MRI examinations may be used to monitor the progress of neurological disease. Arising structural changes can then be quantified using non-rigid registration procedures. However, the interpretation of the resulting large scale vector fields is difficult without further processing. We propose using contraction mapping to detect critical points such as attractors and repellors in order to characterize deforming areas. With the application to time series images we show that critical points help to get a better perception of the brain deformation and the underlying pathological process.