arXiv subjects

Hui Huang

Publications and source records attributed to Hui Huang.

At least 235 records · Page 13Linked to original sources

arXiv2020

On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system

We rigorously justify the mean-field limit of a $N$-particle system subject to the Brownian motion and interacting through a Newtonian potential in $\mathbb{R}^3$. Our result leads to a derivation of the Vlasov-Poisson-Fokkker-Planck (VPFP) equation from the microscopic $N$-particle system. More precisely, we show that the maximal distance between the exact microscopic trajectories and trajectories following the the mean-field is bounded by $N^{-\frac{1}{3}+\varepsilon}$ ($\frac{1}{63}\leq\varepsilon<\frac{1}{36}$) for a system with blob size $N^{-δ}$ ($\frac{1}{3}\leqδ<\frac{19}{54}-\frac{2\varepsilon}{3}$) up to a probability $1-N^{-α}$ for any $α>0$. Moreover, we prove the convergence rate between the empirical measure associated to the particle system and the solution of the VPFP equations. The technical novelty of this paper is that our estimates crucially rely on the randomness coming from the initial data and from the Brownian motion.

math.AP↗

arXiv2019

EFANet: Exchangeable Feature Alignment Network for Arbitrary Style Transfer

Style transfer has been an important topic both in computer vision and graphics. Since the seminal work of Gatys et al. first demonstrates the power of stylization through optimization in the deep feature space, quite a few approaches have achieved real-time arbitrary style transfer with straightforward statistic matching techniques. In this work, our key observation is that only considering features in the input style image for the global deep feature statistic matching or local patch swap may not always ensure a satisfactory style transfer; see e.g., Figure 1. Instead, we propose a novel transfer framework, EFANet, that aims to jointly analyze and better align exchangeable features extracted from content and style image pair. In this way, the style features from the style image seek for the best compatibility with the content information in the content image, leading to more structured stylization results. In addition, a new whitening loss is developed for purifying the computed content features and better fusion with styles in feature space. Qualitative and quantitative experiments demonstrate the advantages of our approach.

cs.CV↗

arXiv2019

SAGNet:Structure-aware Generative Network for 3D-Shape Modeling

We present SAGNet, a structure-aware generative model for 3D shapes. Given a set of segmented objects of a certain class, the geometry of their parts and the pairwise relationships between them (the structure) are jointly learned and embedded in a latent space by an autoencoder. The encoder intertwines the geometry and structure features into a single latent code, while the decoder disentangles the features and reconstructs the geometry and structure of the 3D model. Our autoencoder consists of two branches, one for the structure and one for the geometry. The key idea is that during the analysis, the two branches exchange information between them, thereby learning the dependencies between structure and geometry and encoding two augmented features, which are then fused into a single latent code. This explicit intertwining of information enables separately controlling the geometry and the structure of the generated models. We evaluate the performance of our method and conduct an ablation study. We explicitly show that encoding of shapes accounts for both similarities in structure and geometry. A variety of quality results generated by SAGNet are presented. The data and code are at https://github.com/zhijieW-94/SAGNet.

cs.GR↗

arXiv2019

ETNet: Error Transition Network for Arbitrary Style Transfer

Numerous valuable efforts have been devoted to achieving arbitrary style transfer since the seminal work of Gatys et al. However, existing state-of-the-art approaches often generate insufficiently stylized results under challenging cases. We believe a fundamental reason is that these approaches try to generate the stylized result in a single shot and hence fail to fully satisfy the constraints on semantic structures in the content images and style patterns in the style images. Inspired by the works on error-correction, instead, we propose a self-correcting model to predict what is wrong with the current stylization and refine it accordingly in an iterative manner. For each refinement, we transit the error features across both the spatial and scale domain and invert the processed features into a residual image, with a network we call Error Transition Network (ETNet). The proposed model improves over the state-of-the-art methods with better semantic structures and more adaptive style pattern details. Various qualitative and quantitative experiments show that the key concept of both progressive strategy and error-correction leads to better results. Code and models are available at https://github.com/zhijieW94/ETNet.

