Related papers: Matrix Difference in Pose-Graph Optimization
With the advent of sophisticated cameras, the urge to capture high-quality images has grown enormous. However, the noise contamination of the images results in substandard expectations among the people; thus, image denoising is an essential…
We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…
It has been shown numerically that the performance of the Levenberg-Marquardt algorithm can be improved by including a second order correction known as the geodesic acceleration. In this paper we give the method a more sound theoretical…
One of the fundamental problems in computer vision is the two-frame relative pose optimization problem. Primarily, two different kinds of error values are used: photometric error and re-projection error. The selection of error value is…
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…
Deep learning based camera pose estimation from monocular camera images has seen a recent uptake in Visual SLAM research. Even though such pose estimation approaches have excellent results in small confined areas like offices and apartment…
Simultaneous Localization and Mapping (SLAM) plays an important role in robot autonomy. Reliability and efficiency are the two most valued features for applying SLAM in robot applications. In this paper, we consider achieving a reliable…
Joint optimization of poses and features has been extensively studied and demonstrated to yield more accurate results in feature-based SLAM problems. However, research on jointly optimizing poses and non-feature-based maps remains limited.…
Distributed optimization aims to leverage the local computation and communication capabilities of each agent to achieve a desired global objective. This paper addresses the distributed pose graph optimization (PGO) problem under non-convex…
We study nonconvex optimization for phase retrieval and the more general problem of semidefinite low-rank matrix sensing; in particular, we focus on the global nonconvex landscape of overparametrized versions of the nonsmooth amplitude…
Map-centric SLAM is emerging as an alternative of conventional graph-based SLAM for its accuracy and efficiency in long-term mapping problems. However, in map-centric SLAM, the process of loop closure differs from that of conventional SLAM…
We consider minimization of composite functions of the form $f(g(x))+h(x)$, where $f$ and $h$ are convex functions (which can be nonsmooth) and $g$ is a smooth vector mapping. In addition, we assume that $g$ is the average of finite number…
In this paper, a Gauss-Seidel method with oblique direction (GSO) is proposed for finding the least-squares solution to a system of linear equations, where the coefficient matrix may be full rank or rank deficient and the system is…
The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
We propose a novel camera pose estimation or perspective-n-point (PnP) algorithm, based on the idea of consistency regions and half-space intersections. Our algorithm has linear time-complexity and a squared reconstruction error that…
We propose a new recursive estimator for linear dynamical systems under Gaussian process noise and non-Gaussian measurement noise. Specifically, we develop an approximate maximum a posteriori (MAP) estimator using dynamic programming and…
We present a faster interior-point method for optimizing sum-of-squares (SOS) polynomials, which are a central tool in polynomial optimization and capture convex programming in the Lasserre hierarchy. Let $p = \sum_i q^2_i$ be an…
Nonlinear dynamics has an important role when designing modern synchrotron lattices. In this letter, we introduce a new method of using a square matrix to analyze periodic nonlinear dynamical systems [1, 2]. Applying the method to the…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…