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
Thinning Methodologies-A Comprehensive Survey
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximation of generalized Voronoi diagrams by ordinary Voronoi diagrams
CVGIP: Graphical Models and Image Processing
Efficient binary image thinning using neighborhood maps
Graphics gems IV
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
International Journal of Computer Vision
Constructing Area Voronoi Diagram in Document Images
ICDAR '05 Proceedings of the Eighth International Conference on Document Analysis and Recognition
Cell segmentation using coupled level sets and graph-vertex coloring
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Robust tracking of migrating cells using four-color level set segmentation
ACIVS'06 Proceedings of the 8th international conference on Advanced Concepts For Intelligent Vision Systems
Moving object segmentation using the flux tensor for biological video microscopy
PCM'07 Proceedings of the multimedia 8th Pacific Rim conference on Advances in multimedia information processing
Multiphase level set for automated delineation of membrane-bound macromolecules
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
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Many image segmentation approaches rely upon or are enhanced by using spatial relationship information between image regions and their object correspondences. Spatial relationships are usually captured in terms of relative neighborhood graphs such as the Delaunay graph. Neighborhood graphs capture information about which objects are close to each other in the plane or in space but may not capture complete spatial relationships such as containment or holes. Additionally, the typical approach used to compute the Delaunay graph (or its dual, the Voronoi polytopes) is based on using only the point-based (i.e., centroid) representation of each object. This can lead to incorrect spatial neighborhood graphs for sized objects with complex topology, eventually resulting in poor segmentation. This paper proposes a new algorithm for efficiently, and accurately extracting accurate neighborhood graphs in linear time by computing the Hamilton-Jacobi generalized Voronoi diagram (GVD) using the exact Euclidean-distance transform with Laplacian-of-Gaussian, and morphological operators. The algorithm is validated using synthetic, and real biological imagery of epithelial cells.