Fei Hou

Jiayi Kong, Xuhui Chen, Chen Zong et al.

Neural Signed Distance Functions (SDFs) excel at reconstructing watertight manifolds but fail on thin structures and open boundaries due to strict inside--outside constraints. Conversely, Unsigned Distance Fields (UDFs) accommodate general geometries but suffer from gradient singularities at the zero-level set, hindering optimization and extraction. We introduce Metric--Phase Fields (MPFs), a decoupled implicit representation that separates metric proximity from topological phase. Given an unoriented point cloud, MPFs learn (i) an unsigned metric field $r$ and (ii) a smooth phase field $θ$, for which we derive a bounded phase indicator $P=\tanh(βθ)$ that provides soft inside--outside cues where they are meaningful. We couple the two fields via a gated-metric formulation with a residual phase injection to obtain a signed implicit function with stable near-surface gradients. The phase coefficient $β$ is learnable, allowing MPFs to adaptively control the sharpness of the phase transition and the degree of saturation of the soft sign indicator. Experiments on both synthetic and scanned thin-shell and thin-plate shapes demonstrate that MPFs preserve thin and layered structures more faithfully than recent SDF-based methods, while also enabling more robust training and more reliable surface extraction than UDF-based approaches. Check out \href{https://github.com/JIAYI-Scarlett/ICML2026-MPF}{MPFs-GitHub} for source code and test models.

Junkai Deng, Fei Hou, Xuhui Chen et al.

Recently, building on the foundation of neural radiance field, various techniques have emerged to learn unsigned distance fields (UDF) to reconstruct 3D non-watertight models from multi-view images. Yet, a central challenge in UDF-based volume rendering is formulating a proper way to convert unsigned distance values into volume density, ensuring that the resulting weight function remains unbiased and sensitive to occlusions. Falling short on these requirements often results in incorrect topology or large reconstruction errors in resulting models. This paper addresses this challenge by presenting a novel two-stage algorithm, 2S-UDF, for learning a high-quality UDF from multi-view images. Initially, the method applies an easily trainable density function that, while slightly biased and transparent, aids in coarse reconstruction. The subsequent stage then refines the geometry and appearance of the object to achieve a high-quality reconstruction by directly adjusting the weight function used in volume rendering to ensure that it is unbiased and occlusion-aware. Decoupling density and weight in two stages makes our training stable and robust, distinguishing our technique from existing UDF learning approaches. Evaluations on the DeepFashion3D, DTU, and BlendedMVS datasets validate the robustness and effectiveness of our proposed approach. In both quantitative metrics and visual quality, the results indicate our superior performance over other UDF learning techniques in reconstructing 3D non-watertight models from multi-view images. Our code is available at https://bitbucket.org/jkdeng/2sudf/.

Fei Hou, Xuhui Chen, Wencheng Wang et al.

In this paper, we propose a new method, called DoubleCoverUDF, for extracting the zero level-set from unsigned distance fields (UDFs). DoubleCoverUDF takes a learned UDF and a user-specified parameter $r$ (a small positive real number) as input and extracts an iso-surface with an iso-value $r$ using the conventional marching cubes algorithm. We show that the computed iso-surface is the boundary of the $r$-offset volume of the target zero level-set $S$, which is an orientable manifold, regardless of the topology of $S$. Next, the algorithm computes a covering map to project the boundary mesh onto $S$, preserving the mesh's topology and avoiding folding. If $S$ is an orientable manifold surface, our algorithm separates the double-layered mesh into a single layer using a robust minimum-cut post-processing step. Otherwise, it keeps the double-layered mesh as the output. We validate our algorithm by reconstructing 3D surfaces of open models and demonstrate its efficacy and effectiveness on synthetic models and benchmark datasets. Our experimental results confirm that our method is robust and produces meshes with better quality in terms of both visual evaluation and quantitative measures than existing UDF-based methods. The source code is available at https://github.com/jjjkkyz/DCUDF.

Baixin Xu, Jiangbei Hu, Fei Hou et al.

