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Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
Triangle meshes play a crucial role in 3D applications for efficient manipulation and rendering. While auto-regressive methods generate structured meshes by predicting discrete vertex tokens, they are often constrained by limited face…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding highly resolved, uniform discretitization in numerical…
Surface parameterizations have been widely applied to computer graphics and digital geometry processing. In this paper, we propose a novel stretch energy minimization (SEM) algorithm for the computation of equiareal parameterizations of…
Shape optimization involves the minimization of a cost function defined over a set of shapes, often governed by a partial differential equation (PDE). In the absence of closed-form solutions, one relies on numerical methods to approximate…
Complex geometric tasks such as geometric modeling, physical simulation, and texture parametrization often involve the embedding of many complex sub-domains with potentially different dimensions. These tasks often require evolving the…
Many Multi-View-Stereo algorithms extract a 3D mesh model of a scene, after fusing depth maps into a volumetric representation of the space. Due to the limited scalability of such representations, the estimated model does not capture fine…
Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have…
We consider the problem of obese human mesh recovery, i.e., fitting a parametric human mesh to images of obese people. Despite obese person mesh fitting being an important problem with numerous applications (e.g., healthcare), much recent…
We develop a method to reconstruct, from measured displacements of an underlying elastic substrate, the spatially dependent forces that cells or tissues impart on it. Given newly available high-resolution images of substrate displacements,…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
Edge-preserving image smoothing is an important step for many low-level vision problems. Though many algorithms have been proposed, there are several difficulties hindering its further development. First, most existing algorithms cannot…
Identifiability means that iterates generated by optimization algorithms are eventually confined to an identifiable set. This property is computationally useful because minimizing a nonsmooth function near a critical point reduces to…
In this paper, we propose a stochastic geometric iterative method to approximate the high-resolution 3D models by finite Loop subdivision surfaces. Given an input mesh as the fitting target, the initial control mesh is generated using the…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised $h+p$ refinement approaches on massively parallel computers. Our high-order $h+p$ refinement strategy is based…
The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that…
In this article we consider a priori error and pointwise estimates for finite element approximations of solutions to semilinear elliptic boundary value problems in d>=2 space dimensions, with nonlinearities satisfying critical growth…