Abstract-Variational approaches have been proposed for solving many inverse problems in early vision, such as in the computation of optical flow, shape from shading, and energy-minimizing active contour models. In general however, variational approaches do not guarantee global optimality of the solution, require estimates of higher order derivatives of the discrete data, and do not allow direct and natural enforcement of constraints.In this paper we discuss dynamic programming as a novel approach to solving variational problems in vision. Dynamic programming ensures global optimality of the solution, it is numerically stable, and it allows for hard constraints to be enforced on the behavior of the solution within a natural and straightforward structure. As a specific example of the efficacy of the proposed approach, application of dynamic programming to the energy-minimizing active contours is described. The optimization problem is set up as a discrete multistage decision process and is solved by a "time-delayed" discrete dynamic programming algorithm. A parallel procedure is discussed that can result in savings in computational costs.Zndex Terms-Active contours, contour extraction, deformable models, dynamic programming, variational methods.

This paper reviews state-of-the-art research solutions across the spectrum of medical imaging informatics, discusses clinical translation, and provides future directions for advancing clinical practice. More specifically, it summarizes advances in medical imaging acquisition technologies for different modalities, highlighting the necessity for efficient medical data management strategies in

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Magnetic resonance imaging (MRI) is unique in its ability to noninvasively and selectively alter tissue magnetization and create tagged patterns within a deforming body such as the heart muscle. The resulting patterns define a time-varying curvilinear coordinate system on the tissue, which we track with coupled B-snake grids. B-spline bases provide local control of shape, compact representation, and parametric continuity. Efficient spline warps are proposed which warp an area in the plane such that two embedded snake grids obtained from two tagged frames are brought into registration, interpolating a dense displacement vector field. The reconstructed vector field adheres to the known displacement information at the intersections, forces corresponding snakes to be warped into one another, and for all other points in the plane, where no information is available, a C1 continuous vector field is interpolated. The implementation proposed in this paper improves on our previous variational-based implementation and generalizes warp methods to include biologically relevant contiguous open curves, in addition to standard landmark points. The methods are validated with a cardiac motion simulator, in addition to in-vivo tagging data sets.