Related papers: Point in polygon calculation using vector geometri…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…
3D motion tracking is a critical task in many computer vision applications. Unsupervised markerless 3D motion tracking systems determine the most relevant object in the screen and then track it by continuously estimating its projection…
In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems.…
We improve upon the running time for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set $K\subset \mathbb{R}^n$ contained in a box of radius $R$, we show how to either find a…
We present PolyGNN, a polyhedron-based graph neural network for 3D building reconstruction from point clouds. PolyGNN learns to assemble primitives obtained by polyhedral decomposition via graph node classification, achieving a watertight…
We propose a family of recursive cutting-plane algorithms to solve feasibility problems with constrained memory, which can also be used for first-order convex optimization. Precisely, in order to find a point within a ball of radius…
Vector-based algorithms are novel algorithms in optimal any-angle path planning that are motivated by bug algorithms, bypassing free space by directly conducting line-of-sight checks between two queried points, and searching along obstacle…
Thermodynamic computing has emerged as a promising paradigm for accelerating computation by harnessing the thermalization properties of physical systems. This work introduces a novel approach to solving quadratic programming problems using…
Estimating the position and orientation of a camera with respect to an observed scene is one of the central problems in computer vision, particularly in the context of camera calibration and multi-sensor systems. This paper addresses the…
We study the problem of placing a set $T$ of broadcast towers in a simple polygon $P$ in order for any point to locate itself in the interior of $P$. Let $V(p)$ denote the visibility polygon of a point $p$, as the set of all points $q \in…
We solve the $r$-star covering problem in simple orthogonal polygons, also known as the point guard problem in simple orthogonal polygons with rectangular vision, in quadratic time.
We characterize the problem of pose estimation for rigid objects in terms of determining viewpoint to explain coarse pose and keypoint prediction to capture the finer details. We address both these tasks in two different settings - the…
This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
Point clouds are a fundamental representation for robotic perception tasks such as localization, mapping, and object pose estimation. However, LiDAR-acquired point clouds are inherently sparse and non-uniform, providing incomplete…
This paper proposes an infeasible interior-point algorithm for the convex optimization problem using arc-search techniques. The proposed algorithm simultaneously selects the centering parameter and the step size, aiming at optimizing the…
The fusion of multi-source data is essential for a comprehensive analysis of geographic applications. Due to distinct data structures, the fusion process tends to encounter technical difficulties in terms of preservation of the intactness…
We introduce cilantro, an open-source C++ library for geometric and general-purpose point cloud data processing. The library provides functionality that covers low-level point cloud operations, spatial reasoning, various methods for point…
Polygonal modeling is a core task of content creation in Computer Graphics. The complexity of modeling, in terms of the number and the order of operations and time required to execute them makes it challenging to learn and execute. Our goal…
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…