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We propose a new approach to constructing semistable integral models of hypersurfaces over a discretely valued complete field K. For each stable hypersurface X over K we define a continuous stability function on the Bruhat-Tits building of…

We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…

In this paper, we present a generalizable method for 3D surface reconstruction from raw point clouds or pre-estimated 3D Gaussians by 3DGS from RGB images. Unlike existing coordinate-based methods which are often computationally intensive…

A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…

Implicit function based surface reconstruction has been studied for a long time to recover 3D shapes from point clouds sampled from surfaces. Recently, Signed Distance Functions (SDFs) and Occupany Functions are adopted in learning-based…

3D point clouds are increasingly vital for applications like autonomous driving and robotics, yet the raw data captured by sensors often suffer from noise and sparsity, creating challenges for downstream tasks. Consequently, point cloud…

Accurate reconstruction of leaf surfaces from 3D point cloud is essential for agricultural applications such as phenotyping. However, real-world plant data (i.e., irregular 3D point cloud) are often complex to reconstruct plant parts…

Neural surface reconstruction has been dominated by implicit representations with marching cubes for explicit surface extraction. However, those methods typically require high-quality normals for accurate reconstruction. We propose…

Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…

We propose the use of a Transformer to accurately predict normals from point clouds with noise and density variations. Previous learning-based methods utilize PointNet variants to explicitly extract multi-scale features at different input…

We propose a method for unsupervised reconstruction of a temporally-consistent sequence of surfaces from a sequence of time-evolving point clouds. It yields dense and semantically meaningful correspondences between frames. We represent the…

Point clouds collected by real-world sensors are always unaligned and sparse, which makes it hard to reconstruct the complete shape of object from a single frame of data. In this work, we manage to provide complete point clouds from sparse…

Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…

We describe a two-level method for computing a function whose zero-level set is the surface reconstructed from given points scattered over the surface and associated with surface normal vectors. The function is defined as a linear…

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…

Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…

Accurate and consistent construction of point clouds from LiDAR scanning data is fundamental for 3D modeling applications. Current solutions, such as multiview point cloud registration and LiDAR bundle adjustment, predominantly depend on…

Surface reconstruction from point clouds is a crucial task in the fields of computer vision and computer graphics. SDF-based methods excel at reconstructing smooth meshes with minimal error and artefacts but struggle with representing open…

Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…

Point clouds are a fundamental 3D representation in computer vision, enabling a wide range of perception tasks. However, real-world point clouds often suffer from degradations such as incompleteness, noise, outliers, and irregular density,…