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We consider a sketched implementation of the finite element method for elliptic partial differential equations on high-dimensional models. Motivated by applications in real-time simulation and prediction we propose an algorithm that…
Reliable multimodal sensor fusion algorithms require accurate spatiotemporal calibration. Recently, targetless calibration techniques based on implicit neural representations have proven to provide precise and robust results. Nevertheless,…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
This paper designs a technique route to generate high-quality panoramic image with depth information, which involves two critical research hotspots: fusion of LiDAR and image data and image stitching. For the fusion of 3D points and image…
In this work, we address the limitation of surface fitting-based grasp planning algorithm, which primarily focuses on geometric alignment between the gripper and object surface while overlooking the stability of contact point distribution,…
A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…
We introduce a novel learning-based method for encoding and manipulating 3D surface meshes. Our method is specifically designed to create an interpretable embedding space for deformable shape collections. Unlike previous 3D mesh…
3D volumetric reconstruction from incomplete or noisy measurements is a fundamental problem in medical imaging and computational tomography. Deep image prior (DIP)-based methods have recently shown strong capability for solving inverse…
A new approach for 2D to 3D garment retexturing is proposed based on Gaussian mixture models and thin plate splines (TPS). An automatically segmented garment of an individual is matched to a new source garment and rendered, resulting in…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
In Spectrally Efficient Frequency Division Multiplexing systems the input data stream is divided into several adjacent subchannels where the distance of the subchannels is less than that of Orthogonal Frequency Division…
Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…
3D Gaussian Splatting (3DGS) has emerged as a powerful technique for generating photorealistic renderings of a scene in real-time. However, the volumetric nature of 3DGS limits its ability to accurately capture surface geometry. To address…
In this thesis, we propose new theoretical frameworks for the analysis of stochastic and distributed methods with error compensation and local updates. Using these frameworks, we develop more than 20 new optimization methods, including the…
This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…
Converting quad meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distributions of recent G-spline constructions with the refinability of subdivision surfaces. Specifically, we present a C2…
We propose a sequential quadratic programming (SQP) method that can incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization problems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed as…
We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…