Related papers: Square Root Marginalization for Sliding-Window Bun…
We propose a new formulation for the bundle adjustment problem which relies on nullspace marginalization of landmark variables by QR decomposition. Our approach, which we call square root bundle adjustment, is algebraically equivalent to…
The line is a prevalent element in man-made environments, inherently encoding spatial structural information, thus making it a more robust choice for feature representation in practical applications. Despite its apparent advantages,…
We present DM-VIO, a monocular visual-inertial odometry system based on two novel techniques called delayed marginalization and pose graph bundle adjustment. DM-VIO performs photometric bundle adjustment with a dynamic weight for visual…
Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
Bundle adjustment (BA) is the standard way to optimise camera poses and to produce sparse representations of a scene. However, as the number of camera poses and features grows, refinement through bundle adjustment becomes inefficient.…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
Current bundle adjustment solvers such as the Levenberg-Marquardt (LM) algorithm are limited by the bottleneck in solving the Reduced Camera System (RCS) whose dimension is proportional to the camera number. When the problem is scaled up,…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
The sliced Wasserstein barycenter (SWB) is a widely acknowledged method for efficiently generalizing the averaging operation within probability measure spaces. However, achieving marginal fairness SWB, ensuring approximately equal distances…
The bundle adjustment (BA) algorithm is a widely used nonlinear optimization technique in the backend of Simultaneous Localization and Mapping (SLAM) systems. By leveraging the co-view relationships of landmarks from multiple perspectives,…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order…
The proliferation of saddle points, rather than poor local minima, is increasingly understood to be a primary obstacle in large-scale non-convex optimization for machine learning. Variable elimination algorithms, like Variable Projection…
We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
We present VI-DSO, a novel approach for visual-inertial odometry, which jointly estimates camera poses and sparse scene geometry by minimizing photometric and IMU measurement errors in a combined energy functional. The visual part of the…
Classical Bundle Adjustment (BA) is fundamentally limited by its reliance on precise metric initialization and prior camera intrinsics. While modern dense matchers offer high-fidelity correspondences, traditional Structure-from-Motion (SfM)…
We present closed-form expressions for marginalizing and conditioning Gaussians onto linear manifolds, and demonstrate how to apply these expressions to smooth nonlinear manifolds through linearization. Although marginalization and…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…