This paper proposed a new method called homeomorphic non-rigid image registration based on physical model. We analyze the conditions for homeomorphic map over continuous space and discrete rectangular grid. The method keeps the Jacobian of deformation within bounds and ensures that the results are one-to-one and reversible. The constrained optimization is solved by interior penalty function method and steepest descent algorithm. Experiments using artificial and magnetic resonance images show the new method gives better registration results than the no constrains one.
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