Related papers: Subdivision Directional Fields
We propose SDFDiff, a novel approach for image-based shape optimization using differentiable rendering of 3D shapes represented by signed distance functions (SDFs). Compared to other representations, SDFs have the advantage that they can…
Recently, numerous handcrafted and searched networks have been applied for semantic segmentation. However, previous works intend to handle inputs with various scales in pre-defined static architectures, such as FCN, U-Net, and DeepLab…
Differentiable rendering is a technique that aims to invert the rendering process to enable optimizing rendering parameters from a set of images. In this article, we present a differentiable volume rendering solution called DiffTetVR for…
Recent advances in 3D deep learning have shown that it is possible to train highly effective deep models for 3D shape generation, directly from 2D images. This is particularly interesting since the availability of 3D models is still limited…
The hybrid high-order method is a modern numerical framework for the approximation of elliptic PDEs. We present here an extension of the hybrid high-order method to meshes possessing curved edges/faces. Such an extension allows us to…
We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at…
A grid-overlay finite difference method is proposed for the numerical approximation of the fractional Laplacian on arbitrary bounded domains. The method uses an unstructured simplicial mesh and an overlay uniform grid for the underlying…
Let $X/k$ be a noetherian scheme over a field $k$ of characteristic 0, such that the residue field at its closed points are algebraic extensions of $k$. Let ${\mathfrak g}_{X/k}\subset T_{{X/k}}$ be an ${\mathcal O}_{X}$-submodule of the…
We propose a novel framework for representing neural fields on triangle meshes that is multi-resolution across both spatial and frequency domains. Inspired by the Neural Fourier Filter Bank (NFFB), our architecture decomposes the spatial…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
We propose a novel approach for performing convolution of signals on curved surfaces and show its utility in a variety of geometric deep learning applications. Key to our construction is the notion of directional functions defined on the…
This paper presents a new mesh segmentation method that integrates geometrical and topological features through a flexible Reeb graph representation. The algorithm consists of three phases: construction of the Reeb graph using the improved…
Various computer simulations regarding, e.g., the weather or structural mechanics, solve complex problems on a two-dimensional domain. They mostly do so by splitting the input domain into a finite set of smaller and simpler elements on…
We present a novel structure-preserving semi-implicit finite volume method on vertex-based staggered meshes for the compatible discretization of first order systems of time-dependent partial differential equations (PDEs). The method…
We propose Medial Atom Ray Fields (MARFs), a novel neural object representation that enables accurate differentiable surface rendering with a single network evaluation per camera ray. Existing neural ray fields struggle with multi-view…
Extracting surfaces from Signed Distance Fields (SDFs) can be accomplished using traditional algorithms, such as Marching Cubes. However, since they rely on sign flips across the surface, these algorithms cannot be used directly on Unsigned…
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
This paper introduces a 3D shape generative model based on deep neural networks. A new image-like (i.e., tensor) data representation for genus-zero 3D shapes is devised. It is based on the observation that complicated shapes can be well…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are non-spherical. The most expensive part within such a simulation code…