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Dezhong Chen

Publications and source records attributed to Dezhong Chen.

9 recordsLinked to original sources

Synthetic Aperture Radar Image Change Detection Based on Global Dynamic Context-Aware Network

Convolutional neural networks (CNNs) have been extensively and successfully applied to the task of synthetic aperture radar (SAR) image change detection. However, conventional convolutional layers are inherently limited by their local receptive fields, which mainly capture spatially localized patterns while neglecting the global context that is often crucial for accurately distinguishing subtle or large-scale changes in SAR imagery. To address these limitations, we propose a novel Global Dynamic Context-Aware Network (GDNet) specifically tailored for SAR image change detection. At the core of our approach lies a novel global dynamic convolution module, which adaptively modulates convolution kernel weights according to the global semantic information extracted from the input features. By dynamically incorporating long-range dependencies, this mechanism enables the network to integrate both local detail and global context, thus improving its ability to detect diverse change patterns. In addition, we introduce a carefully designed two-stage Mixup strategy for model training. Unlike conventional single-stage Mixup, our two-stage design generates more diverse and informative training samples, effectively regularizing the model and yielding more stable and reliable classification results even under limited data scenarios. Extensive experiments on three SAR datasets demonstrate the superiority of the proposed GDNet compared to other state-of-the-art methods. These findings highlight the potential of global dynamic modeling and advanced data augmentation strategies for advancing SAR image interpretation. Source codes are available at \url{https://github.com/oucailab/GDNet}.

cs.CV

Singular Ricci solitons and their stability under the Ricci flow

We introduce certain spherically symmetric singular Ricci solitons and study their stability under the Ricci flow from a dynamical PDE point of view. The solitons in question exist for all dimensions $n+1\ge 3$, and all have a point singularity where the curvature blows up; their evolution under the Ricci flow is in sharp contrast to the evolution of their smooth counterparts. In particular, the family of diffeomorphisms associated with the Ricci flow "pushes away" from the singularity causing the evolving soliton to open up immediately becoming an incomplete (but non-singular) metric. In the second part of this paper we study the local-in time stability of this dynamical evolution, under spherically symmetric perturbations of the initial soliton metric. We prove a local well-posedness result for the Ricci flow near the singular initial data, which in particular implies that the "opening up" of the singularity persists for the perturbations also.

math.AP

Examples of Einstein manifolds in odd dimensions

We construct Einstein metrics of non-positive scalar curvature on certain solid torus bundles over a Fano Kahler-Einstein manifold. We show, among other things, that the negative Einstein metrics are conformally compact, and the Ricci-flat metrics have slower-than-Euclidean volume growth and quadratic curvature decay. Also we construct positive Einstein metrics on certain 3-sphere bundles over a Fano Kahler-Einstein manifold. We classify the homeomorphism and diffeomorphism types of the total spaces when the base is the complex projective plane.

math.DG

Construction of Conformally Compact Einstein Manifolds

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kahler-Einstein manifolds. We compute the associated conformal invariants, i.e., the renormalized volume in even dimensions and the conformal anomaly in odd dimensions. As a by-product, we obtain some Riemannian products with vanishing Q-curvature.

math.DG

Some remarks on sub-elliptic equations

In this paper, we consider the principal eigenvalue problem for Hormander's laplacian on $R^n$. We also study a related semi-linear sub-elliptic equation in the whole $R^n$ and prove that under a suitable condition, we have infinite many positive solutions of the problem.

math.AP

Remarks on non-compact complete Ricci expanding solitons

In this paper, we study gradient Ricci expanding solitons $(X,g)$ satisfying $$ Rc=cg+D^2f, $$ where $Rc$ is the Ricci curvature, $c<0$ is a constant, and $D^2f$ is the Hessian of the potential function $f$ on $X$. We show that for a gradient expanding soliton $(X,g)$ with non-negative Ricci curvature, the scalar curvature $R$ has at least one maximum point on $X$, which is the only minimum point of the potential function $f$. Furthermore, $R>0$ on $X$ unless $(X,g)$ is Ricci flat. We also show that there is exponentially decay for scalar curvature for $ε$-pinched complete non-compact expanding solitons.

math.DG

Interior Gradient Bound For Minimal Graphs in a Product Manifold

Let $(M, g)$ be an $n$-dimensional complete Riemannian manifold with $Ric(M)\geq-(n-1)Q$, where $Q\geq0$ is a constant. We obtain an interior gradient bound for minimal graphs in $M\times R$ under some technical assumptions. For details, see Theorem 2.

math.DG

Examples for Cross Curvature Flow on 3-Manifolds

Recently, B.Chow and R.S.Hamilton introduced the cross curvature flow on 3-manifolds. In this paper, we analyze two interesting examples for this new flow. One is on a square torus bundle over a circle, and the other is on a $S^{2}$ bundle over a circle. We show that the global flow exist in both cases. But on the former the flow diverges at time infinity, and on the latter the flow converges at time infinity.

math.DG

Curve Shortening Flow in a Riemannian Manifold

In this paper, we systemally study the long time behavior of the curve shortening flow in a closed or non-compact complete locally Riemannian symmetric manifold. Assume that we have a global flow. Then we can exhibit a a limit for the global behavior of the flow. In particular, we show the following results. 1). Let $\mathbf{M}$ be a compact locally symmetric space. If the curve shortening flow exists for infinite time, and $$ \lim_{t\to\infty}L(γ_{t})>0, $$ then for every $n>0$, $$ \lim_{t\to \infty}\sup(|\frac{D^{n}T}{\partial s^{n}}|)=0. $$ In particular, the limiting curve exists and is a closed geodesic in $\mathbf{M}$. 2). For $γ_{0}$ is a ramp, we have a global flow and the flow converges to a geodesic in $C^{\infty}$ norm.

math.DG