相关论文: The consistency principle for a digitization proce…

Surfaces with constant mean curvature (CMC) are critical points of the area with volume constraint. They serve as a mathematical model of surfaces of soap bubbles and tiny liquid drops. CMC surfaces are said to be stable if the second…

We study the minimum membership geometric set cover, i.e., MMGSC problem [SoCG, 2023] in the continuous setting. In this problem, the input consists of a set $P$ of $n$ points in $\mathbb{R}^{2}$, and a geometric object $t$, the goal is to…

Here are two of our main results: Theorem 1. Let X be a normal space with dim X=n and m\geq n+1. Then the space C*(X,R^m) of all bounded maps from X into R^m equipped with the uniform convergence topology contains a dense G_{\delta}-subset…

Building on crucial insights into the determining factors of the visual integrity of an image and the property of deep convolutional neural network (CNN), we have developed the Deep Feature Consistent Deep Image Transformation (DFC-DIT)…

Reconstruction-based methods have demonstrated very promising results for 3D anomaly detection. However, these methods face great challenges in handling high-precision point clouds due to the large scale and complex structure. In this…

We consider the problem of digitalizing Euclidean line segments from $\mathbb{R}^d$ to $\mathbb{Z}^d$. Christ {\em et al.} (DCG, 2012) showed how to construct a set of {\em consistent digital segment} (CDS) for $d=2$: a collection of…

We propose a method for self-supervised image representation learning under the guidance of 3D geometric consistency. Our intuition is that 3D geometric consistency priors such as smooth regions and surface discontinuities may imply…

In this paper we present a new dynamical systems algorithm for clustering in hyperspectral images. The main idea of the algorithm is that data points are \`pushed\' in the direction of increasing density and groups of pixels that end up in…

Despite the remarkable progress facilitated by learning-based stereo-matching algorithms, disparity estimation in low-texture, occluded, and bordered regions still remains a bottleneck that limits the performance. To tackle these…

A central objective of topological data analysis is to identify topologically significant features in data represented as a finite point cloud. We consider the setting where the ambient space of the point sample is a compact Riemannian…

In this paper, we consider a class of constrained clustering problems of points in $\mathbb{R}^{d}$, where $d$ could be rather high. A common feature of these problems is that their optimal clusterings no longer have the locality property…

The replication mechanism resolves some challenges with big data such as data durability, data access, and fault tolerance. Yet, replication itself gives birth to another challenge known as the consistency in distributed systems.…

In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…

We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H…

Learning maps between data samples is fundamental. Applications range from representation learning, image translation and generative modeling, to the estimation of spatial deformations. Such maps relate feature vectors, or map between…

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the…

Normal integration reconstructs 3D surfaces from normal maps obtained e.g. by photometric stereo. These normal maps capture surface details down to the pixel level but require large computational resources for integration at high…

Sweeping is a powerful and versatile method of designing objects. Boundary of volumes (henceforth envelope) obtained by sweeping solids have been extensively investigated in the past, though, obtaining an accurate parametrization of the…

Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. The DM procedure consists in constructing a spectral…

We describe a Monte Carlo procedure for the simulation of dynamically triangulate random surfaces with a boundary (topology of a disk). The algorithm keeps the total number of triangles fixed, while the length of the boundary is allowed to…