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M-plicits: Neural Implicit Surfaces via Nested Multiscale Residuals

NeurIPS 2026 · 3D vision › Face and shape · approach: Implicit neural representation design · 0 citations (OpenAlex)

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Proposes M-plicits, a residual sum of SIRENs trained on nested narrow bands around previous zero-level sets, with multiscale sphere tracing and GEMM-based analytical normals for real-time SDF rendering and noise-robust surface reconstruction.

Problem

Implicit neural surface representations (SDFs from oriented point clouds) struggle to jointly balance training efficiency, rendering speed, and robustness to input noise; single large MLPs are costly at inference, grid-based models overfit noise, and prior multiscale methods capture noise via hard s

Approach

Model the SDF as a sum of residual SIRENs, each supervised only within a narrow band around the previous level's zero set (nested neighborhoods), so the coarse network acts as a low-pass prior; pair this with multiscale sphere tracing, adaptive marching cubes, and GEMM-based analytical normals.

Key results

• Ours coarse achieves best mean Chamfer distance (5.36E-05) with 17,153 parameters and 180 FPS vs iNGP coarse 6.87E-05 with about 2.0M parameters.
• Ours fine achieves best median CD (1.87E-05) and best mean IoU (0.586) and median IoU (0.867) on Stanford+Thingi32.
• Under 1% vertex noise, the method's mean CD stays stable (3.36E-05) while IDF's mean CD inflates to 8.37E-02 due to outliers.

Surprising findings

• Screened Poisson reconstruction attains the best mean IoU on clean data (0.910) but degrades to 0.416 under 1% noise, while M-plicits holds 0.687.
• Heavy outlier contamination (1% stray points) collapses M-plicits IoU on Lucy to 0.002 because the max-based band width inflates.

Limitations

• Smoothness prevents very sharp edges.
• Max-based band width is sensitive to isolated outlier points; heavy outlier contamination degrades reconstruction.
• Thingi32 failure cases (non-watertight, multi-component, thin structures) inflate mean error; BANF comparison relies on a custom re-implementation.

Experimental setup

Datasets: Stanford Thingi32

Benchmarks: Stanford Thingi32

Metrics: Chamfer distance IoU Hausdorff distance FPS sampling time parameter count

Baselines: iNGP BACON IDF BANF Screened Poisson reconstruction SIREN

Builds on: SIREN Eikonal regularization instant-ngp BACON implicit displacement fields

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