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Latest methods represent shapes with open surfaces using unsigned distancefunctions (UDFs). They train neural networks to learn UDFs and reconstructsurfaces with the gradients around the zero level set of the UDF. However, thedifferential networks struggle from learning the zero level set where the UDFis not differentiable, which leads to large errors on unsigned distances andgradients around the zero level set, resulting in highly fragmented anddiscontinuous surfaces. To resolve this problem, we propose to learn a morecontinuous zero level set in UDFs with level set projections. Our insight is toguide the learning of zero level set using the rest non-zero level sets via aprojection procedure. Our idea is inspired from the observations that thenon-zero level sets are much smoother and more continuous than the zero levelset. We pull the non-zero level sets onto the zero level set with gradientconstraints which align gradients over different level sets and correctunsigned distance errors on the zero level set, leading to a smoother and morecontinuous unsigned distance field. We conduct comprehensive experiments insurface reconstruction for point clouds, real scans or depth maps, and furtherexplore the performance in unsupervised point cloud upsampling and unsupervisedpoint normal estimation with the learned UDF, which demonstrate our non-trivialimprovements over the state-of-the-art methods. Code is available athttps://github.com/junshengzhou/LevelSetUDF .

Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection