Details Enhancement in Unsigned Distance Field Learning for High-fidelity 3D Surface Reconstruction

TL;DR

This work addresses the limitations of unsigned distance fields (UDFs) for high-fidelity 3D surface reconstruction, notably near the zero level set and gradient instability. It introduces Details Enhanced UDF (DEUDF), which combines normal alignment, unconditioned MLPs with SIREN activations, adaptively weighted Eikonal constraints, and a DCUDF-based surface extraction workflow. The method improves UDF accuracy, preserves open boundaries, and demonstrates robustness to noise and complex internal structures, achieving competitive results with SDF-based approaches. These advances enhance open-surface modeling and non-watertight reconstructions in practical 3D vision tasks.

Abstract

While Signed Distance Fields (SDF) are well-established for modeling watertight surfaces, Unsigned Distance Fields (UDF) broaden the scope to include open surfaces and models with complex inner structures. Despite their flexibility, UDFs encounter significant challenges in high-fidelity 3D reconstruction, such as non-differentiability at the zero level set, difficulty in achieving the exact zero value, numerous local minima, vanishing gradients, and oscillating gradient directions near the zero level set. To address these challenges, we propose Details Enhanced UDF (DEUDF) learning that integrates normal alignment and the SIREN network for capturing fine geometric details, adaptively weighted Eikonal constraints to address vanishing gradients near the target surface, unconditioned MLP-based UDF representation to relax non-negativity constraints, and DCUDF for extracting the local minimal average distance surface. These strategies collectively stabilize the learning process from unoriented point clouds and enhance the accuracy of UDFs. Our computational results demonstrate that DEUDF outperforms existing UDF learning methods in both accuracy and the quality of reconstructed surfaces. Our source code is at https://github.com/GiliAI/DEUDF.

Figures (8)

• Figure 1: Illustration of UDF learning with various neural representations. (a) Existing neural network architectures often use an absolute value or softplus function to prevent negative distances. (b) In contrast, our method relaxes the non-negative condition and employs an unconditioned MLP with the SIREN activation function for predicting the distances. (c) To show the differences between existing representations and ours, we consider a plane $\pi$ and a line perpendicular to $\pi$. We plot the unsigned distance to $\pi$ on this line learned by our method, but with different MLP output layers. (d) The horizontal axis represents a signed distance range from -0.05 to 0.05, while the vertical axis measures the learned unsigned distance. Ideally, the unsigned distance should exhibit a perfect "V" shape relative to the signed distance. (e) However, UDFs parameterized by conditioned MLPs can present defects. For example, learning a negative value followed by taking the absolute value results in a "W"-shaped distance field around the zero level set. (f) Employing the softplus activation function to eliminate negative values yields learned UDFs with vanishing gradients across a relatively large distance range near the zero value. (g) In contrast, our method, which employs unconditioned MLPs, significantly narrows this range of vanishing gradients.
• Figure 2: Visual comparison with two recent UDF learning approaches, DUDF fainstein2024dudf and LevelSetUDF Zhou2023levelset, and one recent SDF learning method, NSH NSH, on surfaces with fine geometric details. Our method yields visually pleasing results, reconstructing significantly more details than the other methods.
• Figure 3: Visual results of the ablation studies: (a) Applying the absolute value to the output of the SIREN network. (b) Applying the softplus function to the output of the SIREN network. (c) Using uniform Eikonal constraints. (d) Removing normal alignment. (e) Replacing estimated normals with random vector. (f) Applying all components.
• Figure 4: Visual comparisons with DUDF, CAP-UDF and LevelSetUDF on an indoor scene of the Stanford 3D Scene dataset featuring noise, an imperfect scan, and two car models of the ShapeNet-Cars dataset showcasing complex structures. Our method remains the open boundaries, such as, the bookshelves, inner structures of the vehicle, car window and car exhaust vent.
• Figure 5: Visual results for reconstruction on noisy point clouds. We separately add $N(0, 0.0025)$, $N(0, 0.005)$ Gaussian noise to input point cloud. Specially, we changed our method to SIREN with frequency 30 for better performance.