Related papers: GraphWalks: Efficient Shape Agnostic Geodesic Shor…

Geodesic problems involve computing trajectories between prescribed initial and final states to minimize a user-defined measure of distance, cost, or energy. They arise throughout physics and engineering -- for instance, in determining…

A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. For a probability distribution, the length along a path between two points can be defined as the amount of probability mass accumulated…

Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…

Graph Convolutional Neural Networks (GCNNs) extend classical CNNs to graph data domain, such as brain networks, social networks and 3D point clouds. It is critical to identify an appropriate graph for the subsequent graph convolution.…

Geodesic models are known as an efficient tool for solving various image segmentation problems. Most of existing approaches only exploit local pointwise image features to track geodesic paths for delineating the objective boundaries.…

Geodesics are essential in many geometry processing applications. However, traditional algorithms for computing geodesic distances and paths on 3D mesh models are often inefficient and slow. This makes them impractical for scenarios that…

Many geometric machine learning and image analysis applications, require a left-invariant metric on the 5D homogeneous space of 3D positions and orientations SE(3)/SO(2). This is done in Equivariant Neural Networks (G-CNNs), or in PDE-Based…

Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it…

By "geodesic" we mean any sequence of vertices $(v_1,v_2,...,v_k)$ of a graph $G$ that constitute a shortest path from $v_1$ to $v_k$. We propose a novel, natural algorithm to enumerate all geodesics of $G$, and pit it (using Mathematica)…

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…

Graph Neural Networks (GNNs) have achieved tremendous success in a variety of real-world applications by relying on the fixed graph data as input. However, the initial input graph might not be optimal in terms of specific downstream tasks,…

We aim to solve the problem of data-driven collision-distance estimation given 3-dimensional (3D) geometries. Conventional algorithms suffer from low accuracy due to their reliance on limited representations, such as point clouds. In…

Sampling-based path planning is a widely used method in robotics, particularly in high-dimensional state space. Among the whole process of the path planning, collision detection is the most time-consuming operation. In this paper, we…

A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and…

Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…

Learned local descriptors based on Convolutional Neural Networks (CNNs) have achieved significant improvements on patch-based benchmarks, whereas not having demonstrated strong generalization ability on recent benchmarks of image-based 3D…

We give an accessible introduction and elaboration on the methods used in obtaining a geodesic, which is the curve of shortest length connecting two points lying on the surface of a function. This is found through computing what's known as…

Global Route-Planning Algorithms (GRPA) are required to compute paths between several points located on Earth's surface. A geodesic algorithm is employed as an auxiliary tool, increasing the precision of distance calculations. This work…

Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The state-of-the-art solutions for the problem can be…

Graph neural networks (GNNs) have recently become the standard approach for learning with graph-structured data. Prior work has shed light into their potential, but also their limitations. Unfortunately, it was shown that standard GNNs are…