Related papers: Trajectory Grouping with Curvature Regularization …
Acquiring plausible pathways on high-dimensional structural distributions is beneficial in several domains. For example, in the drug discovery field, a protein conformational pathway, i.e. a highly probable sequence of protein structural…
We present a novel clustering approach for moving object trajectories that are constrained by an underlying road network. The approach builds a similarity graph based on these trajectories then uses modularity-optimization hiearchical graph…
The search is based on the preliminary transformation of matrices or adjacency lists traditionally used in the study of graphs into projections cleared of redundant information (refined) followed by the selection of the desired shortest…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
In this chapter, we give an overview of part of our previous work based on the minimal path framework and the Eikonal partial differential equation (PDE). We show that by designing adequate Riemannian and Randers geodesic metrics the…
In this paper, we present a flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Merge trees are topological descriptors that record the…
Line segment detection is an essential task in computer vision and image analysis, as it is the critical foundation for advanced tasks such as shape modeling and road lane line detection for autonomous driving. We present a robust…
Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…
Minimal paths are regarded as a powerful and efficient tool for boundary detection and image segmentation due to its global optimality and the well-established numerical solutions such as fast marching method. In this paper, we introduce a…
Tree-like structures such as retinal images are widely studied in computer-aided diagnosis systems for large-scale screening programs. Despite several segmentation and tracking methods proposed in the literature, there still exist several…
We present a flexible discretization technique for computational models of thin tubular networks embedded in a bulk domain, for example a porous medium. These systems occur in the simulation of fluid flow in vascularized biological tissue,…
Accurate segmentation of tubular structures in medical images, such as vessels and airway trees, is crucial for computer-aided diagnosis, radiotherapy, and surgical planning. However, significant challenges exist in algorithm design when…
Curvilinear structures, which include line-like continuous objects, are fundamental geometrical elements in image-based applications. Reconstructing these structures from images constitutes a pivotal research area in computer vision.…
This paper presents a robust tracking controller for tracking curvature-constrained paths by vehicles/robots with uncertain Dubins dynamics. Although Dubins paths have been widely used in vehicular and robotic applications, robust and…
A Dubins path is a shortest path with bounded curvature. The seminal result in non-holonomic motion planning is that (in the absence of obstacles) a Dubins path consists either from a circular arc followed by a segment followed by another…
The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with…
Extracting complex structures from grid-based data is a common key step in automated medical image analysis. The conventional solution to recovering tree-structured geometries typically involves computing the minimal cost path through…
Detection of curvilinear structures in images has long been of interest. One of the most challenging aspects of this problem is inferring the graph representation of the curvilinear network. Most existing delineation approaches first…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and an iterative method for doing so in 3D space. Such a network will be…