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Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…
Dimensionality reduction methods are employed to decrease data dimensionality, either to enhance machine learning performance or to facilitate data visualization in two or three-dimensional spaces. These methods typically fall into two…
A central problem in topological data analysis is that of computing the homology of a given simplicial complex. Said complexes can have arbitrary large number of simplices, as can happen, for example, if the space is the Rips-Vietoris or…
We propose a template-driven triangulation framework that embeds raster- or segmentation-derived boundaries into a regular triangular grid for stable PDE discretization on image-derived domains. Unlike constrained Delaunay triangulation…
The global topology of the Universe can affect long-range gravitational forces via boundary conditions. Detailed studies of non-trivial topologies require simulations that natively adopt such geometries. Cosmological $N$-body simulations…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichm\"uller space…
There is a growing interest in characterizing circular data found in biological systems. Such data are wide ranging and varied, from signal phase in neural recordings to nucleotide sequences in round genomes. Traditional clustering…
We introduce MeshGPT, a new approach for generating triangle meshes that reflects the compactness typical of artist-created meshes, in contrast to dense triangle meshes extracted by iso-surfacing methods from neural fields. Inspired by…
We present STITCH, a novel approach for neural implicit surface reconstruction of a sparse and irregularly spaced point cloud while enforcing topological constraints (such as having a single connected component). We develop a new…
We view the reconstruction of CAD models in the boundary representation (B-Rep) as the detection of geometric primitives of different orders, i.e. vertices, edges and surface patches, and the correspondence of primitives, which are…
Modeling in Computer Vision has evolved to MLPs. Vision MLPs naturally lack local modeling capability, to which the simplest treatment is combined with convolutional layers. Convolution, famous for its sliding window scheme, also suffers…
In this paper, we reconsider the early computer vision bottom-up program, according to which higher level features (geometric structures) in an image could be built up recursively from elementary features by simple grouping principles…
Accurate, real-time 3D reconstruction of human heads from monocular images and videos underlies numerous visual applications. As 3D ground truth data is hard to come by at scale, previous methods have sought to learn from abundant 2D videos…
We present new finite elements for solving the Riesz maps of the de Rham complex on triangular and tetrahedral meshes at high order. The finite elements discretize the same spaces as usual, but with different basis functions, so that the…
Point cloud completion aims to recover partial geometric and topological shapes caused by equipment defects or limited viewpoints. Current methods either solely rely on the 3D coordinates of the point cloud to complete it or incorporate…
Supervised 3D part segmentation models are tailored for a fixed set of objects and parts, limiting their transferability to open-set, real-world scenarios. Recent works have explored vision-language models (VLMs) as a promising alternative,…
In this paper we define, implement, and investigate a simplicial complex construction for computing persistent homology of Euclidean point cloud data, which we call the Delaunay-Rips complex (DR). Assigning the Vietoris-Rips weights to…
We provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one can reason geometrically about dynamics…
3D face reconstruction technology aims to generate a face stereo model naturally and realistically. Previous deep face reconstruction approaches are typically designed to generate convincing textures and cannot generalize well to multiple…