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

Identifying the connected components of a graph, apart from being a fundamental problem with countless applications, is a key primitive for many other algorithms. In this paper, we consider this problem in parallel settings. Particularly,…

In the context of 3D mapping, larger and larger point clouds are acquired with LIDAR sensors. The Iterative Closest Point (ICP) algorithm is used to align these point clouds. However, its complexity is directly dependent of the number of…

In this paper we consider online mirror descent (OMD) algorithms, a class of scalable online learning algorithms exploiting data geometric structures through mirror maps. Necessary and sufficient conditions are presented in terms of the…

This paper proposes to generalize linear subdivision schemes to nonlinear subdivision schemes for curve and surface modeling by refining vertex positions together with refinement of unit control normals at the vertices. For each round of…

Metric embeddings into structured spaces, particularly hierarchically well-separated trees (HSTs), are a fundamental tool in the design of online algorithms. In the classical online embedding setting, points arrive sequentially and must be…

Establishing point-to-point correspondences across multiple 3D shapes is a fundamental problem in computer vision and graphics. In this paper, we introduce DcMatch, a novel unsupervised learning framework for non-rigid multi-shape matching.…

The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement, then by an advanced study launched by the Direction de la Recherche et des Etudes Technologiques in France in…

This paper presents some applications using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain decomposition…

Our concern is the digitalization of line segments in two dimensions as considered by Chun et al.[Discrete Comput. Geom., 2009] and Christ et al.[Discrete Comput. Geom., 2012]. The key property that differentiates the research of Chun et…

This paper deals with computing topological invariants such as connected components, boundary surface genus, and homology groups. For each input data set, we have designed or implemented algorithms to calculate connected components,…

Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…

The constraint of neighborhood consistency or local consistency is widely used for robust image matching. In this paper, we focus on learning neighborhood topology consistent descriptors (TCDesc), while former works of learning descriptors,…

Dimensionality reduction techniques are widely used for visualizing high-dimensional data in two dimensions. Existing methods are typically designed to preserve either local (e.g., $t$-SNE, UMAP) or global (e.g., MDS, PCA) structure of the…

The first main result is a topological rigidity theorem for complete immersed hypersurfaces of spherical space forms which extends similar results due to do Carmo/Warner, Wang/Xia and Longa/Ripoll. Under certain sharp conditions on the…

This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…

For any smooth compact manifold $W$ of dimension at least two we prove that the classifying spaces of its group of diffeomorphisms which fix a set of $k$ points or $k$ embedded disks (up to permutation) satisfy homology stability. The same…

Most unsupervised image anomaly localization methods suffer from overgeneralization because of the high generalization abilities of convolutional neural networks, leading to unreliable predictions. To mitigate the overgeneralization, this…

We consider the problem of reconstructing a compact 3-manifold (with boundary) embedded in $\mathbb{R}^3$ from its cross-sections $\mathcal S$ with a given set of cutting planes $\mathcal P$ having arbitrary orientations. Using the obvious…

Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…

In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel…