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We introduce a fast solver for registration problems that include image-based local rigidity constraints. Such problems arise in many applications, and the constraints are useful for incorporating prior knowledge about expected solutions for these typically ill-posed problems. Locally rigid registration can be posed as a nonlinear optimization which is nonlinear in two blocks of variables: one set of large dimension representing the nonlinear motion on the unconstrained portion of the domain and the other set of small dimension representing the rigid motion parameters on the constrained regions of the image. We propose a fast solver based on a Gauss-Newton framework that includes a tailored linear solver for improved efficiency. The linearized subproblems for the search direction are solved iteratively using our Linearize and Project (LAP) approach. Specifically, we eliminate the set of variables associated with the rigid motion and iteratively compute an update of the nonlinear motion parameters. We show numerical examples that demonstrate the effectiveness of our approach both regarding iterations and time-to-solution.
This presentation is part of Minisymposium “MS22 - Mapping problems in imaging, graphics and vision (3 parts)”
organized by: Ronald Lui (Chinese University of Hong Kong) , Ke Chen (University of Liverpool) .