signed distance encoding

This work addresses the fundamental challenge in multi-object signed distance function (SDF) modeling—balancing geometric fidelity and encoding compactness when sharing a latent space. To this end, we propose a joint learning framework that synergistically leverages the strengths of generalization and controlled overfitting. Our method introduces an adaptive query sampling strategy to suppress inter-SDF interference while preserving high-frequency geometric details; it further integrates compact latent-space learning with cooperative multi-SDF training. Evaluated on standard benchmarks including ShapeNet, our approach achieves state-of-the-art performance: a 12.3% reduction in Chamfer distance for reconstruction accuracy, a 38% decrease in latent code length for improved compression, and 2.1× faster convergence for enhanced training efficiency. Both quantitative metrics and qualitative visualizations consistently validate its superiority.

该研究提出了一种结合切向球结构和径向基函数插值的方法，以提高从符号距离场样本重建几何表面的精度，并保留尖锐特征。

This work addresses the geometric inconsistency that arises when interpolating signed distance functions (SDFs) from discrete samples. To resolve this issue, the authors propose a hard geometric constraint framework grounded in the theoretical properties of SDFs, which for the first time rigorously guarantees that interpolated results are both compatible with the original data and correspond to realizable geometric surfaces. The method integrates an efficient greedy interpolation algorithm with GPU-accelerated preprocessing, enabling high-quality, geometrically consistent outputs across three representative tasks: global SDF refinement, mesh reconstruction, and pseudo-SDF correction. This approach overcomes a key limitation of existing techniques, which lack formal guarantees of geometric consistency.

To address the high computational and memory overhead of curvature regularization in neural signed distance field (SDF) learning—stemming from reliance on second-order automatic differentiation—this paper proposes a lightweight finite-difference-based regularization framework. We introduce, for the first time, an O(h²)-accurate finite-difference stencil for explicit SDF curvature modeling, bypassing Hessian construction and second-order gradients entirely. The method enables plug-and-play approximations of both Gaussian curvature and rank-deficiency loss. Empirically, it matches the reconstruction accuracy of automatic-differentiation-based curvature regularization while reducing GPU memory consumption and training time by up to 50%. Moreover, it demonstrates strong robustness to sparse, incomplete, and non-CAD data. Our core contribution is achieving high-fidelity geometric regularization at the cost of only low-order differentiation, thereby significantly improving the efficiency and scalability of neural SDF learning.

To address the challenge of learning signed distance functions (SDFs) from sparse point clouds—where insufficient geometric detail impairs surface reconstruction—this paper proposes an end-to-end dynamic deformation framework. The method jointly optimizes an explicit parametric surface and an implicit SDF field through three core components: (1) a bijective surface parameterization (BSP) that establishes invertible mappings between local surface patches and the global shape; (2) a grid-based deformation optimization (GDO) strategy that co-refines both the parameterized surface and the implicit field; and (3) a synergistic learning mechanism integrating bijective neural mappings, local patch embeddings, and differentiable rendering. Evaluated on both synthetic and real-world scanned datasets, the approach achieves significant improvements in SDF reconstruction accuracy and topological consistency over state-of-the-art methods.

This work addresses the lack of physical plausibility in multi-object signed distance field (SDF) modeling, which often suffers from geometric interpenetration. The authors propose S2MDF—a lightweight, plug-and-play hard-constraint module that enforces non-overlapping conditions on vector-valued SDFs without modifying the underlying network architecture. To the best of our knowledge, this is the first approach to completely eliminate geometric intersections among multiple SDFs through hard constraints, avoiding the need for intricate loss function tuning. S2MDF can be flexibly applied during either training or post-processing and, when combined with a Marching Cubes–compatible linear interpolation-based meshing strategy, reduces object overlap to numerical precision across several state-of-the-art methods while preserving high-fidelity geometry reconstruction—significantly outperforming existing soft-constraint alternatives.

This work addresses the problem of signed distance function (SDF) reconstruction from unoriented point clouds by proposing a high-order variational method that achieves geometrically consistent, high-fidelity reconstructions both locally and globally. The key innovation lies in explicitly incorporating the medial axis of the underlying surface—defined as the jump set of the SDF gradient—into the learning process. This is accomplished through an Ambrosio–Tortorelli-type phase-field approximation to model gradient discontinuities, combined with the Eikonal equation and a zero-level-set constraint. The method jointly optimizes a neural representation of the SDF alongside the phase-field function. Experimental results demonstrate that the proposed approach significantly outperforms existing techniques in both quantitative metrics and qualitative visual quality.

Existing methods for real-time, large-scale signed distance function (SDF) estimation with uncertainty quantification are often hindered by fixed resolution, high training overhead, or poor scalability. This work proposes Kernel-SDF, an open-source library that uniquely integrates kernel regression with Gaussian processes. The front-end constructs a continuous occupancy field via kernel regression, while the back-end leverages surface-boundary samples to perform Gaussian process regression, enabling accurate estimation of the SDF, its gradient, and well-calibrated uncertainties—all while supporting real-time mesh reconstruction. By unifying these components, Kernel-SDF significantly enhances SDF accuracy and geometric continuity without compromising real-time performance, thereby overcoming the traditional trade-off among efficiency, precision, and uncertainty quantification. The approach is particularly suited for robotics applications demanding high geometric reliability, such as navigation, planning, and manipulation.

This work addresses the limitations of existing rasterization-based methods, which lack a globally consistent explicit surface representation, and traditional signed distance field (SDF) approaches that rely on computationally expensive ray marching for mesh reconstruction. The paper introduces SDFRaster, the first method to combine the efficiency of rasterization with the geometric clarity of SDFs. It optimizes a continuous SDF over a Delaunay tetrahedral grid and enables efficient rendering through tetrahedral rasterization and alpha blending. Furthermore, it incorporates a differentiable Marching Tetrahedra algorithm to support end-to-end mesh reconstruction. Without requiring post-processing, SDFRaster produces consistent, watertight triangle meshes, achieving higher-quality and more complete reconstructions on the DTU and Tanks and Temples benchmarks while reducing memory overhead.

This work addresses the challenge of partial-to-complete geometric reconstruction of deformable objects under severe occlusion in point cloud observations. The authors propose a two-stage reconstruction framework that requires no object-specific shape priors. The approach first leverages a temporal geometry encoder to capture structural similarities across input sequences, then integrates this information into a FiLM-conditioned implicit signed distance function (SDF) network to achieve high-fidelity surface reconstruction. By fusing temporal cues with a lightweight conditioning mechanism, the method enhances generalization and training stability while preserving expressive power. Experiments on a rubber band manipulation dataset demonstrate that the proposed approach significantly outperforms existing methods, achieving robust and accurate reconstructions even in highly occluded scenarios.