Related papers: Nonlinear Mapping and Distance Geometry
The Maximally Diverse Grouping Problem (MDGP) is the problem of assigning a set of elements to mutually disjoint groups in order to maximise the overall diversity between the elements. Because the MDGP is NP-complete, most studies have…
This paper presents an optimization-based solution to task and motion planning (TAMP) on mobile manipulators. Logic-geometric programming (LGP) has shown promising capabilities for optimally dealing with hybrid TAMP problems that involve…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Given a graph $G$, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of $G$ with the maximum number of edges. There are several heuristic, approximative, and exact algorithms to tackle the problem, but---to the…
In this paper, we address the challenge of solving large-scale graph-structured nonlinear programs (gsNLPs) in a scalable manner. GsNLPs are problems in which the objective and constraint functions are associated with nodes on a graph and…
We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient discretisation method (GDM). GDM is a unified convergence…
Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…
Local learning of sparse image models has proven to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean…
We propose unsupervised representation learning and feature extraction from dendrograms. The commonly used Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level…
Given a set of $n$ terminals, which are points in $d$-dimensional Euclidean space, the minimum Manhattan network problem (MMN) asks for a minimum-length rectilinear network that connects each pair of terminals by a Manhattan path, that is,…
In this paper, we leverage the properties of non-Euclidean Geometry to define the Geodesic distance (GD) on the space of statistical manifolds. The Geodesic distance is a real and intuitive similarity measure that is a good alternative to…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…
An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
The main contribution of this paper is a new submap joining based approach for solving large-scale Simultaneous Localization and Mapping (SLAM) problems. Each local submap is independently built using the local information through solving a…
Consider a set $P$ of $n$ points in $\mathbb{R}^d$. In the discrete median line segment problem, the objective is to find a line segment bounded by a pair of points in $P$ such that the sum of the Euclidean distances from $P$ to the line…
Small object segmentation, like tumor segmentation, is a difficult and critical task in the field of medical image analysis. Although deep learning based methods have achieved promising performance, they are restricted to the use of binary…
This paper introduces a novel method to estimate distance fields from noisy point clouds using Gaussian Process (GP) regression. Distance fields, or distance functions, gained popularity for applications like point cloud registration,…
A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon…
Estimating the absolute orientation of a local system relative to a global navigation satellite system (GNSS) reference often suffers from local minima and high dependency on satellite availability. Existing methods for this alignment task…