Related papers: Delaunay-Rips filtration: a study and an algorithm

We consider the problem of maintaining the Euclidean Delaunay triangulation $\DT$ of a set $P$ of $n$ moving points in the plane, along algebraic trajectories of constant description complexity. Since the best known upper bound on the…

Reconstruction of a continuous surface of two-dimensional manifold from its raw, discrete point cloud observation is a long-standing problem. The problem is technically ill-posed, and becomes more difficult considering that various sensing…

As a popular representation of 3D data, point cloud may contain noise and need to be filtered before use. Existing point cloud filtering methods either cannot preserve sharp features or result in uneven point distribution in the filtered…

Point cloud registration is a fundamental problem in computer vision that aims to estimate the transformation between corresponding sets of points. Non-rigid registration, in particular, involves addressing challenges including various…

Complex heterogeneous dynamic networks like knowledge graphs are powerful constructs that can be used in modeling data provenance from computer systems. From a security perspective, these attributed graphs enable causality analysis and…

Iterative Closest Point (ICP) solves the rigid point cloud registration problem iteratively in two steps: (1) make hard assignments of spatially closest point correspondences, and then (2) find the least-squares rigid transformation. The…

Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in…

In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology,…

Existing position based point cloud filtering methods can hardly preserve sharp geometric features. In this paper, we rethink point cloud filtering from a non-learning non-local non-normal perspective, and propose a novel position based…

DUSt3R has recently shown that one can reduce many tasks in multi-view geometry, including estimating camera intrinsics and extrinsics, reconstructing the scene in 3D, and establishing image correspondences, to the prediction of a pair of…

Navigation of mobile robots within crowded environments is an essential task in various use cases, such as delivery, health care, or logistics. Deep Reinforcement Learning (DRL) emerged as an alternative method to replace overly…

Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…

Numerous remarkable advancements have been made in accuracy, speed, and parallelism for solving the Unmanned Aerial Vehicle Route Planing (UAVRP). However, existing UAVRP solvers face challenges when attempting to scale effectively and…

Deep recommender systems (DRS) often face challenges in balancing computational efficiency and model accuracy, especially when handling high-dimensional input features. Existing methods either focus on improving accuracy while neglecting…

Estimation of interface curvature in surface-tension dominated flows is a remaining challenge in Volume of Fluid (VOF) methods. Data-driven methods are recently emerging as a promising alternative in this domain. They outperform…

The cost volume, capturing the similarity of possible correspondences across two input images, is a key ingredient in state-of-the-art optical flow approaches. When sampling correspondences to build the cost volume, a large neighborhood…

We study the problem of extracting correspondences between a pair of point clouds for registration. For correspondence retrieval, existing works benefit from matching sparse keypoints detected from dense points but usually struggle to…

We present DeepICP - a novel end-to-end learning-based 3D point cloud registration framework that achieves comparable registration accuracy to prior state-of-the-art geometric methods. Different from other keypoint based methods where a…

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…

Although remarkable progress has been made on single image super-resolution due to the revival of deep convolutional neural networks, deep learning methods are confronted with the challenges of computation and memory consumption in…