Related papers: A Rank-based Convex Hull method for Dense Data Set…
Consider a random set of points on the unit sphere in $\mathbb{R}^d$, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the…
One of the main challenges for hierarchical clustering is how to appropriately identify the representative points in the lower level of the cluster tree, which are going to be utilized as the roots in the higher level of the cluster tree…
The pooling problem is a classical NP-hard problem in the chemical process and petroleum industries. This problem is modeled as a nonlinear, nonconvex network flow problem in which raw materials with different specifications are blended in…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
Computation of the vertices of the convex hull of a set $S$ of $n$ points in $\mathbb{R} ^m$ is a fundamental problem in computational geometry, optimization, machine learning and more. We present "All Vertex Triangle Algorithm" (AVTA), a…
In this paper we introduce a novel neural network architecture based on Fast Hough Transform layer. The layer of this type allows our neural network to accumulate features from linear areas across the entire image instead of local areas. We…
The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem…
Let $\mathcal{P}$ be the surface of a convex polyhedron with $n$ vertices. We consider the two-point shortest path query problem for $\mathcal{P}$: Constructing a data structure so that given any two query points $s$ and $t$ on…
In the framework of shape constrained estimation, we review methods and works done in convex set estimation. These methods mostly build on stochastic and convex geometry, empirical process theory, functional analysis, linear programming,…
This paper introduces a new method for 3D point cloud registration based on deep learning. The architecture is composed of three distinct blocs: (i) an encoder composed of a convolutional graph-based descriptor that encodes the immediate…
The goal of feature selection is to choose the optimal subset of features for a recognition task by evaluating the importance of each feature, thereby achieving effective dimensionality reduction. Currently, proposed feature selection…
This work presents a compact, cumulative and coalescible probabilistic voxel mapping method to enhance performance, accuracy and memory efficiency in LiDAR odometry. Probabilistic voxel mapping requires storing past point clouds and…
In this work, for a given oriented graph $D$, we study its interval and hull numbers, respectively, in the oriented geodetic, P3 and P3* convexities. This last one, we believe to be formally defined and first studied in this paper, although…
Point cloud registration is the task of estimating the rigid transformation that aligns a pair of point cloud fragments. We present an efficient and robust framework for pairwise registration of real-world 3D scans, leveraging Hough voting…
CAT(0) metric spaces and hyperbolic spaces play an important role in combinatorial and geometric group theory. In this paper, we present efficient algorithms for distance problems in CAT(0) planar complexes. First of all, we present an…
Let a polytope $P$ be defined by a system $A x \leq b$. We consider the problem of counting the number of integer points inside $P$, assuming that $P$ is $\Delta$-modular, where the polytope $P$ is called $\Delta$-modular if all the rank…
This paper studies the problem of enumerating all maximal collinear subsets of size at least three in a given set of $n$ points. An algorithm for this problem, besides solving degeneracy testing and the exact fitting problem, can also help…
Compressed indexing is a powerful technique that enables efficient querying over data stored in compressed form, significantly reducing memory usage and often accelerating computation. While extensive progress has been made for…
The convex hull peeling of a point set consists in taking the convex hull, then removing the extreme points and iterating that procedure until no point remains. The boundary of each hull is called a layer. Following on from [15], we study…
We consider the Minimum Convex Partition problem: Given a set P of n points in the plane, draw a plane graph G on P, with positive minimum degree, such that G partitions the convex hull of P into a minimum number of convex faces. We show…