Globally Convergent SDM
As we have proposed above, the global convergence of SDM still entails the provision of a properly specified initial B-spline curve. In order to make SDM more capable in terms of global convergence, we are just trying to devise a fully automatic method where SDM could always converge to a target shape from a simple initial shape.
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We also expect to see more studies on SDM and related problems, both theoretically and from the viewpoint of application. Some significant problems include the analysis of the convergence rate of PDM, the application of SDM to a large class of shape reconstruction and geometric optimization problems, such as optimization over an analytical surface or a mesh surface, surface registration, and so on.