Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance

A neural signed distance function (SDF) is a convenient shape representation for many tasks, such as surface recon-struction, editing and generation. However, neural SDFs are difficult to fit to raw point clouds, such as those sam-pled from the surface of a shape by a scanner. A major is-sue occurs when the shape's geometry is very differentfrom the structural biases implicit in the network's initialization. In this case, we observe that the standard loss formulation does not guide the network towards the correct SDF val-ues. We circumvent this problem by introducing guiding points, and use them to steer the optimization towards the true shape via small incremental changes for which the loss formulation has a good descent direction. We show that this point-guided homotopy-based optimization scheme fa-cilitates a deformation from an easy problem to the diffi-cult reconstruction problem. We also propose a metric to quantify the difference in surface geometry between a target shape and an initial surface, which helps indicate whether the standard loss formulation is guiding towards the target shape. Our method outperforms previous state-of-the-art approaches, with large improvements on shapes identified by this metric as particularly challenging.