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Three dimensional surface reconstruction based on two dimensional sparse information in the form of only a small number of level lines of the surface with moderately complex structures, containing both structured and unstructured geometries, is considered in this paper. A new model has been proposed which is based on the idea of using normal vector matching combined with a first order and a second order total variation regularizers. A fast algorithm based on the augmented Lagrangian is also proposed. Numerical experiments are provided showing the effectiveness of the model and the algorithm in reconstructing surfaces with detailed features and complex structures for both synthetic and real world digital maps.
In this paper, we consider the sparse regularization of manifold-valued data with respect to an interpolatory wavelet/multiscale transform. We propose and study variational models for this task and provide results on their well-posedness. We present
We consider reconstructing multi-channel images from measurements performed by photon-counting and energy-discriminating detectors in the setting of multi-spectral X-ray computed tomography (CT). Our aim is to exploit the strong structural correlatio
High dimensional B-splines are catching tremendous attentions in fields of Iso-geometry Analysis, dynamic surface reconstruction and so on. However, the actual measured data are usually sparse and nonuniform, which might not meet the requirement of t
Surface reconstruction from magnetic resonance (MR) imaging data is indispensable in medical image analysis and clinical research. A reliable and effective reconstruction tool should: be fast in prediction of accurate well localised and high resoluti
The reconstruction of an objects shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process of aligning intra-operative navigation and pre