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Compressive Neural Representations of Volumetric Scalar Fields

Yuzhe Lu, Kairong Jiang, Joshua A. Levine, Matthew Berger

arXiv:2104.04523v1cs.LGcs.GR

TL;DR

Large scalar-field volumes create storage and visualization challenges, and existing compression quality can vary with how well fields match method assumptions. This paper compresses fields as capacity-limited coordinate-based neural networks with quantized weights, yielding compact representations and supporting gradient-aware fitting, time-varying data, and arbitrary-point evaluation.

  • Problem

    Large scalar-field datasets challenge visualization through storage, bandwidth, and interactivity demands, while existing methods show variable compression ratios and approximation quality as their assumptions fit fields to differing degrees.

    Source: §1 · pp. 1–2

  • Method

    A capacity-limited coordinate-based neural network learns scalar-field values and serves as the compressed representation, with weight quantization further compacting it.

    Source: §1 · p. 2

  • Results

    Capacity limits and weight quantization yield highly compact scalar-field representations, and high-compression renderings show smoother magnetic-field surfaces than tthresh.

    Source: §1 · p. 2, §4.1 · p. 8

  • Takeaways & Limitations

    The approach supports spatial-gradient regularization, time-varying fields, and arbitrary-point evaluation, including volume rendering without reconstructing the whole volume first.

    Source: §1 · p. 2

    Training has high computation time, although the authors consider the reported times pessimistic.

    Source: §5 · p. 10

Abstract

from arXiv · show

We present an approach for compressing volumetric scalar fields using implicit neural representations. Our approach represents a scalar field as a learned function, wherein a neural network maps a point in the domain to an output scalar value. By setting the number of weights of the neural network to be smaller than the input size, we achieve compressed representations of scalar fields, thus framing compression as a type of function approximation. Combined with carefully quantizing network weights, we show that this approach yields highly compact representations that outperform state-of-the-art volume compression approaches. The conceptual simplicity of our approach enables a number of benefits, such as support for time-varying scalar fields, optimizing to preserve spatial gradients, and random-access field evaluation. We study the impact of network design choices on compression performance, highlighting how simple network architectures are effective for a broad range of volumes.

1. Introduction

Large scalar-field volumes challenge visualization through storage, bandwidth, and interactivity demands, while transform-based compressors can vary in quality when fields do not match their assumptions. The paper proposes capacity-limited neural representations with quantized weights and studies their compactness and additional capabilities.

1. Introduction

  • Transform compressors rely on assumptions such as low-frequency content or low-rank structure, and varying degrees of match lead to variable compression ratios and approximation quality.The cited transforms include Fourier and wavelet bases and data-dependent bases.Source: §1 · pp. 1–2
  • A coordinate-based neural network learns field values, and fewer network weights than volume samples make the network itself the compressed representation.Evaluating the network at sampled positions reconstructs the original field values.Source: §1 · p. 2
  • The approach builds on SIREN, using sinusoidal activations and residual connections, and its learned per-layer weights can be quantized to few bits with minimal performance impact.The authors say residual connections that preserve SIREN activation distributions make networks robust across architecture choices.Source: §1 · p. 2
  • Limiting network capacity and quantizing weights yields highly compact scalar-field representations with gradient regularization, time-varying data, and arbitrary-point access.Available spatial gradients can regularize the network, producing less noisy isosurfaces at high compression ratios.Source: §1 · p. 2
  • The paper compares its approach directly with tthresh and studies network design, gradient preservation, and time-varying data.These are listed as evaluation and experimental contributions.Source: §1 · p. 2

2. Related Work

Prior volume-compression work includes transforms, data fitting, and models tailored to particular data properties. Deep-learning work spans visualization representations, super-resolution, and implicit fields, while this paper investigates implicit representations specifically for compressing arbitrary scalar fields.

2.1. Compression of Volumetric Data

  • Transform methods use Fourier, wavelet, block, or tensor decompositions, while data-fitting approaches include curve fitting, prediction, NURBS, topology-aware models, and precision-resolution selection.TTHRESH is identified as a recent state-of-the-art technique that this paper compares against.Source: §2.1 · p. 2
  • Transform compression depends on data matching assumptions such as low-frequency content or low-rank structure, whereas data fitting trades off sample count against precision per sample.The paper distinguishes its neural-network fitting approach from other data-fitting methods.Source: §2.1 · p. 2

2.2. Deep Learning for Volume Representation

  • Deep-learning volume representations combine data representation with tasks such as rendering, interpolation, ensemble translation, and transfer-function design.The related work describes these applications as distinct from the present paper's compression focus.Source: §2.2 · p. 2
  • Deep-learning super-resolution methods can be compressive but were not specifically designed for compression, while implicit representations had been applied to shapes, textures, and views.This work investigates making implicit neural representations compressive for arbitrary scalar fields.Source: §2.2 · p. 3

3. Compression Method

The method compresses a sampled scalar field by fitting a smaller coordinate-based neural network, then encoding its weights. SIREN-based design choices support compact storage, gradient-aware fitting, and evaluation at arbitrary positions.

