On the Effectiveness of Weight-Encoded Neural Implicit 3D Shapes

TL;DR

The paper argues that weight-encoded neural implicits can serve as a first-class 3D shape representation by dedicating a small neural network to each shape to learn its signed distance field (SDF). It introduces an architecture (8 layers × 32 hidden units), an integrated loss with importance sampling, and robust handling for real-world, non-watertight meshes, enabling efficient visualization via sphere tracing and CSG operations. Empirical results show high reconstruction fidelity with massive compression (e.g., Thingi10k reduced from 38.85 GB to 590 MB) and interactive rendering speeds, outperforming latent-encoded counterparts in robustness and scalability. The work highlights limitations on highly complex geometries and outlines future directions, including Eikonal consistency and meta-learning with weight-encoded representations.

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 _latent-encoded_ 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.

Figures (13)

• Figure 1: We visualize the role that varying the number of network layers and hidden layer sizes: (left to right) average reconstruction error, memory footprint and first-frame render time (DeepSDF, other setups, and our defaults in red, gray, and blue, respectively).
• Figure 2: Unlike our representation, DeepSDF reconstruction quality degrades quickly for geometries not aligned to default, per-class orientations. See accompanying video for animation.
• Figure 3: Latent-encoded SDFs (red) struggle to reconstruct "unique" features (grey, plane's tail) despite training on a single class of objects (planes). Our representation (blue) does not. gpvillamil under CC BY.
• Figure 4: Thingi10k models compressed to 59kB, reducing the dataset from 38.85 GB to 590 MB.
• Figure 5: Loss and surface error distributions over the entirety of the Thingi10k dataset.