Learning Smooth Neural Functions via Lipschitz Regularization
This work addresses the need for smooth shape editing in computer graphics and 3D modeling, though it is incremental as it builds on prior Lipschitz regularization techniques.
The paper tackles the problem of ensuring smooth latent spaces in neural implicit fields for 3D shapes by introducing a Lipschitz regularization method, resulting in improved performance in shape interpolation, extrapolation, and partial reconstruction tasks with both qualitative and quantitative gains over existing methods.
Neural implicit fields have recently emerged as a useful representation for 3D shapes. These fields are commonly represented as neural networks which map latent descriptors and 3D coordinates to implicit function values. The latent descriptor of a neural field acts as a deformation handle for the 3D shape it represents. Thus, smoothness with respect to this descriptor is paramount for performing shape-editing operations. In this work, we introduce a novel regularization designed to encourage smooth latent spaces in neural fields by penalizing the upper bound on the field's Lipschitz constant. Compared with prior Lipschitz regularized networks, ours is computationally fast, can be implemented in four lines of code, and requires minimal hyperparameter tuning for geometric applications. We demonstrate the effectiveness of our approach on shape interpolation and extrapolation as well as partial shape reconstruction from 3D point clouds, showing both qualitative and quantitative improvements over existing state-of-the-art and non-regularized baselines.