Neural implicit function based on signed distance field (SDF) has achieved impressiveprogress inreconstructing 3Dmodels withhighfidelity. However,such approaches canonlyrepresent closed surfaces.

In this work we target a learnableoutputrepresentation that allows continuous, high resolution outputs of arbitrary shape. Recent works represent 3D surfaces implicitly with a Neural Network, thereby breaking previous barriers in resolution, and ability to represent diverse topologies. However, neural implicit representations arelimited to closed surfaces, which divide the space into inside and outside. Many real world objects such as walls of a scene scannedby a sensor,clothing,or a car with innerstructuresare not closed. Thisconstitutesa significant barrier,in termsof datapre-processing (objects need to be artificially closed creating artifacts), and the ability to output open surfaces. In this work, we proposeNeural Distance Fields (NDF), a neural network based model which predicts the unsigned distance field for arbitrary 3D shapes given sparse point clouds. NDF represent surfaces at high resolutions as prior implicit models, but do not require closed surface data, and significantly broaden the class of representable shapes in the output.

Geodesics play a critical role in many geometry processing applications.

More specifically, one lossisLalpha = C 1 thatencourages aminimal alpha mask butmight result inagrainymask, so the other loss isLdiv = d, i.e., minimizing the divergence of the distance field to achieve more smooth/continuous alphamask.

In the first case, the non-standard representation prevents benefiting from latest network architectures for neural representations; while, in the latter case, therasterized representation, when encoded vianetworks, results inlossof data fidelity, as font-specific discontinuities like edges and corners are difficult torepresent using neural networks.