Related papers: Reconstructing Curves from Sparse Samples on Riema…

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in…

Currently, the area of geometric modeling and the construction of 3D models based on point clouds from laser sensors is actively developing. One of the basic tasks of geometric modeling is the reconstruction of a surface from a cloud of…

In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches)…

In this work, we present a solution to the challenging problem of reconstructing liquids from image data. The challenges in reconstructing liquids, which is not faced in previous reconstruction works on rigid and deforming surfaces, lies in…

We present a novel method for reconstructing a 3D implicit surface from a large-scale, sparse, and noisy point cloud. Our approach builds upon the recently introduced Neural Kernel Fields (NKF) representation. It enjoys similar…

Incomplete or missing data in three-dimensional (3D) models can lead to erroneous or flawed renderings, limiting their usefulness in applications such as visualization, geometric computation, and 3D printing. Conventional surface-repair…

We are witnessing an explosion of neural implicit representations in computer vision and graphics. Their applicability has recently expanded beyond tasks such as shape generation and image-based rendering to the fundamental problem of…

The boundary representation (B-Rep) models a 3D solid as its explicit boundaries: trimmed corners, edges, and faces. Recovering B-Rep representation from unstructured data is a challenging and valuable task of computer vision and graphics.…

3D modeling based on point clouds is an efficient way to reconstruct and create detailed 3D content. However, the geometric procedure may lose accuracy due to high redundancy and the absence of an explicit structure. In this work, we…

The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for…

3D Gaussian Splatting has achieved impressive performance in novel view synthesis with real-time rendering capabilities. However, reconstructing high-quality surfaces with fine details using 3D Gaussians remains a challenging task. In this…

The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art…

This paper investigates an open research challenge of reconstructing high-quality, large 3D open scenes from images. It is observed existing methods have various limitations, such as requiring precise camera poses for input and dense…

Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex…

In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…

Ridge surfaces represent important features for the analysis of 3-dimensional (3D) datasets in diverse applications and are often derived from varying underlying data including flow fields, geological fault data, and point data, but they…

Surface reconstruction from point clouds is a fundamental step in many applications in computer vision. In this paper, we develop an efficient iterative method on a variational model for the surface reconstruction from point clouds. The…

Cascaded regression has been recently applied to reconstructing 3D faces from single 2D images directly in shape space, and achieved state-of-the-art performance. This paper investigates thoroughly such cascaded regression based 3D face…

Traditional sampling schemes often assume that the sampling locations are known. Motivated by the recent bioimaging technique known as cryogenic electron microscopy (cryoEM), we consider the problem of reconstructing an unknown 3D structure…