arXiv subjects

Fei Hou

Publications and source records attributed to Fei Hou.

At least 37 records · Page 2Linked to original sources

arXiv2025

Global existence for 2-D wave maps equation in exterior domains

In the paper [H. Kubo, Global existence for exterior problems of semilinear wave equations with the null condition in 2D, Evol. Equ. Control Theory 2 (2013), no. 2, 319-335], for the 2-D semilinear wave equation system $(\partial_t^2-Δ)v^I=Q^I(\partial_tv, \nabla_xv)$ ($1\le I\le M$) in the exterior domain with Dirichlet boundary condition, it is shown that the small data smooth solution $v=(v^1, \cdot\cdot\cdot, v^M)$ exists globally when the cubic nonlinearities $Q^I(\partial_tv, \nabla_xv)=O(|\partial_tv|^3+|\nabla_xv|^3)$ satisfy the null condition. We now focus on the global Dirichelt boundary value problem of 2-D wave maps equation with the form $\Box u^I=\sum_{J,K,L=1}^MC_{IJKL}u^JQ_0(u^K,u^L)$ $(1\le I\le M)$ and $Q_0(f,g)=\partial_tf\partial_tg-\sum_{j=1}^2\partial_jf\partial_jg$ in exterior domain. By establishing some crucial classes of pointwise spacetime decay estimates for the small data solution $u=(u^1, \cdot\cdot\cdot, u^M)$ and its derivatives, the global existence of $u$ is shown.

math.AP↗

arXiv2025

From Transparent to Opaque: Rethinking Neural Implicit Surfaces with $α$-NeuS

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.

cs.CV↗

arXiv2024

Global existence and scattering of small data smooth solutions to quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$, II

In our previous paper [Fei Hou, Fei Tao, Huicheng Yin, Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$, Preprint (2024), arXiv:2405.03242], for the $Q_0$-type quadratic nonlinearities, we have shown the global well-posedness and scattering properties of small data smooth solutions to the quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$. In this paper, we start to solve the global existence problem for the remaining $Q_{αβ}$-type nonlinearities. By combining these results, we have established the global well-posedness of small solutions on $\mathbb{R}^2\times\mathbb{T}$ for the general 3-D quadratically quasilinear wave systems when the related 2-D null conditions are fulfilled.

math.AP↗

arXiv2024

Diffusing Winding Gradients (DWG): A Parallel and Scalable Method for 3D Reconstruction from Unoriented Point Clouds

This paper presents a new method, Diffusing Winding Gradients (DWG), for reconstructing watertight 3D surfaces from unoriented point clouds. Our method exploits the alignment between the gradients of the generalized winding number (GWN) field and globally consistent normals to orient points effectively. Starting with an unoriented point cloud, DWG initially assigns a random normal to each point. It computes the corresponding GWN field and extract a level set whose iso-value is the average GWN values across all input points. The gradients of this level set are then utilized to update the point normals. This cycle of recomputing the GWN field and updating point normals is repeated until the GWN level sets stabilize and their gradients cease to change. Unlike conventional methods, our method does not rely on solving linear systems or optimizing objective functions, which simplifies its implementation and enhances its suitability for efficient parallel execution. Experimental results demonstrate that our method significantly outperforms existing methods in terms of runtime performance. For large-scale models with 10 to 20 million points, our CUDA implementation on an NVIDIA GTX 4090 GPU achieves speeds 30-120 times faster than iPSR, the leading sequential method, tested on a high-end PC with an Intel i9 CPU. Additionally, by employing a screened variant of GWN, DWG demonstrates enhanced robustness against noise and outliers, and proves effective for models with thin structures and real-world inputs with overlapping and misaligned scans. For source code and more details, visit our project webpage: https://dwgtech.github.io/.

cs.GR↗

arXiv2024

DCUDF2: Improving Efficiency and Accuracy in Extracting Zero Level Sets from Unsigned Distance Fields

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.

cs.CV↗

arXiv2024

UGrid: An Efficient-And-Rigorous Neural Multigrid Solver for Linear PDEs

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.

math.NA↗

arXiv2024

Parameterization-driven Neural Surface Reconstruction for Object-oriented Editing in Neural Rendering

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.

cs.CV↗

arXiv2024

GS-Octree: Octree-based 3D Gaussian Splatting for Robust Object-level 3D Reconstruction Under Strong Lighting

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.

cs.CV↗

arXiv2024

Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$

In this paper, we are concerned with the global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on the product space $\mathbb{R}^2\times\mathbb{T}$. These quasilinear wave systems include 3D irrotational potential flow equation of Chaplygin gases, 3D relativistic membrane equation, some 3D quasilinear wave equations which come from the corresponding Lagrangian functionals as perturbations of the Lagrangian densities of linear waves, and nonlinear wave maps system. Through looking for some suitable transformations of unknown functions, the nonlinear wave system can be reduced into a more tractable form. Subsequently, by applying the vector-field method together with the ghost weight technique as well as deriving some kinds of weighted $L^\infty-L^\infty$ and $L^\infty-L^2$ estimates of solution $w$ to the 2D linear wave equation $\Box w=f(t,x)$, the global existence and scattering of small data solutions are established.

math.AP↗

arXiv2024

2S-UDF: A Novel Two-stage UDF Learning Method for Robust Non-watertight Model Reconstruction from Multi-view Images

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/.

cs.CV↗

arXiv2024

Topology-Aware Latent Diffusion for 3D Shape Generation

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.

cs.CV↗

arXiv2024

Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering

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.

