Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
An Efficient Uniform Cost Algorithm Applied to Distance Transforms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Fast Euclidean distance transformation by propagation using multiple neighborhoods
Computer Vision and Image Understanding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algorithmic Foundations of Geographic Information Systems, this book originated from the CISM Advanced School on the Algorithmic Foundations of Geographic Information Systems
Eighteenth national conference on Artificial intelligence
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
2D Euclidean distance transform algorithms: A comparative survey
ACM Computing Surveys (CSUR)
Incremental reconstruction of generalized Voronoi diagrams on grids
Robotics and Autonomous Systems
Efficient C-space and cost function updates in 3D for unmanned aerial vehicles
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Improved Techniques for Grid Mapping With Rao-Blackwellized Particle Filters
IEEE Transactions on Robotics
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In robotics, grid maps are often used for solving tasks like collision checking, path planning, and localization. Many approaches to these problems use Euclidean distance maps (DMs), generalized Voronoi diagrams (GVDs), or configuration space (c-space) maps. A key challenge for their application in dynamic environments is the efficient update after potential changes due to moving obstacles or when mapping a previously unknown area. To this end, this paper presents novel algorithms that perform incremental updates that only visit cells affected by changes. Furthermore, we propose incremental update algorithms for DMs and GVDs in the configuration space of non-circular robots. These approaches can be used to implement highly efficient collision checking and holonomic path planning for these platforms. Our c-space representations benefit from parallelization on multi-core CPUs and can also be integrated with other state-of-the-art path planners such as rapidly-exploring random trees. In various experiments using real-world data we show that our update strategies for DMs and GVDs require substantially less cell visits and computation time compared to previous approaches. Furthermore, we demonstrate that our GVD algorithm deals better with non-convex structures, such as indoor areas. All our algorithms consider actual Euclidean distances rather than grid steps and are easy to implement. An open source implementation is available online.