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural implicit surfaces to simple parametric domains like spheres and polycubes. Our method allows users to specify the number of cubes in the parametric domain, learning a configuration that closely resembles the target 3D object's geometry. It computes bi-directional deformation between the object and the domain using a forward mapping from the object's zero level set and an inverse deformation for backward mapping. We ensure nearly bijective mapping with a cycle loss and optimize deformation smoothness. The parameterization quality, assessed by angle and area distortions, is guaranteed using a Laplacian regularizer and an optimized learned parametric domain. Our framework integrates with existing neural rendering pipelines, using multi-view images of a single object or multiple objects of similar geometries to reconstruct 3D geometry and compute texture maps automatically, eliminating the need for any prior information. We demonstrate the method's effectiveness on images of human heads and man-made objects.

Shengchun Wang, Wencheng Wang, Fei Hou

Image smoothing is by reducing pixel-wise gradients to smooth out details. As existing methods always rely on gradients to determine smoothing manners, it is difficult to distinguish structures and details to handle distinctively due to the overlapped ranges of gradients for structures and details. Thus, it is still challenging to achieve high-quality results, especially on preserving weak structures and removing high-contrast details. In this paper, we address this challenge by improving the real-time optimization-based method via iterative least squares (called ILS). We observe that 1) ILS uses gradients as the independent variable in its penalty function for determining smoothing manners, and 2) the framework of ILS can still work for image smoothing when we use some values instead of gradients in the penalty function. Thus, corresponding to the properties of pixels on structures or not, we compute some values to use in the penalty function to determine smoothing manners, and so we can handle structures and details distinctively, no matter whether their gradients are high or low. As a result, we can conveniently remove high-contrast details while preserving weak structures. Moreover, such values can be adjusted to accelerate optimization computation, so that we can use fewer iterations than the original ILS method for efficiency. This also reduces the changes onto structures to help structure preservation. Experimental results show our advantages over existing methods on efficiency and quality.

Xuhui Chen, Fugang Yu, Fei Hou et al.

Unsigned distance fields (UDFs) allow for the representation of models with complex topologies, but extracting accurate zero level sets from these fields poses significant challenges, particularly in preserving topological accuracy and capturing fine geometric details. To overcome these issues, we introduce DCUDF2, an enhancement over DCUDF--the current state-of-the-art method--for extracting zero level sets from UDFs. Our approach utilizes an accuracy-aware loss function, enhanced with self-adaptive weights, to improve geometric quality significantly. We also propose a topology correction strategy that reduces the dependence on hyper-parameter, increasing the robustness of our method. Furthermore, we develop new operations leveraging self-adaptive weights to boost runtime efficiency. Extensive experiments on surface extraction across diverse datasets demonstrate that DCUDF2 outperforms DCUDF and existing methods in both geometric fidelity and topological accuracy. We will make the source code publicly available.

Linlin Liu, Qian Fu, Fei Hou et al.

We develop a new method for portrait image editing, which supports fine-grained editing of geometries, colors, lights and shadows using a single neural network model. We adopt a novel asymmetric conditional GAN architecture: the generators take the transformed conditional inputs, such as edge maps, color palette, sliders and masks, that can be directly edited by the user; the discriminators take the conditional inputs in the way that can guide controllable image generation more effectively. Taking color editing as an example, we feed color palettes (which can be edited easily) into the generator, and color maps (which contain positional information of colors) into the discriminator. We also design a region-weighted discriminator so that higher weights are assigned to more important regions, like eyes and skin. Using a color palette, the user can directly specify the desired colors of hair, skin, eyes, lip and background. Color sliders allow the user to blend colors in an intuitive manner. The user can also edit lights and shadows by modifying the corresponding masks. We demonstrate the effectiveness of our method by evaluating it on the CelebAMask-HQ dataset with a wide range of tasks, including geometry/color/shadow/light editing, hand-drawn sketch to image translation, and color transfer. We also present ablation studies to justify our design.

Haoran Zhang, Junkai Deng, Xuhui Chen et al.

Traditional 3D shape reconstruction techniques from multi-view images, such as structure from motion and multi-view stereo, face challenges in reconstructing transparent objects. Recent advances in neural radiance fields and its variants primarily address opaque or transparent objects, encountering difficulties to reconstruct both transparent and opaque objects simultaneously. This paper introduces $α$-Neus -- an extension of NeuS -- that proves NeuS is unbiased for materials from fully transparent to fully opaque. We find that transparent and opaque surfaces align with the non-negative local minima and the zero iso-surface, respectively, in the learned distance field of NeuS. Traditional iso-surfacing extraction algorithms, such as marching cubes, which rely on fixed iso-values, are ill-suited for such data. We develop a method to extract the transparent and opaque surface simultaneously based on DCUDF. To validate our approach, we construct a benchmark that includes both real-world and synthetic scenes, demonstrating its practical utility and effectiveness. Our data and code are publicly available at https://github.com/728388808/alpha-NeuS.

