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Intelligent 3D geometry reconstruction using dynamic and evolution-based techniques


"The reconstruction of 3D shapes from unorganized point cloud data is a challenging problem, which has recently attracted much interest in various branches of applied geometry, such as computer vision, computational geometry, computer aided design and computer graphics. This is due to the availability of new and powerful 3D scanning technology, such as optical scanners and CT (computer tomography) equipment. Depending on the application, various techniques for solving this problem have been proposed (and will be analyzed in Activity 1 of this project): Level set techniques are used in medical applications and image processing. The methods developed in Computer Graphics and Computational geometry rely mainly on triangular meshes. Methods for generating full NURBS models (Non-Uniform Rational B-Splines, the universally accepted standard in Computer Aided Design) have been investigated in Computer Aided Geometric Design. The planned project aims at developing a unifying framework, by treating the different techniques as dynamic (evolution) processes (Activity 2 of the project). Many non-linear optimization techniques (such as Newton-type methods used for surface fitting) can be seen to define evolution processes. Consequently, it seems to be natural to study them within a dynamic framework, where a (possibly self-organizing) model evolves towards a target shape (such as an 'active contour model' in computer vision). We expect that this viewpoint improves the global convergence of the nonlinear methods. It will be helpful for generating hybrid models, which combine standard geometries (simple surfaces such as natural quadrics) with free-form geometries (NURBS surfaces or triangular meshes). The use of such models (which may combine different representations of an object) will help to include shape and topological constraints in the framework, leading to ""intelligent"" methods for shape reconstruction (Activity 3 of the project)."

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