Related papers: ProHD: Projection-Based Hausdorff Distance Approxi…
The Hausdorff distance is a metric commonly used to compute the set similarity of geometric sets. For sets containing a total of $n$ points, the exact distance can be computed na\"{i}vely in $O(n^2)$ time. In this paper, we show how to…
The Hausdorff distance is a fundamental measure for comparing sets of vectors, widely used in database theory and geometric algorithms. However, its exact computation is computationally expensive, often making it impractical for large-scale…
We consider the directed Hausdorff distance between point sets in the plane, where one or both point sets consist of imprecise points. An imprecise point is modelled by a disc given by its centre and a radius. The actual position of an…
The Hausdorff distance is a fundamental metric with widespread applications across various fields. However, its computation remains computationally expensive, especially for large-scale datasets. In this work, we present RT-HDIST, the first…
The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
We introduce PHD, a novel approach for personalized 3D human mesh recovery (HMR) and body fitting that leverages user-specific shape information to improve pose estimation accuracy from videos. Traditional HMR methods are designed to be…
Computing the similarity of two point sets is a ubiquitous task in medical imaging, geometric shape comparison, trajectory analysis, and many more settings. Arguably the most basic distance measure for this task is the Hausdorff distance,…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
Graph similarity metrics serve far-ranging purposes across many domains in data science. As graph datasets grow in size, scientists need comparative tools that capture meaningful differences, yet are lightweight and scalable. Graph Relative…
The Hough transform (HT) is a fundamental tool across various domains, from classical image analysis to neural networks and tomography. Two key aspects of the algorithms for computing the HT are their computational complexity and accuracy -…
Estimating the 3D pose of an object is a challenging task that can be considered within augmented reality or robotic applications. In this paper, we propose a novel approach to perform 6 DoF object pose estimation from a single RGB-D image.…
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…
Digital fringe projection (DFP) enables micrometer-level 3D reconstruction, yet extending it to large-scale mapping remains challenging because six-degree-of-freedom pose estimation often cannot match the reconstruction's precision.…
The Hausdorff Distance (HD) is widely used in evaluating medical image segmentation methods. However, existing segmentation methods do not attempt to reduce HD directly. In this paper, we present novel loss functions for training…
The Progressive-X algorithm, Prog-X in short, is proposed for geometric multi-model fitting. The method interleaves sampling and consolidation of the current data interpretation via repetitive hypothesis proposal, fast rejection, and…
We prove that, for every norm on $\mathbb{R}^d$ and every $E \subseteq \mathbb{R}^d$, the Hausdorff dimension of the distance set of $E$ with respect to that norm is at least $\dim_{\mathrm{H}} E - (d-1)$. An explicit construction follows,…
Approximate K Nearest Neighbor (AKNN) search in high-dimensional spaces is a critical yet challenging problem. In AKNN search, distance computation is the core task that dominates the runtime. Existing approaches typically use approximate…
Distance-based metrics, such as the Hausdorff distance (HD), are widely used to validate segmentation performance in (bio)medical imaging. However, their implementation is complex, and critical differences across open-source tools remain…