ON THE EFFECTIVENESS OF WEIGHT-ENCODED NEURAL IMPLICIT 3D SHAPES Anonymous

Abstract

A neural implicit outputs a number indicating whether the given query point in space is inside, outside, or on a surface. Many prior works have focused on latentencoded neural implicits, where a latent vector encoding of a specific shape is also fed as input. While affording latent-space interpolation, this comes at the cost of reconstruction accuracy for any single shape. Training a specific network for each 3D shape, a weight-encoded neural implicit may forgo the latent vector and focus reconstruction accuracy on the details of a single shape. While previously considered as an intermediary representation for 3D scanning tasks or as a toy-problem leading up to latent-encoding tasks, weight-encoded neural implicits have not yet been taken seriously as a 3D shape representation. In this paper, we establish that weight-encoded neural implicits meet the criteria of a first-class 3D shape representation. We introduce a suite of technical contributions to improve reconstruction accuracy, convergence, and robustness when learning the signed distance field induced by a polygonal mesh -the de facto standard representation. Viewed as a lossy compression, our conversion outperforms standard techniques from geometry processing. Compared to previous latent-and weight-encoded neural implicits we demonstrate superior robustness, scalability, and performance.

1. INTRODUCTION

While 3D surface representation has been a foundational topic of study in the computer graphics community for over four decades, recent developments in machine learning have highlighted the potential that neural networks can play as effective parameterizations of solid shapes. The success of neural approaches to shape representations has been evidenced both through their ability of representing complex geometries as well as their utility in end-to-end 3D shape learning, reconstruction, and understanding and tasks. These approaches also make use of the growing availability of user generated 3D content and high-fidelity 3D capture devices, e.g., point cloud scanners. For these 3D tasks, one powerful configuration is to represent a 3D surface S as the set containing any point x ∈ R 3 for which an implicit function (i.e., a neural network) evaluates to zero: S := x ∈ R 3 |f θ ( x; z) = 0 , ( ) Implicit Explicit (mesh) where θ ∈ R m are the network weights and z ∈ R k is an input latent vector encoding a particular shape. In contrast to the de facto standard polygonal mesh representation which explicitly discretizes a surface's geometry, the function f implicitly defines the shape S encoded in z. We refer to the representation in Eq. ( 1) as a latent-encoded neural implicit. et al. (2019) propose to optimize the weights θ so each shape S i ∈ D in a dataset or shape distribution D is encoded into a corresponding latent vector z i . If successfully trained, the weights θ of their DEEPSDF implicit function f θ can be said to generalize across the "shape space" of D. As always with supervision, reducing the training set from D will affect f 's ability to generalize and can lead to overfitting. Doing so may seem, at first, to be an ill-fated and uninteresting idea.

Park

Our work considers an extreme case -when the training set is reduced to a single shape S i . We can draw a simple but powerful conclusion: in this setting, one can completely forgo the latent vector