cs.CV↗

arXiv2023

Photoconductive Effects in Single Crystals of BaZrS$_3$

Chalcogenide perovskites, such as BaZrS$_3$, are emerging semiconductors with potential for high photovoltaic power conversion efficiency. The role of defects in the efficiency of the generation and collection of photo-excited carriers has not been experimentally investigated extensively. We study the effect of processing-induced defects on the photoconductive properties of single crystals of BaZrS$_3$. We achieved ohmic contacts to single crystals of BaZrS$_3$ and observed positive surface photovoltage, which is typically observed in p-type semiconductors. However, mechanical polishing of BaZrS$_3$ to remove the surface oxide leads to dense deformation grain boundaries and leads to trap-dominated photoconductive response. In comparison, ohmic contacts achieved in cleaved crystals leave fewer deformation defects and greatly improve optoelectronic properties. Defect-controlled crystal growth and contact fabrication are potentially limiting factors for achieving high photon-to-excited electron conversion efficiency in BaZrS$_3$.

physics.app-ph↗

arXiv2023

Almost global solutions of 1D nonlinear Klein-Gordon equations with small weakly decaying initial data

It has been known that if the initial data decay sufficiently fast at space infinity, then 1D Klein-Gordon equations with quadratic nonlinearity admit classical solutions up to time $e^{C/ε^2}$ while $e^{C/ε^2}$ is also the upper bound of the lifespan, where $C>0$ is some suitable constant and $ε>0$ is the size of the initial data. In this paper, we will focus on the 1D nonlinear Klein-Gordon equations with weakly decaying initial data. It is shown that if the $H^s$-Sobolev norm with $(1+|x|)^{1/2+}$ weight of the initial data is small, then the almost global solutions exist; if the initial $H^s$-Sobolev norm with $(1+|x|)^{1/2}$ weight is small, then for any $M>0$, the solutions exist on $[0,ε^{-M}]$. Our proof is based on the dispersive estimate with a suitable $Z$-norm and a delicate analysis on the phase function.

math.AP↗

arXiv2023

Improved Real-time Image Smoothing with Weak Structures Preserved and High-contrast Details Removed

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.

cs.CV↗

arXiv2023

The partial null conditions and global smooth solutions of the nonlinear wave equations on $\mathbb{R}^d\times\mathbb{T}$ with $d=2,3$

In this paper, we investigate the fully nonlinear wave equations on the product space $\mathbb{R}^3\times\mathbb{T}$ with quadratic nonlinearities and on $\mathbb{R}^2\times\mathbb{T}$ with cubic nonlinearities, respectively. It is shown that for the small initial data satisfying some space-decay rates at infinity, these nonlinear equations admit global smooth solutions when the corresponding partial null conditions hold and while have almost global smooth solutions when the partial null conditions are violated. Our proof relies on the Fourier mode decomposition of the solutions with respect to the periodic direction, the efficient combinations of time-decay estimates for the solutions to the linear wave equations and the linear Klein-Gordon equations, and the global weighted energy estimates. In addition, an interesting auxiliary energy is introduced. As a byproduct, our results can be applied to the 4D irrotational compressible Euler equations of polytropic gases or Chaplygin gases on $\mathbb{R}^3\times\mathbb{T}$, the 3D relativistic membrane equation and the 3D nonlinear membrane equation on $\mathbb{R}^2\times\mathbb{T}$.

math.AP↗

arXiv2023

Long time solutions of quasilinear Klein-Gordon equations with small weakly decaying initial data

It is well known that for the quasilinear Klein-Gordon equation with quadratic nonlinearity and sufficiently decaying small initial data, there exists a global smooth solution if the space dimensions $d\geq2$. When the initial data are of size $\varepsilon>0$ in the Sobolev space, for the semilinear Klein-Gordon equation satisfying the null condition, the authors in the article (J.-M. Delort, Daoyuan Fang, Almost global existence for solutions of semilinear Klein-Gordon equations with small weakly decaying Cauchy data, Comm. Partial Differential Equations 25 (2000), no. 11-12, 2119--2169) prove that the solution exists in time $[0,T_\varepsilon)$ with $T_\varepsilon\ge Ce^{C\varepsilon^{-μ}}$ ($μ=1$ if $d\ge3$, $μ=2/3$ if $d=2$). In the present paper, we will focus on the general quasilinear Klein-Gordon equation without the null condition and further show that the existence time of the solution can be improved to $T_\varepsilon=+\infty$ if $d\geq3$ and $T_\varepsilon\ge e^{C\varepsilon^{-2}}$ if $d=2$. In addition, for $d=2$ and any fixed number $α>0$, if the weighted $L^2$ norm of the initial data with the weight $(1+|x|)^α$ is small, then the solution exists globally and scatters to a free solution. The arguments are based on the introduction of a good unknown, the Strichartz estimate, the weighted $L^2$-norm estimate and the resonance analysis.

math.AP↗

arXiv2022

Iterative Poisson Surface Reconstruction (iPSR) for Unoriented Points

Poisson surface reconstruction (PSR) remains a popular technique for reconstructing watertight surfaces from 3D point samples thanks to its efficiency, simplicity, and robustness. Yet, the existing PSR method and subsequent variants work only for oriented points. This paper intends to validate that an improved PSR, called iPSR, can completely eliminate the requirement of point normals and proceed in an iterative manner. In each iteration, iPSR takes as input point samples with normals directly computed from the surface obtained in the preceding iteration, and then generates a new surface with better quality. Extensive quantitative evaluation confirms that the new iPSR algorithm converges in 5-30 iterations even with randomly initialized normals. If initialized with a simple visibility based heuristic, iPSR can further reduce the number of iterations. We conduct comprehensive comparisons with PSR and other powerful implicit-function based methods. Finally, we confirm iPSR's effectiveness and scalability on the AIM@SHAPE dataset and challenging (indoor and outdoor) scenes. Code and data for this paper are at https://github.com/houfei0801/ipsr.

cs.GR↗