相关论文: Advances in Global Solvers for 3D Vision

Estimating the absolute orientation of a local system relative to a global navigation satellite system (GNSS) reference often suffers from local minima and high dependency on satellite availability. Existing methods for this alignment task…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…

AI-assisted coding has rapidly reshaped software practice and research workflows, yet today's models still struggle to produce correct code for complex 3D geometric vision. If models could reliably write such code, the research of our…

In this work, we address three non-convex optimization problems associated with the training of shallow neural networks (NNs) for exact and approximate representation, as well as for regression tasks. Through a mean-field approach, we…

A recent trend among generalizable novel view synthesis methods is to learn a rendering operator acting over single camera rays. This approach is promising because it removes the need for explicit volumetric rendering, but it effectively…

Reconstructing 3D representations from 2D inputs is a fundamental task in computer vision and graphics, serving as a cornerstone for understanding and interacting with the physical world. While traditional methods achieve high fidelity,…

In this paper, we consider solving nonconvex quadratic programming problems using modern solvers such as Gurobi and SCIP. It is well-known that the classical techniques of quadratic convex reformulation can improve the computational…

UAV missions often require specific geometric constraints to be satisfied between ground locations and the vehicle location. Such requirements are typical for contexts where line-of-sight must be maintained between the vehicle location and…

In this paper we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. With this in mind, we present a comparison of the convergence performances of commonly used solvers for both unconstrained…

Spatial intelligence, encompassing 3D reconstruction, perception, and reasoning, is fundamental to applications such as robotics, aerial imaging, and extended reality. A key enabler is the real-time, accurate estimation of core 3D…

While 3D Gaussian Splatting (3DGS) enables high-quality, real-time rendering for bounded scenes, its extension to large-scale urban environments gives rise to critical challenges in terms of geometric consistency, memory efficiency, and…

The dissertation presents four key contributions toward fairness and robustness in vision learning. First, to address the problem of large-scale data requirements, the dissertation presents a novel Fairness Domain Adaptation approach…

In this paper, we consider the problem of unsupervised video object segmentation via background subtraction. Specifically, we pose the nonsemantic extraction of a video's moving objects as a nonconvex optimization problem via a sum of…

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

We provide the global optimization community with new optimality proofs for six deceptive benchmark functions (five bound-constrained functions and one nonlinearly constrained problem). These highly multimodal nonlinear test problems are…

Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…

3D reconstruction and view synthesis are foundational problems in computer vision, graphics, and immersive technologies such as augmented reality (AR), virtual reality (VR), and digital twins. Traditional methods rely on computationally…

This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are…

Recent developments in generative models and large-scale datasets have substantially advanced 3D world generation, facilitating a broad range of domains including spatial intelligence, embodied intelligence, and autonomous driving. While…

We propose a general theory for studying the \xl{landscape} of nonconvex \xl{optimization} with underlying symmetric structures \tz{for a class of machine learning problems (e.g., low-rank matrix factorization, phase retrieval, and deep…