Visualising deformation fields computed by non-linear image registration

Magnetic resonance imaging (MRI) is used in clinical routine to map the brain’s morphology. Structural changes due to brain growth, ageing, surgical intervention or pathological processes may be detected by non-linear image registration of time-series imaging data. The resulting displacement field is large and therefore, hard to interpret. For a simplified but sufficient description of the displacement field contraction mapping is proposed to detect vector field singularities. This allows the detection and analysis of singularities of any order as critical points which reflect the topology of the vector field. An application demonstrates how this method helps to increase the understanding of pathological processes in the brain