[Paper Review] Iso-Points: Optimizing Neural Implicit Surfaces with Hybrid Representations

Yifan Wang, Shihao Wu+2 more|arXiv (Cornell University)|Dec 11, 2020

3D Shape Modeling and Analysis50 references4 citations

TL;DR

This paper introduces Iso-Points, a hybrid neural surface representation that combines neural implicit functions with dynamically updated, geometry-aware point clouds to improve optimization stability and reconstruction quality. By projecting, resampling, and upsampling iso-points on-the-fly during training, the method enables effective geometric regularization, leading to faster convergence, better generalization, and superior recovery of fine details and topology from noisy or incomplete data such as sparse or corrupted point clouds and multi-view images.

ABSTRACT

Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the parameters for accurate and robust reconstructions remains a challenge, especially when the input data is noisy or incomplete. In this work, we develop a hybrid neural surface representation that allows us to impose geometry-aware sampling and regularization, which significantly improves the fidelity of reconstructions. We propose to use \emph{iso-points} as an explicit representation for a neural implicit function. These points are computed and updated on-the-fly during training to capture important geometric features and impose geometric constraints on the optimization. We demonstrate that our method can be adopted to improve state-of-the-art techniques for reconstructing neural implicit surfaces from multi-view images or point clouds. Quantitative and qualitative evaluations show that, compared with existing sampling and optimization methods, our approach allows faster convergence, better generalization, and accurate recovery of details and topology.

Motivation & Objective

• To address the challenge of optimizing neural implicit surfaces from noisy or incomplete 3D data, such as sparse or corrupted point clouds and multi-view images.
• To improve reconstruction fidelity by incorporating geometric constraints into the optimization process through an explicit, adaptive point representation.
• To enable faster convergence and better generalization in neural implicit surface fitting by leveraging dynamic, geometry-aware sampling.
• To bridge the gap between implicit neural representations and explicit geometry processing tools by introducing a two-way conversion between implicit functions and iso-points.
• To enhance topological accuracy and detail preservation in 3D reconstruction without requiring ground-truth supervision.

Proposed method

• The method introduces iso-points as an explicit, on-the-fly sampled point cloud representation derived from the neural implicit function’s zero level set.
• A multi-stage sampling pipeline is used: projection of points onto the implicit surface, resampling to fix under-sampled regions, and upsampling to achieve dense coverage.
• All operations are GPU-accelerated and rely only on local point neighborhoods, ensuring efficiency and scalability during training.
• Geometry-aware regularization is applied by leveraging the spatial distribution and curvature of iso-points to guide optimization and suppress noise and artifacts.
• The hybrid representation allows integration into existing optimization pipelines, such as those using ray-marching or differentiable rendering, with minimal overhead.
• Iso-points are filtered to remove occluded points before projection, reducing computational cost and improving optimization efficiency.

Experimental results

Research questions

• RQ1 Can a hybrid representation combining neural implicit functions and explicit point clouds improve optimization stability and reconstruction quality for 3D surfaces from imperfect data?
• RQ2 How can geometry-aware sampling and regularization be effectively integrated into neural implicit surface optimization without increasing computational cost?
• RQ3 To what extent can iso-points enhance detail recovery and topological accuracy in reconstruction from noisy or sparse inputs?
• RQ4 Can the proposed method be efficiently integrated into existing multi-view or point cloud reconstruction pipelines with minimal modification?
• RQ5 Does the use of on-the-fly iso-point extraction lead to faster convergence and better generalization compared to standard optimization strategies?

Key findings

• The proposed method achieves faster convergence than baseline optimization, reaching a given chamfer distance threshold up to 2x faster, as shown in Fig. 10.
• On the DTU-MVS dataset, the method reduces average L1-Chamfer distance to 0.53, outperforming the baseline (0.61), screened Poisson (0.47), and Points2Surf (0.52).
• For model 122 of the DTU-MVS dataset, the method achieves a Chamfer distance of 0.42, significantly lower than the baseline (0.50), indicating superior reconstruction accuracy on noisy, sparse inputs.
• The method effectively suppresses topological noise and surface artifacts such as 'droplets' and bumps caused by outliers and holes in the input data.
• The overhead of iso-point extraction is minimal—typically equivalent to 3 training iterations—making it practical for real-time or iterative optimization pipelines.
• The method preserves fine geometric details in multi-view reconstruction, as demonstrated by improved feature recovery compared to baseline and state-of-the-art methods.