3. Compression Method

  • A coordinate-based neural network maps domain positions to scalar values, with fewer parameters than field samples, to form a compact approximation.The method frames compression as learning a function under a capacity limit.Source: §3 · p. 3

3.1. Neural Encoder

  • The encoder uses SIREN’s fully connected sinusoidal layers; residual blocks improve training stability and performance as depth increases.The network shape is set by layer count and total weight count.Source: §3.1 · pp. 4–5

3.1.1. Network Weight Quantization

  • At 9-bit quantization, weights incur a minimal PSNR drop; the method quantizes intermediary layers and uses this setting for all paper networks.The first and last layers remain unquantized because experiments found they require higher precision.Source: §3.1.1 · p. 5

3.1.2. Gradient Regularization

  • Gradient regularization improves target-gradient capture with a small scalar-field PSNR decrease, and produces smoother, ground-truth-reflective isosurfaces.The comparison uses the jet volume at a 677:1 compression ratio.Source: Table 1 · p. 5, Figure 5 · p. 5, §3.1.2 · p. 6

3.2. Neural Decoder

  • The network can be evaluated at arbitrary positions and differentiated directly, supporting ray-marched volume rendering and gradient-based direct illumination.Rendered-image quality suggests it interpolates beyond the sampled field values.Source: §3.2 · p. 6

4. Experiments

Across static and time-varying scalar-field experiments, neurcomp generally outperforms tthresh, with stronger gains at higher compression ratios. The experiments also examine spatial resolution and gradient regularization.

4. Experiments

  • The evaluation covers static simulation fields and two time-varying volumes, comparing neurcomp with tthresh and training networks with Adam.The reported implementation uses 75 iterations, with a learning-rate decay every 20 iterations.Source: §4 · p. 6

4.1. 3D Scalar Fields

  • Neurcomp largely improves over tthresh on 3D scalar fields, except for the jet volume at low compression ratios, with larger gains at higher ratios.The comparison plots compression ratio against PSNR.Source: Figure 8 · p. 7, §4.1 · p. 8
  • At high compression, neurcomp produces smoother fields than tthresh; for rt, its representations are about half the size at roughly the same PSNR.For the magneto-hydrodynamic fields, the visual comparisons also show smoother surfaces and better feature retention; on rt, tthresh reproduces high frequencies.Source: §4.1 · p. 8, Figure 9 · p. 8, Figure 10 · p. 8

4.2. Time-varying Scalar Fields

  • On asteroid, neurcomp outperforms tthresh with greater stability; on isabel, it is comparable at low compression and gains more at higher ratios.At low compression on isabel, neurcomp also outperforms at the first and last timesteps.Source: §4.2 · pp. 8–9, Figure 11 · p. 9

4.3. Spatial Resolution

  • For isotropic_p crops, PSNR improves with spatial resolution despite similarly configured network sizes and higher compression ratios for larger volumes.The experiments use centered 256^3 and 128^3 crops from a 512^3 volume, hold the network-size-to-volume ratio constant, and quantize weights to 9 bits.Source: §4.3 · p. 9, Figure 12 · p. 9

4.4. Gradient Regularization

  • With gradient regularization, neurcomp can incorporate gradient preservation during optimization, while tthresh produces noisy isosurfaces despite comparable PSNR.For rt, target gradients come from central finite differencing; the methods differ in gradient-based PSNR.Source: §4.4 · pp. 9–10, Figure 13 · p. 9, Table 3 · p. 9

5. Discussion

The discussion identifies training cost and per-volume fitting as key constraints, while describing random-sample training and flexible regularization as useful properties. Noisy volumes remain difficult because preserving noise and extracting useful gradients are challenging.

5. Discussion

  • Training is the primary drawback: large volumes can take a few hours per volume, although higher compression ratios take less time with smaller network architectures.The authors envision running compression jobs as large simulations complete.Source: §5 · p. 10
  • Training uses random field samples, avoiding the need to hold the entire volume in memory, while multiresolution training is proposed to address its time cost.The authors identify multiresolution methods that account for spatial locality as future work.Source: §5 · p. 10
  • The learned function is specific to one volume; the authors demonstrate time-varying fields and plan to incorporate multiple fields and simulation parameters.They state their approach is general enough to accommodate these factors.Source: §5 · p. 10
  • For noisy medical volumes such as the foot, predominant features are captured, but preserving noise and obtaining useful gradients for regularization remain challenging.The authors report that simple finite-difference schemes help regularize simulation data and expect higher-order derivative estimates to be useful.Source: §5 · p. 10, Figure 15 · p. 10
  • Coordinate-based MLPs offer flexibility in designing data-preservation constraints, and future work may improve preservation of varied volumetric features.Source: §5 · p. 10

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