M-plicits: Neural Implicit Surfaces via Nested Multiscale Residuals

2026-09-23

AI Summary

This study addresses the inherent trade-off among training efficiency, rendering speed, and noise robustness in implicit neural surfaces by proposing a nested multi-scale residual MLP framework. The framework introduces nested neighborhood residual modeling and localized supervision, combined with sinusoidal positional encoding to enhance representational capacity. Furthermore, it replaces automatic differentiation with multi-scale sphere tracing and GEMM-based analytical normal computation, while incorporating low-pass filtering to suppress noise artifacts. Experimental results on the Stanford dataset demonstrate that the proposed method achieves state-of-the-art Chamfer distance performance while reducing the parameter count by an order of magnitude compared to baselines. Ultimately, this approach enables high-fidelity real-time rendering and substantially improves overall performance across key evaluation metrics.

Abstract

Encoding input coordinates with sinusoidal functions into multi-layer perceptrons (MLPs) has proven effective for implicit neural representations (INRs) of surfaces defined as zero-level sets. However, existing methods often struggle to balance training efficiency, rendering speed, and noise robustness: single-MLP approaches are expensive at inference, grid-based representations are fast but can limit surface smoothness and overfit input noise, and previous multiscale approaches frequently capture noise and produce artifacts due to hard spectral truncation. To address these limitations, we propose M-plicits, a multiscale framework that models surfaces as a residual sum of MLPs trained via a sequence of nested neighborhoods. Unlike existing residual approaches that rely on standard domain-wide sampling and require costly mesh extraction for visualization, our method strictly localizes supervision to narrow bands around the previous zero-level sets. This nested design naturally provides robustness against noisy input data: the coarse network acts as a low-pass filter that establishes a clean geometric prior, while subsequent residuals progressively refine the geometry without fitting to high-frequency artifacts. We further introduce a multiscale sphere-tracing algorithm and a GEMM-based analytical normal computation that bypasses auto-differentiation entirely, yielding high-fidelity real-time rendering. On Stanford and Thingi32, M-plicits achieves the best mean Chamfer distance in the coarse configuration and the best median Chamfer distance and IoU in the fine configuration, with substantially better noise robustness than iNGP, BACON, and IDF, while using an order of magnitude fewer parameters than grid-based baselines. Code, models, and data will be released at https://github.com/dsilvavinicius/m-plicits.

Problem

• implicit neural representations
• multiscale residuals
• noise robustness
• neural implicit surfaces
• rendering efficiency

Innovation

• Neural Implicit Surfaces
• Multiscale Residuals
• Sphere Tracing
• Noise Robustness
• Implicit Neural Representations