cs.CV↗

arXiv2019

LOGAN: Unpaired Shape Transform in Latent Overcomplete Space

We introduce LOGAN, a deep neural network aimed at learning general-purpose shape transforms from unpaired domains. The network is trained on two sets of shapes, e.g., tables and chairs, while there is neither a pairing between shapes from the domains as supervision nor any point-wise correspondence between any shapes. Once trained, LOGAN takes a shape from one domain and transforms it into the other. Our network consists of an autoencoder to encode shapes from the two input domains into a common latent space, where the latent codes concatenate multi-scale shape features, resulting in an overcomplete representation. The translator is based on a generative adversarial network (GAN), operating in the latent space, where an adversarial loss enforces cross-domain translation while a feature preservation loss ensures that the right shape features are preserved for a natural shape transform. We conduct ablation studies to validate each of our key network designs and demonstrate superior capabilities in unpaired shape transforms on a variety of examples over baselines and state-of-the-art approaches. We show that LOGAN is able to learn what shape features to preserve during shape translation, either local or non-local, whether content or style, depending solely on the input domains for training.

cs.CV↗

arXiv2019

Patch-based Progressive 3D Point Set Upsampling

We present a detail-driven deep neural network for point set upsampling. A high-resolution point set is essential for point-based rendering and surface reconstruction. Inspired by the recent success of neural image super-resolution techniques, we progressively train a cascade of patch-based upsampling networks on different levels of detail end-to-end. We propose a series of architectural design contributions that lead to a substantial performance boost. The effect of each technical contribution is demonstrated in an ablation study. Qualitative and quantitative experiments show that our method significantly outperforms the state-of-the-art learning-based and optimazation-based approaches, both in terms of handling low-resolution inputs and revealing high-fidelity details.

cs.CV↗

arXiv2019

Bias detection of $PM_{2.5}$ monitor readings using hidden dynamic geostatistical calibration model

Accurate and reliable data stream plays an important role in air quality assessment. Air pollution data collected from monitoring networks, however, could be biased due to instrumental error or other interventions, which covers up the real pollution status and misleads policy making. In this study, motivated by the needs for objective bias detection, we propose a hidden dynamic geostatistical calibration (HDGC) model to automatically identify monitoring stations with constantly biased readings. The HDGC model is a two-level hierarchical model whose parameters are estimated through an efficient Expectation-Maximization algorithm. Effectiveness of the proposed model is demonstrated by a simple numerical study. Our method is applied to hourly $PM_{2.5}$ data from 36 stations in Hebei province, China, over the period from March 2014 to February 2017. Significantly abnormal readings are detected from stations in two cities.

stat.AP↗

arXiv2018

Learning interacting particle systems: diffusion parameter estimation for aggregation equations

In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation and Brownian diffusion. Specifically, we construct an estimator $\widehatν$ with partial observed data to approximate the diffusion parameter $ν$, and the estimation error is achieved. Furthermore, we extend this result to general aggregation equations with a bounded Lipschitz interaction field.

math.AP↗

arXiv2018

Propagation of chaos for the Keller-Segel equation over bounded domains

In this paper we rigorously justify the propagation of chaos for the parabolic-elliptic Keller-Segel equation over bounded convex domains. The boundary condition under consideration is the no-flux condition. As intermediate steps, we establish the well-posedness of the associated stochastic equation as well as the well-posedness of the Keller-Segel equation for bounded weak solutions.

math.AP↗

arXiv2018

Zero-diffusion Limit for Aggregation Equations over Bounded Domains

We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in [44], our approach is different and relies on a coupling method connecting PDEs with their underlying SDEs. Moreover, our result relaxes the regularity assumptions on the interaction and external potentials and improves the convergence rate (in terms of the diffusion coefficient). The particular rate we derive is shown to be consistent with numerical computations.

math.AP↗

arXiv2018

Neural Material: Learning Elastic Constitutive Material and Damping Models from Sparse Data

