square with decreasing intensities and no oscillations during movement; (b) moving and oscillating square with alternating intensities. For both cases, the base image is the first one. Top row: measurement images, middle row: metamorphic regression results, bottom row: momenta images (left: time-weighted average of the initial momenta, to the right: momenta of the measurement images with respect to the base image).

Fig 3

Representative data-sets at 3, 6 and 12 months (left to right)

Fig 4

Regression results for monkey data: LDDMM (top) metamorphosis (bottom). (a) Images on geodesic at 12, 6, 3 months; (b) Zoom in for images on geodesic at 12, 6, 3 months; (c) Zoom in for images at 3 months to illustrate spatial deformation.