Self-Supervised Implicit Attention Priors for Point Cloud Reconstruction

TL;DR

The paper tackles the ill-posed problem of reconstructing continuous surfaces from irregular point clouds by learning a shape-specific implicit prior directly from the input. It introduces a dictionary-conditioned neural field whose queries attend to a learnable token dictionary via cross-attention, producing a non-local self-prior that guides surface prediction. After learning, the zero-level set is densified and normals are derived from gradients, followed by a Robust Implicit MLS refinement to yield high-fidelity meshes with preserved detail and flexible topology. The method achieves state-of-the-art performance on self-similar shapes and demonstrates robustness to noise and sparsity, while operating without external training data and enabling accurate normal estimation through the gradient of the learned field.

Abstract

Recovering high-quality surfaces from irregular point cloud is ill-posed unless strong geometric priors are available. We introduce an implicit self-prior approach that distills a shape-specific prior directly from the input point cloud itself and embeds it within an implicit neural representation. This is achieved by jointly training a small dictionary of learnable embeddings with an implicit distance field; at every query location, the field attends to the dictionary via cross-attention, enabling the network to capture and reuse repeating structures and long-range correlations inherent to the shape. Optimized solely with self-supervised point cloud reconstruction losses, our approach requires no external training data. To effectively integrate this learned prior while preserving input fidelity, the trained field is then sampled to extract densely distributed points and analytic normals via automatic differentiation. We integrate the resulting dense point cloud and corresponding normals into a robust implicit moving least squares (RIMLS) formulation. We show this hybrid strategy preserves fine geometric details in the input data, while leveraging the learned prior to regularize sparse regions. Experiments show that our method outperforms both classical and learning-based approaches in generating high-fidelity surfaces with superior detail preservation and robustness to common data degradations.

Figures (13)

• Figure 1: Comparison with NKSR huang2022neural on the 'Bust of Marcus Aurelius' fitzwilliam_head_2025. Though NKSR is trained on a large 3D dataset and configured for maximum detail preservation, our method better captures fine surface details, particularly at the back of the head.
• Figure 2: Deformation-based reconstruction methods, such as Point2Mesh, are limited by their reliance on a fixed input topology. In contrast, our implicit approach provides greater flexibility in representing complex geometries.
• Figure 3: We present a self-supervised surface reconstruction method based on a neural field conditioned via cross-attention. We assume access to an unoriented point cloud $\mathcal{P}$. Each input query point $x$ is encoded via positional encoding $\gamma(x)$ and interacts with a shared, learnable embedding dictionary to produce a latent representation $z(x)$ that captures shape-specific geometric priors. An MLP then predicts geometric field, which we train with a number of geometric losses to recover the surface from the point cloud. Finally, Moving Least Squares (MLS) reconstruction is applied to refine the implicit surface.
• Figure 4: Our method combines a learned self-prior with explicit point cloud control to preserve surface detail, outperforming approaches that rely solely on learned priors (Point2Mesh) or neural fields without attention.
• Figure 5: We present qualitative comparison between our method and other leading reconstruction methods on shapes with high amounts of self-similarity; Our approach excels at capturing global shape properties while retaining local shape details.