The accuracy and fidelity of deformation simulations are highly dependent upon the underlying constitutive material model. Commonly used linear or nonlinear constitutive material models only cover a tiny part of possible material behavior. In this work we propose a unified framework for modeling deformable material. The key idea is to use a neural network to correct a nominal model of the elastic and damping properties of the object. The neural network encapsulates a complex function that is hard to explicitly model. It injects force corrections that help the forward simulation to more accurately predict the true behavior of a given soft object, which includes non-linear elastic forces and damping. Attempting to satisfy the requirement from real material interference and animation design scenarios, we learn material models from examples of dynamic behavior of a deformable object's surface. The challenge is that such data is sparse as it is consistently given only on part of the surface. Sparse reduced space-time optimization is employed to gradually generate increasingly accurate training data, which further refines and enhances the neural network. We evaluate our choice of network architecture and show evidence that the modest amount of training data we use is suitable for the problem tackled. Our method is demonstrated with a set of synthetic examples.

cs.GR↗

arXiv2018

Specular-to-Diffuse Translation for Multi-View Reconstruction

Most multi-view 3D reconstruction algorithms, especially when shape-from-shading cues are used, assume that object appearance is predominantly diffuse. To alleviate this restriction, we introduce S2Dnet, a generative adversarial network for transferring multiple views of objects with specular reflection into diffuse ones, so that multi-view reconstruction methods can be applied more effectively. Our network extends unsupervised image-to-image translation to multi-view "specular to diffuse" translation. To preserve object appearance across multiple views, we introduce a Multi-View Coherence loss (MVC) that evaluates the similarity and faithfulness of local patches after the view-transformation. Our MVC loss ensures that the similarity of local correspondences among multi-view images is preserved under the image-to-image translation. As a result, our network yields significantly better results than several single-view baseline techniques. In addition, we carefully design and generate a large synthetic training data set using physically-based rendering. During testing, our network takes only the raw glossy images as input, without extra information such as segmentation masks or lighting estimation. Results demonstrate that multi-view reconstruction can be significantly improved using the images filtered by our network. We also show promising performance on real world training and testing data.

cs.CV↗

arXiv2018

D-finite Numbers

D-finite functions and P-recursive sequences are defined in terms of linear differential and recurrence equations with polynomial coefficients. In this paper, we introduce a class of numbers closely related to D-finite functions and P-recursive sequences. It consists of the limits of convergent P-recursive sequences. Typically, this class contains many well-known mathematical constants in addition to the algebraic numbers. Our definition of the class of D-finite numbers depends on two subrings of the field of complex numbers. We investigate how different choices of these two subrings affect the class. Moreover, we show that D-finite numbers are essentially limits of D-finite functions at the point one, and evaluating D-finite functions at non-singular algebraic points typically yields D-finite numbers. This result makes it easier to recognize certain numbers to be D-finite.

math.NT↗

arXiv2018

Object-Aware Guidance for Autonomous Scene Reconstruction

To carry out autonomous 3D scanning and online reconstruction of unknown indoor scenes, one has to find a balance between global exploration of the entire scene and local scanning of the objects within it. In this work, we propose a novel approach, which provides object-aware guidance for autoscanning, for exploring, reconstructing, and understanding an unknown scene within one navigation pass. Our approach interleaves between object analysis to identify the next best object (NBO) for global exploration, and object-aware information gain analysis to plan the next best view (NBV) for local scanning. First, an objectness-based segmentation method is introduced to extract semantic objects from the current scene surface via a multi-class graph cuts minimization. Then, an object of interest (OOI) is identified as the NBO which the robot aims to visit and scan. The robot then conducts fine scanning on the OOI with views determined by the NBV strategy. When the OOI is recognized as a full object, it can be replaced by its most similar 3D model in a shape database. The algorithm iterates until all of the objects are recognized and reconstructed in the scene. Various experiments and comparisons have shown the feasibility of our proposed approach.

