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.

Abstract. Without any prior knowledge, the non-rigid registration of two images is a symmetric problem, i.e. we expect to find inverse results if we exchange these images. This symmetry is nonetheless broken in most of intensity-based algorithms. In this paper, we explain the reasons why most non-rigid registration algorithms are asymmetric. We show that the asymmetry of quadratic regularization energies causes an oversmoothing of expending regions relatively to shrinking regions, hampering in particular registration-based detection of evolving processes. We therefore propose to use an inversion-invariant energy to symmetrize the registration problem. To minimize this energy, two methods are used, depending on whether we compute the inverse transformation or not. Finally, we illustrate the interest of the theory using both synthetic and real data, in particular to improve the detection and segmentation of evolving lesions in MR images of patients suffering from multiple sclerosis.

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