Related papers: Discretized boundary surface reconstruction
We present first a brief review of the existing literature on shape optimization, stressing the recent use of Hamiltonian systems in topology optimization. In the second section, we collect some preliminaries on the implicit parametrization…
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…
We present an algorithm for computing the nonlinear interface dynamics of the Mullins-Sekerka model for interfaces that are defined implicitly (e.g. by a level set function) using integral equations . The computation of the dynamics…
Reconstructing a 3D shape based on a single sketch image is challenging due to the large domain gap between a sparse, irregular sketch and a regular, dense 3D shape. Existing works try to employ the global feature extracted from sketch to…
Implicit surface representations, such as signed-distance functions, combined with deep learning have led to impressive models which can represent detailed shapes of objects with arbitrary topology. Since a continuous function is learned,…
Computing the envelope of deforming planar domains is a significant and challenging problem with a wide range of potential applications. We approximate the envelope using circular arc splines, curves that balance geometric flexibility and…
A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…
The discretization of elliptic PDEs leads to large coupled systems of equations. Domain decomposition methods (DDMs) are one approach to the solution of these systems, and can split the problem in a way that allows for parallel computing.…
In this paper we construct developable surface patches which are bounded by two rational or NURBS curves, though the resulting patch is not a rational or NURBS surface in general. This is accomplished by reparameterizing one of the boundary…
Reconstructing complex structures from planar cross-sections is a challenging problem, with wide-reaching applications in medical imaging, manufacturing, and topography. Out-of-the-box point cloud reconstruction methods can often fail due…
We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is…
Surface reconstruction from an unorganized point cloud is an important problem due to its widespread applications. White noise, possibly clustered outliers, and noisy perturbation may be generated when a point cloud is sampled from a…
We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with…
We present an adaptive refinement algorithm for T-splines on unstructured 2D meshes. While for structured 2D meshes, one can refine elements alternatingly in horizontal and vertical direction, such an approach cannot be generalized directly…
Existing deep learning methods for the reconstruction and denoising of point clouds rely on small datasets of 3D shapes. We circumvent the problem by leveraging deep learning methods trained on billions of images. We propose a method to…
We propose a level-set-based semi-Lagrangian method on graded adaptive Cartesian grids to address the problem of surface reconstruction from point clouds. The goal is to obtain an implicit, high-quality representation of real shapes that…
Whole-brain surface extraction is an essential topic in medical imaging systems as it provides neurosurgeons with a broader view of surgical planning and abnormality detection. To solve the problem confronted in current deep learning skull…
3D object reconstruction from a single-view image is a long-standing challenging problem. Previous work was difficult to accurately reconstruct 3D shapes with a complex topology which has rich details at the edges and corners. Moreover,…
Domain Adaptation is a technique to address the lack of massive amounts of labeled data in unseen environments. Unsupervised domain adaptation is proposed to adapt a model to new modalities using solely labeled source data and unlabeled…
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…