An Image Understanding System Using Attributed Symbolic Representation and Inexact Graph-Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the representation and estimation of spatial uncertainly
International Journal of Robotics Research
Tracking and data association
Simple fast algorithms for the editing distance between trees and related problems
SIAM Journal on Computing
Object recognition by computer: the role of geometric constraints
Object recognition by computer: the role of geometric constraints
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
On the editing distance between unordered labeled trees
Information Processing Letters
Voronoi diagrams of polygons: a framework for shape representation
Journal of Mathematical Imaging and Vision
The spatial semantic hierarchy
Artificial Intelligence
Mobile Robot Relocation from Echolocation Constraints
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robot Motion Planning
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
FastSLAM: a factored solution to the simultaneous localization and mapping problem
Eighteenth national conference on Artificial intelligence
A shock grammar for recognition
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Towards a general theory of topological maps
Artificial Intelligence
Recognition of Shapes by Editing Their Shock Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient computation of continuous skeletons
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Spatial Representation and Reasoning for Robot Mapping: A Shape-Based Approach
Spatial Representation and Reasoning for Robot Mapping: A Shape-Based Approach
Matching Annotated Generalized Voronoi Graphs for Autonomous Robot Localization and Mapping
ISVD '09 Proceedings of the 2009 Sixth International Symposium on Voronoi Diagrams
Hierarchical Voronoi Graphs: Spatial Representation and Reasoning for Mobile Robots
Hierarchical Voronoi Graphs: Spatial Representation and Reasoning for Mobile Robots
Specification of an ontology for route graphs
SC'04 Proceedings of the 4th international conference on Spatial Cognition: reasoning, Action, Interaction
Autonomous construction of hierarchical voronoi-based route graph representations
SC'04 Proceedings of the 4th international conference on Spatial Cognition: reasoning, Action, Interaction
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In this article, we develop a localization and map building approach for a mobile robot in which annotated generalized Voronoi graphs are used as the robot's spatial representation of the environment. The core of our approach is a matching scheme for solving the data association problem of identifying corresponding parts in two tree-formed Voronoi graphs, one representing a local observation and the other one representing the robot's internal map. Our approach is based on the notion of edit distance which means it computes the cost optimal way to transform both graphs into the same graph. The costs for adding or deleting branches are based on a measure that assesses the stability of nodes and edges in the graphs as well as their relevance for navigation. In addition, we incorporate spatial constraints based on the graph annotations which leads to a top-down dynamic programming implementation that performs reliably and efficiently in practice.