Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
Distance transforms: properties and machine vision applications
CVGIP: Graphical Models and Image Processing
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Fast Euclidean distance transformation by propagation using multiple neighborhoods
Computer Vision and Image Understanding
On Computing the Exact Euclidean Distance Transform on Rectangular and Hexagonal Grids
Journal of Mathematical Imaging and Vision
A quadtree medial axis transform
Communications of the ACM
Multidimensional binary search trees used for associative searching
Communications of the ACM
Thinning algorithms on rectangular, hexagonal, and triangular arrays
Communications of the ACM
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Quantitative Assessment of Two Skeletonization Algorithms Adapted to Rectangular Grids
ICIAP '97 Proceedings of the 9th International Conference on Image Analysis and Processing-Volume I - Volume I
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Weighted distance transforms for volume images digitized in elongated voxel grids
Pattern Recognition Letters - Special issue: Discrete geometry for computer imagery (DGCI'2002)
A Skeletonization Algorithm Using Chamfer Distance Transformation Adapted to Rectangular Grids
ICPR '96 Proceedings of the 13th International Conference on Pattern Recognition - Volume 2
IEEE Transactions on Pattern Analysis and Machine Intelligence
Weighted distances based on neighbourhood sequences
Pattern Recognition Letters
IEEE Transactions on Computers
2D Euclidean distance transform algorithms: A comparative survey
ACM Computing Surveys (CSUR)
Finding a minimum medial axis of a discrete shape is NP-hard
Theoretical Computer Science
Distance transforms for three-dimensional grids with non-cubic voxels
Computer Vision and Image Understanding
3-D chamfer distances and norms in anisotropic grids
Image and Vision Computing
Thinning algorithms based on quadtree and octree representations
Information Sciences: an International Journal
Distance map based enhancement for interpolated images
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Distance transformation on two-dimensional irregular isothetic grids
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Thinning on quadratic, triangular, and hexagonal cell complexes
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
A novel algorithm for distance transformation on irregular isothetic grids
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
A comparison among distances based on neighborhood sequences in regular grids
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Topological and geometrical reconstruction of complex objects on irregular isothetic grids
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
The delaunay triangulation by grid subdivision
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Separable algorithms for distance transformations on irregular grids
Pattern Recognition Letters
Unsupervised polygonal reconstruction of noisy contours by a discrete irregular approach
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
A combined multi-scale/irregular algorithm for the vectorization of noisy digital contours
Computer Vision and Image Understanding
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In this article, we propose a new fast algorithm to compute the squared Euclidean distance transform (E^2DT) on every two-dimensional (2-D) irregular isothetic grids (regular square grids, quadtree based grids, etc.). Our new fast algorithm is an extension of the E^2DT method proposed by Breu et al. [3]. It is based on the implicit order of the cells in the grid, and builds a partial Voronoi diagram of the centers of background cells thanks to a data structure of lists. We compare the execution time of our method with the ones of others approaches we developed in previous works. In those experiments, we consider various kinds of classical 2-D grids in imagery to show the interest of our methodology, and to point out its robustness. We also show that our method may be interesting regarding an application where we extract an adaptive medial axis construction based on a quadtree decomposition scheme.