Deformable image registration is a widely used technique in the field of computer vision and medical image processing. Basically, the task of deformable image registration is to find the displacement field between the moving image and the fixed image. Many variational models are proposed for deformable image registration, under the assumption that the displacement field is continuous and smooth. However,displacement fields may be discontinuous, especially for medical images with intensity in homogeneity, pathological tissues or heavy noises. In the mathematical theory of elastoplasticity, when the displacement fields are possibly discontinuous, a suitable frame work for describing the displacement fields is the space of functions of bounded deformation (BD). Inspired by this,we propose a novel deformable registration model, called BD model, which allows discontinuities of displacement fields in images. BD model is formulated in a variational framework by supposing the displacement field to be a function of bounded deformation. Existence of solutions of this model is proven.Numerical experiments on two-dimensional images show that BD model outperforms the classical demons model, the log-do maindiffeomorphic demons model and the state-of-the-art vectorial total variation model. Numerical experiments on two public three-dimensional databases show that the target registration error (TRE) of BD model is competitive comparing with more than ten other models.
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