Related papers: Medial Meshes for Volume Approximation
Voxels are a geometric representation used for rendering volumes, multi-resolution models, and indirect lighting effects. Since the memory consumption of uncompressed voxel volumes scales cubically with resolution, past works have…
Recent work has demonstrated that volumetric scene representations combined with differentiable volume rendering can enable photo-realistic rendering for challenging scenes that mesh reconstruction fails on. However, these methods entangle…
High-quality view synthesis relies on volume rendering, splatting, or surface rendering. While surface rendering is typically the fastest, it struggles to accurately model fuzzy geometry like hair. In turn, alpha-blending techniques excel…
Voxel art is a distinctive stylization widely used in games and digital media, yet automated generation from 3D meshes remains challenging due to conflicting requirements of geometric abstraction, semantic preservation, and discrete color…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
The goal of this paper is to compare surface-based and volumetric 3D object shape representations, as well as viewer-centered and object-centered reference frames for single-view 3D shape prediction. We propose a new algorithm for…
Speakman and Lee (2017) gave a formula for the volume of the convex hull of the graph of a trilinear monomial, $y=x_1x_2x_3$, over a box in the nonnegative orthant, in terms of the upper and lower bounds on the variables. This was done in…
This paper presents a new algorithm, Weighted Squared Volume Minimization (WSVM), for generating high-quality tetrahedral meshes from closed triangle meshes. Drawing inspiration from the principle of minimal surfaces that minimize squared…
This paper presents a new progressive compression method for triangular meshes. This method, in fact, is based on a schema of irregular multi-resolution analysis and is centered on the optimization of the rate-distortion trade-off. The…
Current 3D representations like meshes, voxels, point clouds, and NeRF-based neural implicit fields exhibit significant limitations: they are often task-specific, lacking universal applicability across reconstruction, generation, editing,…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
Segmentation is often an essential intermediate step in image analysis. A volume segmentation characterizes the underlying volume image in terms of geometric information--segments, faces between segments, curves in which several faces…
Volume rendering using neural fields has shown great promise in capturing and synthesizing novel views of 3D scenes. However, this type of approach requires querying the volume network at multiple points along each viewing ray in order to…
We present a suite of techniques for jointly optimizing triangle meshes and shading models to match the appearance of reference scenes. This capability has a number of uses, including appearance-preserving simplification of extremely…
Estimating a mesh from an unordered set of sparse, noisy 3D points is a challenging problem that requires carefully selected priors. Existing hand-crafted priors, such as smoothness regularizers, impose an undesirable trade-off between…
Meshes are fundamental representations of 3D surfaces. However, creating high-quality meshes is a labor-intensive task that requires significant time and expertise in 3D modeling. While a delicate object often requires over $10^4$ faces to…
Three-dimensional ultrasound enables real-time volumetric visualization of anatomical structures. Unlike traditional 2D ultrasound, 3D imaging reduces reliance on precise probe orientation, potentially making ultrasound more accessible to…
We introduce an approach for selecting objects in neural volumetric 3D representations, such as multi-plane images (MPI) and neural radiance fields (NeRF). Our approach takes a set of foreground and background 2D user scribbles in one view…
This article introduces a representation of dynamic meshes, adapted to some numerical simulations that require controlling the volume of objects with free boundaries, such as incompressible fluid simulation, some astrophysical simulations…
Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This…