Implicit Geometric Regularization for Learning Shapes

TL;DR

This paper introduces a new implicit neural representation method for shapes that uses a simple loss function encouraging smoothness and natural surfaces, achieving high fidelity reconstructions directly from raw point cloud data.

Contribution

The paper proposes a novel loss function with implicit geometric regularization for neural shape representations, enabling high-quality reconstructions without pre-computed shapes or explicit loss functions.

Findings

Achieves state-of-the-art detail and fidelity in shape reconstructions

The simple loss function promotes smooth, natural zero level set surfaces

Theoretical analysis supports the regularization property in the linear case

Abstract

Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape representations; or (ii) loss functions explicitly defined over the neural level sets. In this paper we offer a new paradigm for computing high fidelity implicit neural representations directly from raw data (i.e., point clouds, with or without normal information). We observe that a rather simple loss function, encouraging the neural network to vanish on the input point cloud and to have a unit norm gradient, possesses an implicit geometric regularization property that favors smooth and natural zero level set surfaces, avoiding bad zero-loss solutions. We provide a theoretical analysis of this property for the linear case, and show that, in practice, our method leads to state of the art implicit neural representations with higher level-of-details and fidelity compared to previous methods.