cs.GR↗

arXiv2018

P2P-NET: Bidirectional Point Displacement Net for Shape Transform

We introduce P2P-NET, a general-purpose deep neural network which learns geometric transformations between point-based shape representations from two domains, e.g., meso-skeletons and surfaces, partial and complete scans, etc. The architecture of the P2P-NET is that of a bi-directional point displacement network, which transforms a source point set to a target point set with the same cardinality, and vice versa, by applying point-wise displacement vectors learned from data. P2P-NET is trained on paired shapes from the source and target domains, but without relying on point-to-point correspondences between the source and target point sets. The training loss combines two uni-directional geometric losses, each enforcing a shape-wise similarity between the predicted and the target point sets, and a cross-regularization term to encourage consistency between displacement vectors going in opposite directions. We develop and present several different applications enabled by our general-purpose bidirectional P2P-NET to highlight the effectiveness, versatility, and potential of our network in solving a variety of point-based shape transformation problems.

cs.GR↗

arXiv2018

Full 3D Reconstruction of Transparent Objects

Numerous techniques have been proposed for reconstructing 3D models for opaque objects in past decades. However, none of them can be directly applied to transparent objects. This paper presents a fully automatic approach for reconstructing complete 3D shapes of transparent objects. Through positioning an object on a turntable, its silhouettes and light refraction paths under different viewing directions are captured. Then, starting from an initial rough model generated from space carving, our algorithm progressively optimizes the model under three constraints: surface and refraction normal consistency, surface projection and silhouette consistency, and surface smoothness. Experimental results on both synthetic and real objects demonstrate that our method can successfully recover the complex shapes of transparent objects and faithfully reproduce their light refraction properties.

cs.GR↗

arXiv2018

Non-Stationary Texture Synthesis by Adversarial Expansion

The real world exhibits an abundance of non-stationary textures. Examples include textures with large-scale structures, as well as spatially variant and inhomogeneous textures. While existing example-based texture synthesis methods can cope well with stationary textures, non-stationary textures still pose a considerable challenge, which remains unresolved. In this paper, we propose a new approach for example-based non-stationary texture synthesis. Our approach uses a generative adversarial network (GAN), trained to double the spatial extent of texture blocks extracted from a specific texture exemplar. Once trained, the fully convolutional generator is able to expand the size of the entire exemplar, as well as of any of its sub-blocks. We demonstrate that this conceptually simple approach is highly effective for capturing large-scale structures, as well as other non-stationary attributes of the input exemplar. As a result, it can cope with challenging textures, which, to our knowledge, no other existing method can handle.

cs.GR↗

arXiv2017

Definite Sums of Hypergeometric Terms and Limits of P-Recursive Sequences

The ubiquity of the class of D-finite functions and P-recursive sequences in symbolic computation is widely recognized. In this thesis, the presented work consists of two parts related to this class. In the first part, we generalize the reduction-based creative telescoping algorithms to the hypergeometric setting, which allows to deal with definite sums of hypergeometric terms more quickly. We first modify the Abramov-Petkovsek reduction, and then design a new algorithm to compute minimal telescopers for bivariate hypergeometric terms based on the modified reduction. This new algorithm can avoid the costly computation of certificates, and outperforms the classical Zeilberger algorithm no matter whether certificates are computed or not according to the computational experiments. Moreover, we also derive order bounds for minimal telescopers. These bounds are sometimes better, and never worse than the known ones. In the second part of the thesis, we study the class of D-finite numbers. It consists of the limits of convergent P-recursive sequences. Typically, this class contains many well-known mathematical constants in addition to the algebraic numbers. Our definition of the class of D-finite numbers depends on two subrings of the field of complex numbers. We investigate how different choices of these two subrings affect the class. Moreover, we show that D-finite numbers over the Gaussian rational field are essentially the same as the values of D-finite functions at non-singular algebraic number arguments (so-called the regular holonomic constants). This result makes it easier to recognize certain numbers as belonging to this class.

cs.SC↗