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Bingyuan Liu

Publications and source records attributed to Bingyuan Liu.

29 records · Page 2Linked to original sources
arXiv2020

Furnishing Your Room by What You See: An End-to-End Furniture Set Retrieval Framework with Rich Annotated Benchmark Dataset

Understanding interior scenes has attracted enormous interest in computer vision community. However, few works focus on the understanding of furniture within the scenes and a large-scale dataset is also lacked to advance the field. In this paper, we first fill the gap by presenting DeepFurniture, a richly annotated large indoor scene dataset, including 24k indoor images, 170k furniture instances and 20k unique furniture identities. On the dataset, we introduce a new benchmark, named furniture set retrieval. Given an indoor photo as input, the task requires to detect all the furniture instances and search a matched set of furniture identities. To address this challenging task, we propose a feature and context embedding based framework. It contains 3 major contributions: (1) An improved Mask-RCNN model with an additional mask-based classifier is introduced for better utilizing the mask information to relieve the occlusion problems in furniture detection context. (2) A multi-task style Siamese network is proposed to train the feature embedding model for retrieval, which is composed of a classification subnet supervised by self-clustered pseudo attributes and a verification subnet to estimate whether the input pair is matched. (3) In order to model the relationship of the furniture entities in an interior design, a context embedding model is employed to re-rank the retrieval results. Extensive experiments demonstrate the effectiveness of each module and the overall system.

cs.CV↗
arXiv2019

The $\bar{\partial}$-Neumann operator with the Sobolev norm of integer orders

Let $Ω\subset\mathbb{C}^m$ be a bounded pseudoconvex domain with smooth boundary. For each $k\in\mathbb{N}$, we give a sufficient condition to estimate the $\bar\partial$-Neumann operator in the Sobolev space $W^k(Ω)$. The key feature of our results is a precise formula for $k$ in terms of the geometry of the boundary of $Ω$.

math.CV↗
arXiv2017

Geometric Analysis on the Diederich-Fornæss Index

We derive a sufficient condition on a bounded pseudoconvex domain $Ω\subset\mathbb{C}^2$ with smooth boundary such that $-(-ρ)^η$ is plurisubharmonic on $Ω$ for $η>0$ arbitrarily close to $1$ (the supremum of $η$ is called Diederich-Fornæss index, see Definition (df)). This condition (see Theorem prop) extends a theorem of Fornæss and Herbig in 2007 and only requires restriction on Levi-flat sets of the boundary $\partialΩ$. Since the condition is on Levi-flat sets, it contains more geometric information. As an application of this new condition, we discuss how the geometry of the Levi-flat sets affects the Diederich-Fornæss index. Among other results, we show that the Diederich-Fornæss index is $1$ if only the Levi-flat sets form a real curve transversal to the holomorphic tangent vector fields on $\partialΩ$ (see Theorem [main]). We also give a specific example (see Theorem [example]) on the bounded pseudoconvex domains which verify the application but are neither of finite type nor admit a plurisubharmonic defining function on the boundary.

math.CV↗
arXiv2017

The Diederich-Fornæss index I: for domains of non-trivial index

We study bounded pseudoconvex domains in complex Euclidean space. We define an index associated to the boundary and show this new index is equivalent to the Diederich-Fornæss index defined in 1977. This connects the Diederich-Fornæss index to boundary conditions and refines the Levi pseudoconvexity. We also prove the $β$-worm domain is of index $π/{(2β)}$. It is the first time that a precise non-trivial Diederich-Fornæss index in Euclidean spaces is obtained. This finding also indicates that the Diederich-Fornæss index is a continuum in $(0,1]$, not a discrete set. The ideas of proof involve a new complex geometric analytic technique on the boundary and detailed estimates on differential equations.

math.CV↗
arXiv2017

The Diederich--Fornæss index II: for domains of trivial index

We study bounded pseudoconvex domains in complex Euclidean spaces. We find analytical necessary conditions and geometric sufficient conditions for a domain being of trivial Diederich--Fornæss index (i.e. the index equals to 1). We also connect a differential equation to the index. This reveals how a topological condition affects the solution of the associated differential equation and consequently obstructs the index being trivial. The proofs relies on a new method of study of the complex geometry of the boundary. The method was motivated by geometric analysis of Riemannian manifolds. We also generalize our main theorems under the context of de Rham cohomology.

math.CV↗
arXiv2017

The intrinsic geometry on bounded pseudoconvex domains

The Diederich--Fornæss index has been introduced since 1977 to classify bounded pseudoconvex domains. In this article, we derive several intrinsic, geometric conditions on boundary of domains for arbitrary indexes. Many results, in the past, by various mathematicians estimated the index by assuming some properties of domains. Our motivation of this paper is, the other way around, to look for how the index effects properties and shapes of domains. Especially, we look for a necessary condition of all bounded pseudoconvex domains $Ω\subset\mathbb{C}^2$ with the Diederich--Fornæss index 1. We also show that, when the Levi-flat set of $\partialΩ$ is a closed Riemann surface, then the necessary condition can be simplified.

math.CV↗
arXiv2016

The limit set for discrete complex hyperbolic groups

Given a discrete subgroup $Γ$ of $PU(1,n)$ it acts by isometries on the unit complex ball $\Bbb{H}^n_{\Bbb{C}}$, in this setting a lot of work has been done in order to understand the action of the group. However when we look at the action of $Γ$ on all of $ \Bbb{P}^n_{\Bbb{C}}$ little or nothing is known, in this paper study the action in the whole projective space and we are able to show that its equicontinuity agree with its Kulkarni discontuity set. Morever, in the non-elementary case, this set turns out to be the largest open set on which the group acts properly and discontinuously and can be described as the complement of the union of all complex projective hyperplanes in $ \Bbb{P}^n_{\Bbb{C}}$ which are tangent to $\partial \Bbb{H}^n_{\Bbb{C}}$ at points in the Chen-Greenberg limit set $Λ_{CG}(Γ)$.

math.DS↗
arXiv2015

Two applications of the Schwarz lemma

The Schwarz lemmas are well-known characterizations for holomorphic maps and we exhibit two examples of their applications. For a sequence family of biholomorphisms $f_j$, it is useful to determine the location of $f_j(q)$ for a fixed point $q$ in source manifolds (see Proposition \ref{2.5}). With it, we extend the Fornaess-Stout's theorem of \citep{FS77} in monotone unions of balls to ellipsoids in Section \ref{sec2}. In Section \ref{sec3}, we discuss the curvature bounds of complete Kähler metric on $\rtimes$ domains defined in \citep{Liu004} with an idea of \citep{Ya76}.

math.CV↗
arXiv2014

Analysis of orbit accumulation points and the Greene-Krantz conjecture

In $\mathbb{C}^2$, we classify the domains for which $\rm Aut(Ω)$ is noncompact and describe these domains by their defining functions. This note is based on the technique of the scaling method introduced by Frankel \cite{Fr86} and Kim \cite{Ki90}. One feature of this article is that we are able to analyze the defining functions of infinite type boundary. As a corollary, we also prove a result that under some conditions, $\rm Aut(Ω)$ contains $\mathbb{R}$, which is an extension of \cite{Fr86}.

math.CV↗
arXiv2014

Finite type domains with hyperbolic orbit accumulation points

In this paper, finite type domains with hyperbolic orbit accumulation points are studied. We prove, in case of $\mathbb{C}^2$, it has to be a (global) pseudoconvex domain, after an assumption of boundary regularity. Moreover, one of the applications will realize the classification of domains within this class, precisely the domain is biholomorphic to one of the ellipsoids $\lbrace (z, w): | z|^{2m}+| w|^2<1, m\in\mathbb{Z}^+\rbrace$. This application generalizes \cite{BP98} in which the boundary is assumed to be real analytic for the case of hyperbolic orbit accumulation points.

math.CV↗