相关论文: Computational Geometry Column 45

Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…

The task of reassembly is a significant challenge across multiple domains, including archaeology, genomics, and molecular docking, requiring the precise placement and orientation of elements to reconstruct an original structure. In this…

Computer-Aided Design is ubiquitous in todays world, as almost every manufactured object begins as a digital model across industries. At the same time, advances in 3D sensing have made point clouds a dominant form of raw 3D data. Recovering…

This paper presents a hybrid algorithm that combines features form both Sqrt(3) and Loop Subdivision schemes. The algorithm aims at preserving sharp features and trim regions, during the surfaces subdivision, using a set of rules. The…

We introduce a new method that efficiently computes a set of viewpoints and trajectories for high-quality 3D reconstructions in outdoor environments. Our goal is to automatically explore an unknown area, and obtain a complete 3D scan of a…

We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the…

Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…

In man-made environments such as indoor scenes, when point-based 3D reconstruction fails due to the lack of texture, lines can still be detected and used to support surfaces. We present a novel method for watertight piecewise-planar surface…

In this paper, we propose a framework to reconstruct 3D models from raw scanned points by learning the prior knowledge of a specific class of objects. Unlike previous work that heuristically specifies particular regularities and defines…

In this paper, we explore an open research problem concerning the reconstruction of 3D scenes from images. Recent methods have adopt 3D Gaussian Splatting (3DGS) to produce 3D scenes due to its efficient training process. However, these…

We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $\tau$,…

One major challenge in 3D reconstruction is to infer the complete shape geometry from partial foreground occlusions. In this paper, we propose a method to reconstruct the complete 3D shape of an object from a single RGB image, with…

There are many applications in which a bounding sphere containing the given triangle E3 is needed, e.g. fast collision detection, ray-triangle intersecting in raytracing etc. This is a typical geometrical problem in E3 and it has also…

Key points, correspondences, projection matrices, point clouds and dense clouds are the skeletons in image-based 3D reconstruction, of which point clouds have the important role in generating a realistic and natural model for a 3D…

Reconstructing a surface from a point cloud is an underdetermined problem. We use a neural network to study and quantify this reconstruction uncertainty under a Poisson smoothness prior. Our algorithm addresses the main limitations of…

Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…

We study the distribution of algebraic points on K3 surfaces.

We present a fully automatic approach for reconstructing compact 3D building models from large-scale airborne point clouds. A major challenge of urban reconstruction from airborne LiDAR point clouds lies in that the vertical walls are…

This paper describes an approach for fitting an immersed submanifold of a finite-dimensional Euclidean space to random samples. The reconstruction mapping from the ambient space to the desired submanifold is implemented as a composition of…

To reduce cost in storing, processing and visualizing a large-scale point cloud, we consider a randomized resampling strategy to select a representative subset of points while preserving application-dependent features. The proposed strategy…