Related papers: Matrix Difference in Pose-Graph Optimization

Accurate camera pose estimation result is essential for visual SLAM (VSLAM). This paper presents a novel pose correction method to improve the accuracy of the VSLAM system. Firstly, the relationship between the camera pose estimation error…

We propose a novel approach to Graduated Non-Convexity (GNC) and demonstrate its efficacy through its application in robust pose graph optimization, a key component in SLAM backends. Traditional GNC methods often rely on heuristic methods…

In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…

When minimizing a nonlinear least-squares function, the Levenberg-Marquardt algorithm can suffer from a slow convergence, particularly when it must navigate a narrow canyon en route to a best fit. On the other hand, when the least-squares…

For large nonlinear least squares loss functions in machine learning we exploit the property that the number of model parameters typically exceeds the data in one batch. This implies a low-rank structure in the Hessian of the loss, which…

The Newton, Gauss--Newton and Levenberg--Marquardt methods all use the first derivative of a vector function (the Jacobian) to minimise its sum of squares. When the Jacobian matrix is ill-conditioned, the function varies much faster in some…

Traditional novel view synthesis methods heavily rely on external camera pose estimation tools such as COLMAP, which often introduce computational bottlenecks and propagate errors. To address these challenges, we propose a unified framework…

This paper studies an optimization problem on the sum of traces of matrix quadratic forms in $m$ semi-orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the…

Visual place recognition is an important subproblem of mobile robot localization. Since it is a special case of image retrieval, the basic source of information is the pairwise similarity of image descriptors. However, the embedding of the…

Multiplicative errors in addition to spatially referenced observations often arise in geodetic applications, particularly in surface estimation with light detection and ranging (LiDAR) measurements. However, spatial regression involving…

There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…

In this paper, we consider the problem of recovering random graph signals from nonlinear measurements. We formulate the maximum a-posteriori probability (MAP) estimator, which results in a nonconvex optimization problem. Conventional…

For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized…

The back-end module of Distributed Collaborative Simultaneous Localization and Mapping (DCSLAM) requires solving a nonlinear Pose Graph Optimization (PGO) under a distributed setting, also known as SE(d)-synchronization. Most existing…

Visual and lidar Simultaneous Localization and Mapping (SLAM) algorithms benefit from the Inertial Measurement Unit (IMU) modality. The high-rate inertial data complement the other lower-rate modalities. Moreover, in the absence of constant…

In this work, a new algorithm for solving symmetric indefinite systems of linear equations is presented. It factorizes the matrix into the form LDLt using Jacobi rotations in order to increase the pivot's absolute value. Furthermore, Rook's…

Typical LiDAR SLAM architectures feature a front-end for odometry estimation and a back-end for refining and optimizing the trajectory and map, commonly through loop closures. However, loop closure detection in large-scale missions presents…

The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we address this issue for photoacoustic computed tomography in circular geometry. We investigate the Galerkin…

Achieving real-time Simultaneous Localization and Mapping (SLAM) based on 3D Gaussian splatting (3DGS) in large-scale real-world environments remains challenging, as existing methods still struggle to jointly achieve low-latency pose…

We propose a differentiable nonlinear least squares framework to account for uncertainty in relative pose estimation from feature correspondences. Specifically, we introduce a symmetric version of the probabilistic normal epipolar…