[Paper Review] On the Effectiveness of Weight-Encoded Neural Implicit 3D Shapes

Thomas Davies, Derek Nowrouzezahrai+1 more|arXiv (Cornell University)|Sep 17, 2020

3D Shape Modeling and AnalysisEngineering24 references41 citations

TL;DR

This paper advocates weight-encoded neural implicits as a first-class 3D shape representation, showing they can achieve high surface accuracy, robust performance, and compact memory usage, outperforming latent-encoded approaches. It introduces a compact 8-layer network, an integral loss with importance sampling, and demonstrates strong compression and fast rendering for polygonal meshes.

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.

Motivation & Objective

• Show that weight-encoded neural implicits can serve as a first-class 3D shape representation.
• Develop an architecture and training regime to convert meshes into weight-encoded neural implicits with high accuracy.
• Demonstrate compression and speed advantages over traditional mesh and grid-based SDF representations.
• Assess robustness and scalability on real-world datasets (e.g., Thingi10k).

Proposed method

• Use a feed-forward network with 8 layers and hidden size 32 to encode a single shape as a weight-encoded implicit (no latent vector).
• Regress a signed distance field (SDF) to the mesh surface rather than occupancy, for direct graphics utility.
• Define a loss as an integral over space with an exponential weighting w(x)=exp(-β|gS(x)|) to achieve near-surface sampling without ad hoc point sampling bias.
• Apply importance sampling by drawing samples from a distribution proportional to w to approximate the integral loss.
• Render using sphere tracing with a simple, efficient CUDA-based pipeline and dynamic batching for convergence timing.
• Demonstrate robustness to “in the wild” meshes by using robust insideness tests (generalized winding numbers) and unsigned-distance handling when needed.

Experimental results

Research questions

• RQ1 Can weight-encoded neural implicits faithfully represent a single 3D shape as a first-class representation without a latent code?
• RQ2 How does weight-encoded representation compare to latent-encoded and grid-based SDF representations in terms of accuracy, robustness, and memory usage?
• RQ3 What architecture and training strategies enable robust reconstruction and scalable processing of large real-world mesh datasets?
• RQ4 Is it feasible to convert large mesh datasets (e.g., Thingi10k) into weight-encoded implicits within reasonable time and storage budgets?
• RQ5 What are practical rendering and manipulation benefits (e.g., CSG) of weight-encoded implicits for graphics pipelines?

Key findings

• A weight-encoded neural implicit can encode a single shape without a latent vector, parameterized by θ, yielding a 3D surface as the zero set of fθ.
• An 8-layer, 32-neuron network (7553 weights; ~59 kB) achieves a favorable balance of reconstruction accuracy, rendering speed, and memory use.
• The proposed integral loss with importance sampling improves convergence and surface accuracy over prior sampling schemes (e.g., ~5% surface error improvement vs Park et al. 2019 on Thingi10k).
• The approach compresses the Thingi10k dataset from 38.85 GB to 590 MB (1:66 compression); DeepSDF would compress to 7 MB but with lower quality on real-world, unconstrained data.
• Rendering at 512×512 on a P100 achieves ~34 Hz frame rates for a single implicit, using sphere tracing with CUDA-based visualization.
• Weight-encoded implicits show better surface detail fidelity and smoother reconstructions compared to uniform grids or decimated meshes at comparable memory budgets; they also support efficient SIMD evaluation and parallel rendering.