Jiangbei Hu, Yanggeng Li, Fei Hou et al.

Unsigned distance fields (UDFs) provide a versatile framework for representing a diverse array of 3D shapes, encompassing both watertight and non-watertight geometries. Traditional UDF learning methods typically require extensive training on large 3D shape datasets, which is costly and necessitates re-training for new datasets. This paper presents a novel neural framework, LoSF-UDF, for reconstructing surfaces from 3D point clouds by leveraging local shape functions to learn UDFs. We observe that 3D shapes manifest simple patterns in localized regions, prompting us to develop a training dataset of point cloud patches characterized by mathematical functions that represent a continuum from smooth surfaces to sharp edges and corners. Our approach learns features within a specific radius around each query point and utilizes an attention mechanism to focus on the crucial features for UDF estimation. Despite being highly lightweight, with only 653 KB of trainable parameters and a modest-sized training dataset with 0.5 GB storage, our method enables efficient and robust surface reconstruction from point clouds without requiring for shape-specific training. Furthermore, our method exhibits enhanced resilience to noise and outliers in point clouds compared to existing methods. We conduct comprehensive experiments and comparisons across various datasets, including synthetic and real-scanned point clouds, to validate our method's efficacy. Notably, our lightweight framework offers rapid and reliable initialization for other unsupervised iterative approaches, improving both the efficiency and accuracy of their reconstructions. Our project and code are available at https://jbhu67.github.io/LoSF-UDF.github.io.

Qian Fu, Linlin Liu, Fei Hou et al.

Aiming at developing intuitive and easy-to-use portrait editing tools, we propose a novel vectorization method that can automatically convert raster images into a 3-tier hierarchical representation. The base layer consists of a set of sparse diffusion curves (DC) which characterize salient geometric features and low-frequency colors and provide means for semantic color transfer and facial expression editing. The middle level encodes specular highlights and shadows to large and editable Poisson regions (PR) and allows the user to directly adjust illumination via tuning the strength and/or changing shape of PR. The top level contains two types of pixel-sized PRs for high-frequency residuals and fine details such as pimples and pigmentation. We also train a deep generative model that can produce high-frequency residuals automatically. Thanks to the meaningful organization of vector primitives, editing portraits becomes easy and intuitive. In particular, our method supports color transfer, facial expression editing, highlight and shadow editing and automatic retouching. Thanks to the linearity of the Laplace operator, we introduce alpha blending, linear dodge and linear burn to vector editing and show that they are effective in editing highlights and shadows. To quantitatively evaluate the results, we extend the commonly used FLIP metric (which measures differences between two images) by considering illumination. The new metric, called illumination-sensitive FLIP or IS-FLIP, can effectively capture the salient changes in color transfer results, and is more consistent with human perception than FLIP and other quality measures on portrait images. We evaluate our method on the FFHQR dataset and show that our method is effective for common portrait editing tasks, such as retouching, light editing, color transfer and expression editing. We will make the code and trained models publicly available.

Xi Han, Fei Hou, Hong Qin

Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and exhibits sub-optimal efficiency for certain PDE formulations, while data-driven neural methods typically lack mathematical guarantee of convergence and correctness. This paper articulates a mathematically rigorous neural solver for linear PDEs. The proposed UGrid solver, built upon the principled integration of U-Net and MultiGrid, manifests a mathematically rigorous proof of both convergence and correctness, and showcases high numerical accuracy, as well as strong generalization power to various input geometry/values and multiple PDE formulations. In addition, we devise a new residual loss metric, which enables unsupervised training and affords more stability and a larger solution space over the legacy losses.

Zhuodong Li, Fei Hou, Wencheng Wang et al.

Orienting point clouds is a fundamental problem in computer graphics and 3D vision, with applications in reconstruction, segmentation, and analysis. While significant progress has been made, existing approaches mainly focus on watertight, object-level 3D models. The orientation of large-scale, non-watertight 3D scenes remains an underexplored challenge. To address this gap, we propose DACPO (Divide-And-Conquer Point Orientation), a novel framework that leverages a divide-and-conquer strategy for scalable and robust point cloud orientation. Rather than attempting to orient an unbounded scene at once, DACPO segments the input point cloud into smaller, manageable blocks, processes each block independently, and integrates the results through a global optimization stage. For each block, we introduce a two-step process: estimating initial normal orientations by a randomized greedy method and refining them by an adapted iterative Poisson surface reconstruction. To achieve consistency across blocks, we model inter-block relationships using an an undirected graph, where nodes represent blocks and edges connect spatially adjacent blocks. To reliably evaluate orientation consistency between adjacent blocks, we introduce the concept of the visible connected region, which defines the region over which visibility-based assessments are performed. The global integration is then formulated as a 0-1 integer-constrained optimization problem, with block flip states as binary variables. Despite the combinatorial nature of the problem, DACPO remains scalable by limiting the number of blocks (typically a few hundred for 3D scenes) involved in the optimization. Experiments on benchmark datasets demonstrate DACPO's strong performance, particularly in challenging large-scale, non-watertight scenarios where existing methods often fail. The source code is available at https://github.com/zd-lee/DACPO.

Hanting Niu, Junkai Deng, Fei Hou et al.

Multi-layer perceptrons (MLPs) are a standard tool for learning and function approximation, but they inherently yield outputs that are globally smooth. As a result, they struggle to represent functions that are continuous yet deliberately non-differentiable (i.e., with prescribed $C^0$ sharp features) without relying on ad hoc post-processing. We present SharpNet, a modified MLP architecture capable of encoding functions with user-defined sharp features by enriching the network with an auxiliary feature function, which is defined as the solution to a Poisson equation with jump Neumann boundary conditions. It is evaluated via an efficient local integral that is fully differentiable with respect to the feature locations, enabling our method to jointly optimize both the feature locations and the MLP parameters to recover the target functions/models. The $C^0$-continuity of SharpNet is precisely controllable, ensuring $C^0$-continuity at the feature locations and smoothness elsewhere. We validate SharpNet on 2D problems and 3D CAD model reconstruction, and compare it against several state-of-the-art baselines. In both types of tasks, SharpNet accurately recovers sharp edges and corners while maintaining smooth behavior away from those features, whereas existing methods tend to smooth out gradient discontinuities. Both qualitative and quantitative evaluations highlight the benefits of our approach.

Xuhui Chen, Fei Hou, Wencheng Wang et al.

Unsigned distance fields (UDFs) are widely used in 3D deep learning due to their ability to represent shapes with arbitrary topology. While prior work has largely focused on learning UDFs from point clouds or multi-view images, extracting meshes from UDFs remains challenging, as the learned fields rarely attain exact zero distances. A common workaround is to reconstruct signed distance fields (SDFs) locally from UDFs to enable surface extraction via Marching Cubes. However, this often introduces topological artifacts such as holes or spurious components. Moreover, local SDFs are inherently incapable of representing non-manifold geometry, leading to complete failure in such cases. To address this gap, we propose MIND (Material Interface from Non-manifold Distance fields), a novel algorithm for generating material interfaces directly from UDFs, enabling non-manifold mesh extraction from a global perspective. The core of our method lies in deriving a meaningful spatial partitioning from the UDF, where the target surface emerges as the interface between distinct regions. We begin by computing a two-signed local field to distinguish the two sides of manifold patches, and then extend this to a multi-labeled global field capable of separating all sides of a non-manifold structure. By combining this multi-labeled field with the input UDF, we construct material interfaces that support non-manifold mesh extraction via a multi-labeled Marching Cubes algorithm. Extensive experiments on UDFs generated from diverse data sources, including point cloud reconstruction, multi-view reconstruction, and medial axis transforms, demonstrate that our approach robustly handles complex non-manifold surfaces and significantly outperforms existing methods. The source code is available at https://github.com/jjjkkyz/MIND.

Cheng Xu, Fei Hou, Wencheng Wang et al.

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.

Jiangbei Hu, Ben Fei, Baixin Xu et al.

