  We present a learning-based method, namely GeoUDF,to tackle the long-standing
and challenging problem of reconstructing a discrete surface from a sparse
point cloud.To be specific, we propose a geometry-guided learning method for
UDF and its gradient estimation that explicitly formulates the unsigned
distance of a query point as the learnable affine averaging of its distances to
the tangent planes of neighboring points on the surface. Besides,we model the
local geometric structure of the input point clouds by explicitly learning a
quadratic polynomial for each point. This not only facilitates upsampling the
input sparse point cloud but also naturally induces unoriented normal, which
further augments UDF estimation. Finally, to extract triangle meshes from the
predicted UDF we propose a customized edge-based marching cube module. We
conduct extensive experiments and ablation studies to demonstrate the
significant advantages of our method over state-of-the-art methods in terms of
reconstruction accuracy, efficiency, and generality. The source code is
publicly available at https://github.com/rsy6318/GeoUDF.
