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Multiphase Segmentation of Deformation using Logarithmic Priors

In [8], the authors proposed the large deformation log-unbiased diffeomorphic nonlinear image registration model which has been successfully used to obtain theoretically and intuitively correct deformation maps. In this paper, we extend this idea to simultaneously registering and tracking deforming objects in a sequence of two or more images. We generalize a level set based Chan-Vese multiphase segmentation model to consider Jacobian fields while segmenting regions of growth and shrinkage in deformations. Deforming objects are thus classified based on magnitude of homogeneous deformation. Numerical experiments demonstrating our results include a pair of two-dimensional synthetic images and pairs of two-dimensional and three-dimensional serial MRI images.