Related papers: Lifting Directional Fields to Minimal Sections
Two approaches that use a density field for seeding holes in level set topology optimization are proposed. In these approaches, the level set field describes the material-void interface while the density field describes the material…
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
Boundaries are among the primary visual cues used by human and computer vision systems. One of the key problems in boundary detection is the label representation, which typically leads to class imbalance and, as a consequence, to thick…
Minimization of boundary curvature is a classic regularization technique for image segmentation in the presence of noisy image data. Techniques for minimizing curvature have historically been derived from descent methods which could be…
Hive plots are a graph visualization style placing vertices on a set of radial axes emanating from a common center and drawing edges as smooth curves connecting their respective endpoints. In previous work on hive plots, assignment to an…
We prove that smooth 1-dimensional topological field theories over a manifold are equivalent to vector bundles with connection. The main novelty is our definition of the smooth 1-dimensional bordism category, which encodes cutting laws…
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
Line segment detection is an essential task in computer vision and image analysis, as it is the critical foundation for advanced tasks such as shape modeling and road lane line detection for autonomous driving. We present a robust…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An…
An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as it is often called, computes the best configuration of…
A novel algorithm that produces a quad layout based on imposed set of singularities is proposed. In this paper, we either use singularities that appear naturally, e.g., by minimizing Ginzburg-Landau energy, or use as an input user-defined…
Line fields on surfaces are a means to describe the nematic order that may pattern them. The least distorted nematic fields are called uniform, but they can only exist on surfaces with negative constant Gaussian curvature. To identify the…
Geometric camera calibration is often required for applications that understand the perspective of the image. We propose perspective fields as a representation that models the local perspective properties of an image. Perspective Fields…
We give a global geometric decomposition of continuously differentiable vector fields on $\mathbb{R}^n$. More precisely, given a vector field of class $\mathcal{C}^{1}$ on $\mathbb{R}^{n}$, and a geometric structure on $\mathbb{R}^n$, we…
We propose a novel discretization of tangent vector fields for triangle meshes. Starting with a Phong map continuously assigning normals to all points on the mesh, we define an extrinsic bases for continuous tangent vector fields by using…
Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diverse structure that includes singularities similar to harmonic…
Differentiable rendering is an essential operation in modern vision, allowing inverse graphics approaches to 3D understanding to be utilized in modern machine learning frameworks. Explicit shape representations (voxels, point clouds, or…
We propose a geometric formulation of effective field theories via nonlinear supersymmetry. Non-supersymmetric particles are embedded in constrained superfields governed by a nonlinear sigma model, and operators are collected into…