  We introduce a continuous global optimization method to the field of surface
reconstruction from discrete noisy cloud of points with weak information on
orientation. The proposed method uses an energy functional combining flux-based
data-fit measures and a regularization term. A continuous convex relaxation
scheme assures the global minima of the geometric surface functional. The
reconstructed surface is implicitly represented by the binary segmentation of
vertices of a 3D uniform grid and a triangulated surface can be obtained by
extracting an appropriate isosurface. Unlike the discrete graph-cut solution,
the continuous global optimization entails advantages like memory requirements,
reduction of metrication errors for geometric quantities, allowing globally
optimal surface reconstruction at higher grid resolutions. We demonstrate the
performance of the proposed method on several oriented point clouds captured by
laser scanners. Experimental results confirm that our approach is robust to
noise, large holes and non-uniform sampling density under the condition of very
coarse orientation information.