We introduce a new generative model that combines latent diffusion with persistent homology to create 3D shapes with high diversity, with a special emphasis on their topological characteristics. Our method involves representing 3D shapes as implicit fields, then employing persistent homology to extract topological features, including Betti numbers and persistence diagrams. The shape generation process consists of two steps. Initially, we employ a transformer-based autoencoding module to embed the implicit representation of each 3D shape into a set of latent vectors. Subsequently, we navigate through the learned latent space via a diffusion model. By strategically incorporating topological features into the diffusion process, our generative module is able to produce a richer variety of 3D shapes with different topological structures. Furthermore, our framework is flexible, supporting generation tasks constrained by a variety of inputs, including sparse and partial point clouds, as well as sketches. By modifying the persistence diagrams, we can alter the topology of the shapes generated from these input modalities.

Jiayi Kong, Chen Zong, Junkai Deng et al.

Unsigned Distance Fields (UDFs) provide a flexible representation for 3D shapes with arbitrary topology, including open and closed surfaces, orientable and non-orientable geometries, and non-manifold structures. While recent neural approaches have shown promise in learning UDFs, they often suffer from numerical instability, high computational cost, and limited controllability. We present a lightweight, network-free method, Voronoi-Assisted Diffusion (VAD), for computing UDFs directly from unoriented point clouds. Our approach begins by assigning bi-directional normals to input points, guided by two Voronoi-based geometric criteria encoded in an energy function for optimal alignment. The aligned normals are then diffused to form an approximate UDF gradient field, which is subsequently integrated to recover the final UDF. Experiments demonstrate that VAD robustly handles watertight and open surfaces, as well as complex non-manifold and non-orientable geometries, while remaining computationally efficient and stable.

Xi Han, Jingwei Zhang, Dimitris Samaras et al.

The neural operator (NO) framework has emerged as a powerful tool for solving partial differential equations (PDEs). Recent NOs are dominated by the Transformer architecture, which offers NOs the capability to capture long-range dependencies in PDE dynamics. However, existing Transformer-based NOs suffer from quadratic complexity, lack geometric rigor, and thus suffer from sub-optimal performance on regular grids. As a remedy, we propose the Geometric Mamba Neural Operator (GeoMaNO) framework, which empowers NOs with Mamba's modeling capability, linear complexity, plus geometric rigor. We evaluate GeoMaNO's performance on multiple standard and popularly employed PDE benchmarks, spanning from Darcy flow problems to Navier-Stokes problems. GeoMaNO improves existing baselines in solution operator approximation by as much as 58.9%.

Jiayi Kong, Chen Zong, Jun Luo et al.

The medial axis, a lower-dimensional shape descriptor, plays an important role in the field of digital geometry processing. Despite its importance, robust computation of the medial axis transform from diverse inputs, especially point clouds with defects, remains a significant challenge. In this paper, we tackle the challenge by proposing a new implicit method that diverges from mainstream explicit medial axis computation techniques. Our key technical insight is the difference between the signed distance field (SDF) and the medial field (MF) of a solid shape is the unsigned distance field (UDF) of the shape's medial axis. This allows for formulating medial axis computation as an implicit reconstruction problem. Utilizing a modified double covering method, we extract the medial axis as the zero level-set of the UDF. Extensive experiments show that our method has enhanced accuracy and robustness in learning compact medial axis transform from thorny meshes and point clouds compared to existing methods.

Jiaze Li, Zhengyu Wen, Luo Zhang et al.

The 3D Gaussian Splatting technique has significantly advanced the construction of radiance fields from multi-view images, enabling real-time rendering. While point-based rasterization effectively reduces computational demands for rendering, it often struggles to accurately reconstruct the geometry of the target object, especially under strong lighting. To address this challenge, we introduce a novel approach that combines octree-based implicit surface representations with Gaussian splatting. Our method consists of four stages. Initially, it reconstructs a signed distance field (SDF) and a radiance field through volume rendering, encoding them in a low-resolution octree. The initial SDF represents the coarse geometry of the target object. Subsequently, it introduces 3D Gaussians as additional degrees of freedom, which are guided by the SDF. In the third stage, the optimized Gaussians further improve the accuracy of the SDF, allowing it to recover finer geometric details compared to the initial SDF obtained in the first stage. Finally, it adopts the refined SDF to further optimize the 3D Gaussians via splatting, eliminating those that contribute little to visual appearance. Experimental results show that our method, which leverages the distribution of 3D Gaussians with SDFs, reconstructs more accurate geometry, particularly in images with specular highlights caused by strong lighting.