Related papers: Graduated Non-Convexity for Robust Spatial Percept…

Many problems in robotics, such as estimating the state from noisy sensor data or aligning two point clouds, can be posed and solved as least-squares problems. Unfortunately, vanilla nonminimal solvers for least-squares problems are…

Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association, or to incorrect detections from signal processing and machine learning methods. This paper introduces two unifying formulations…

We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated…

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial…

Global solvers have emerged as a powerful paradigm for 3D vision, offering certifiable solutions to nonconvex geometric optimization problems traditionally addressed by local or heuristic methods. This survey presents the first systematic…

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…

We propose a robust framework for the planar pose graph optimization contaminated by loop closure outliers. Our framework rejects outliers by first decoupling the robust PGO problem wrapped by a Truncated Least Squares kernel into two…

Accurate and globally referenced global navigation satellite system (GNSS) based vehicular positioning can be achieved in outlier-free open areas. However, the performance of GNSS can be significantly degraded by outlier measurements, such…

In this paper, we present IRON (Invariant-based global Robust estimation and OptimizatioN), a non-minimal and highly robust solution for point cloud registration with a great number of outliers among the correspondences. To realize this, we…

We propose the first general and practical framework to design certifiable algorithms for robust geometric perception in the presence of a large amount of outliers. We investigate the use of a truncated least squares (TLS) cost function,…

Imperfect data (noise, outliers and partial overlap) and high degrees of freedom make non-rigid registration a classical challenging problem in computer vision. Existing methods typically adopt the $\ell_{p}$ type robust estimator to…

Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis…

Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…

This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…

We present a continuous nonlinear optimization model for the Spin Glass Problem (SGP), building on a classical result by Rosenberg (1972), which shows that for a class of multilinear polynomial problems the optimal values of the continuous…

Pose Graph Optimization involves the estimation of a set of poses from pairwise measurements and provides a formalization for many problems arising in mobile robotics and geometric computer vision. In this paper, we consider the case in…

We present a novel approach to robust pose graph optimization based on Graduated Non-Convexity (GNC). Unlike traditional GNC-based methods, the proposed approach employs an adaptive shape function using B-spline to optimize the shape of the…

Geometric perception problems are fundamental tasks in robotics and computer vision. In real-world applications, they often encounter the inevitable issue of outliers, preventing traditional algorithms from making correct estimates. In this…

Outlier-robust estimation is a fundamental problem and has been extensively investigated by statisticians and practitioners. The last few years have seen a convergence across research fields towards "algorithmic robust statistics", which…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…