Regularized nonrigid medical image registration algorithms usually estimate the deformation by minimizing a cost function, consisting of a similarity measure and a penalty term that discourages "unreasonable" deformations. Conventional regularization methods enforce homogeneous smoothness properties of the deformation field; less work has been done to incorporate tissue-type-specific elasticity information. Yet ignoring the elasticity differences between tissue types can result in non-physical results, such as bone warping. Bone structures should move rigidly (locally), unlike the more elastic deformation of soft issues. Existing solutions for this problem either treat different regions of an image independently, which requires precise segmentation and incurs boundary issues; or use an empirical spatial varying "filter" to "correct" the deformation field, which requires the knowledge of a stiffness map and departs from the cost-function formulation. We propose a new approach to incorporate tissue rigidity information into the nonrigid registration problem, by developing a space variant regularization function that encourages the local Jacobian of the deformation to be a nearly orthogonal matrix in rigid image regions, while allowing more elastic deformations elsewhere. For the case of X-ray CT data, we use a simple monotonic increasing function of the CT numbers (in HU) as a "rigidity index" since bones typically have the highest CT numbers. Unlike segmentation-based methods, this approach is flexible enough to account for partial volume effects. Results using a B-spline deformation parameterization illustrate that the proposed approach improves registration accuracy in inhale-exhale CT scans with minimal computational penalty.

This paper presents novel techniques for checking the soundness of a type system automatically using a software model checker. Our idea is to systematically generate every type correct intermediate program state (within some finite bounds), execute the program one step forward if possible using its small step operational semantics, and then check that the resulting intermediate program state is also type correct-but do so efficiently by detecting similarities in this search space and pruning away large portions of the search space. Thus, given only a specification of type correctness and the small step operational semantics for a language, our system automatically checks type soundness by checking that the progress and preservation theorems hold for the language (albeit for program states of at most some finite size). Our preliminary experimental results on several languages-including a language of integer and boolean expressions, a simple imperative programming language, an object-oriented language which is a subset of Java, and a language with ownership types-indicate that our approach is feasible and that our search space pruning techniques do indeed significantly reduce what is otherwise an extremely large search space. Our paper thus makes contributions both in the area of checking soundness of type systems, and in the area of reducing the state space of a software model checker.

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Glass box software model checking incorporates novel techniques to identify similarities in the state space of a model checker and safely prune large numbers of redundant states without explicitly checking them. It is significantly more efficient than other software model checking approaches for checking certain kinds of programs and program properties. This paper presents PIPAL, a system for modular glass box software model checking. Extending glass box software model checking to perform modular checking is important to further improve its scalability. It is nontrivial because unlike traditional software model checkers such as Java PathFinder (JPF) and CMC, a glass box software model checker does not check every state separately-instead, it checks a large set of states together in each step. We present a solution and demonstrate PIPAL's effectiveness on a variety of programs.