Computing distance transformations in convex and non-convex domains
Pattern Recognition
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)
Distance transforms: properties and machine vision applications
CVGIP: Graphical Models and Image Processing
Thinning Methodologies-A Comprehensive Survey
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neighborhoods for distance transformations using ordered propagation
CVGIP: Image Understanding
The Euclidean distance transform in arbitrary dimensions
Pattern Recognition Letters
A unified distance transform algorithm and architecture
Machine Vision and Applications
A fast algorithm for Euclidean distance maps of a 2-D binary image
Information Processing Letters
A unified linear-time algorithm for computing distance maps
Information Processing Letters
On digital distance transforms in three dimensions
Computer Vision and Image Understanding
A List-Processing Approach to Compute Voronoi Diagrams and the Euclidean Distance Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
Two fast Euclidean distance transformations in Z2 based on sufficient propagation
Computer Vision and Image Understanding
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
A Euclidean Distance Transform Using Grayscale Morphology Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Classification of the Distance Transformation Algorithms under the Mathematical Morphology Approach
SIBGRAPI '00 Proceedings of the 13th Brazilian Symposium on Computer Graphics and Image Processing
Fast Multidimensional Parallel Euclidean Distance Transform Based on Mathematical Morphology
SIBGRAPI '01 Proceedings of the 14th Brazilian Symposium on Computer Graphics and Image Processing
Weighted digital distance transforms in four dimensions
Discrete Applied Mathematics
The Image Foresting Transform: Theory, