Related papers: PLMP -- Point-Line Minimal Problems for Projective…
This paper investigates the minimal number of inputs/outputs required to guarantees the controllability/observability of a system, under the condition that its state transition matrix (STM) is prescribed. It has been proved that this…
World-wide detailed 2D maps require enormous collective efforts. OpenStreetMap is the result of 11 million registered users manually annotating the GPS location of over 1.75 billion entries, including distinctive landmarks and common urban…
This paper presents a visual SLAM system that uses both points and lines for robust camera localization, and simultaneously performs a piece-wise planar reconstruction (PPR) of the environment to provide a structural map in real-time. One…
While Structure from Motion (SfM) achieves great success in 3D reconstruction, it still meets challenges on large scale scenes. In this work, large scale SfM is deemed as a graph problem, and we tackle it in a divide-and-conquer manner.…
A metro-line crossing minimization problem is to draw multiple lines on an underlying graph that models stations and rail tracks so that the number of crossings of lines becomes minimum. It has several variations by adding restrictions on…
Two-view structure from motion (SfM) is the cornerstone of 3D reconstruction and visual SLAM (vSLAM). Many existing end-to-end learning-based methods usually formulate it as a brute regression problem. However, the inadequate utilization of…
Relative pose estimation using point correspondences (PC) is a widely used technique. A minimal configuration of six PCs is required for two views of generalized cameras. In this paper, we present several minimal solvers that use six PCs to…
The Minimum Linear Arrangement problem (MLA) consists of finding a mapping $\pi$ from vertices of a graph to distinct integers that minimizes $\sum_{\{u,v\}\in E}|\pi(u) - \pi(v)|$. In that setting, vertices are often assumed to lie on a…
The submodular partitioning problem asks to minimize, over all partitions $P$ of a ground set $V$, the sum of a given submodular function $f$ over the parts of $P$. The problem has seen considerable work in approximability, as it…
We presented a separation based optimization algorithm which, rather than optimization the entire variables altogether, This would allow us to employ: 1) a class of nonlinear functions with three variables and 2) a convex quadratic…
Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all…
We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of…
In Few-Shot Learning (FSL), traditional metric-based approaches often rely on global metrics to compute similarity. However, in natural scenes, the spatial arrangement of key instances is often inconsistent across images. This spatial…
We tackle the problem of automatic calibration of radially distorted cameras in challenging conditions. Accurately determining distortion parameters typically requires either 1) solving the full Structure from Motion (SfM) problem involving…
The p-median problem concerns the location of facilities so that the sum of distances between the demand points and their nearest facility is minimized. We study a variant of this classic location problem where minimum distance constraints…
We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents…
When adapting Simultaneous Mapping and Localization (SLAM) to real-world applications, such as autonomous vehicles, drones, and augmented reality devices, its memory footprint and computing cost are the two main factors limiting the…