The study of temporal series of medical images can be helpful for physicians to perform pertinent diagnoses and to help them in the follow-up of a patient: in some diseases, lesions, tumors or anatomical structures vary over time in size, position, composition, etc., either because of a natural pathological process or under the effect of a drug or a therapy. It is a laborious and subjective task to visually and manually analyze such images. Thus the objective of this work was to automatically detect regions with apparent local volume variation with a vector field operator applied to the local displacement field obtained after a non-rigid registration between two successive temporal images. On the other hand, quantitative measurements, such as the volume variation of lesions or segmentation of evolving lesions, are important. By studying the information of apparent shrinking areas in the direct and reverse displacement fields between images, we are able to segment evolving lesions. Then we propose a method to segment lesions in a whole temporal series of images. In this article we apply this approach to automatically detect and segment multiple sclerosis lesions that evolve in time series of MRI scans of the brain. At this stage, we have only applied the approach to a few experimental cases to demonstrate its potential. A clinical validation remains to be done, which will require important additional work.