Related papers: Total Least Squares for Optimal Pose Estimation
This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the…
Pose estimation is essential for many applications within computer vision and robotics. Despite its uses, few works provide rigorous uncertainty quantification for poses under dense or learned models. We derive a closed-form lower bound on…
In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…
As autonomous systems increasingly rely on onboard sensing for localization and perception, the parallel tasks of motion planning and state estimation become more strongly coupled. This coupling is well-captured by augmenting the planning…
Line features are valid complements for point features in man-made environments. 3D-2D constraints provided by line features have been widely used in Visual Odometry (VO) and Structure-from-Motion (SfM) systems. However, how to accurately…
In this work, we derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. The core of our approach is the formulation of the residual covariances as a combination of geometric and photometric…
We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
Projected least squares (PLS) is an intuitive and numerically cheap technique for quantum state tomography. The method first computes the least-squares estimator (or a linear inversion estimator) and then projects the initial estimate onto…
Given multiple point clouds, how to find the rigid transform (rotation, reflection, and shifting) such that these point clouds are well aligned? This problem, known as the generalized orthogonal Procrustes problem (GOPP), has found numerous…
Many statistical estimation procedures lead to nonconvex optimization problems. Algorithms to solve these are often guaranteed to output a stationary point of the optimization problem. Oracle inequalities are an important theoretical…
The coresets approach, also called subsampling or subset selection, aims to select a subsample as a surrogate for the observed sample and has found extensive applications in large-scale data analysis. Existing coresets methods construct the…
This paper proposes to use the three vectors in a rotation matrix as the representation in head pose estimation and develops a new neural network based on the characteristic of such representation. We address two potential issues existed in…
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…
Pose estimation in the wild is a challenging problem, particularly in situations of (i) occlusions of varying degrees and (ii) crowded outdoor scenes. Most of the existing studies of pose estimation did not report the performance in similar…
Estimating position and orientation change of a mobile platform from two consecutive point clouds provided by a high-resolution sensor is a key problem in autonomous navigation. In particular, scan matching algorithms aim to find the…
The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…