Related papers: Approximate Hausdorff Distance for Multi-Vector Da…
We study the computational complexity of determining the Hausdorff distance of two polytopes given in halfspace- or vertex-presentation in arbitrary dimension. Subsequently, a matching problem is investigated where a convex body is allowed…
Approximate nearest neighbour (ANN) search has become a central task in modern data-intensive applications, particularly when operating on large, heterogeneous, or high-dimensional datasets. However, many existing ANN methods struggle in…
We investigate the computational complexity of computing the Hausdorff distance. Specifically, we show that the decision problem of whether the Hausdorff distance of two semi-algebraic sets is bounded by a given threshold is complete for…
Reliable quality assessment of decoded point cloud geometry is essential to evaluate the compression performance of emerging point cloud coding solutions and guarantee some target quality of experience. This paper proposes a novel point…
The distance matrix of a dataset $X$ of $n$ points with respect to a distance function $f$ represents all pairwise distances between points in $X$ induced by $f$. Due to their wide applicability, distance matrices and related families of…
To measure the shape similarity of point sets, various notions of the Hausdorff distance under translation are widely studied. In this context, for an $n$-point set $P$ and $m$-point set $Q$ in $\mathbb{R}^d$, we consider the task of…
Distance function to a compact set plays a central role in several areas of computational geometry. Methods that rely on it are robust to the perturbations of the data by the Hausdorff noise, but fail in the presence of outliers. The…
Given a compact basic semi-algebraic set we provide a numerical scheme to approximate as closely as desired, any finite number of moments of the Hausdorff measure on the boundary of this set. This also allows one to approximate interesting…
We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-matching setup, each point in the smaller set is matched to a…
We consider a similarity measure between two sets $A$ and $B$ of vectors, that balances the average and maximum cosine distance between pairs of vectors, one from set $A$ and one from set $B$. As a motivation for this measure, we present…
A clustering algorithm based on the Hausdorff distance is introduced and compared to the single and complete linkage. The three clustering procedures are applied to a toy example and to the time series of financial data. The dendrograms are…
Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries and present a simple, fast, and highly practical data…
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…
For given $\epsilon>0$ and $b\in\mathbb{R}^m$, we say that a real $m\times n$ matrix $A$ is $\epsilon$-badly approximable for the target $b$ if $$\liminf_{q\in\mathbb{Z}^n, \|q\|\to\infty} \|q\|^n \langle Aq-b \rangle^m \geq \epsilon,$$…
Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm…
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…
The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…
Edit distance similarity search, also called approximate pattern matching, is a fundamental problem with widespread database applications. The goal of the problem is to preprocess $n$ strings of length $d$, to quickly answer queries $q$ of…
Large-scale approximate nearest neighbor search (ANN) has been gaining attention along with the latest machine learning researches employing ANNs. If the data is too large to fit in memory, it is necessary to search for the most similar…
Fast k-Nearest Neighbor search over real-valued vector spaces (KNN) is an important algorithmic task for information retrieval and recommendation systems. We present a method for using reduced precision to represent vectors through…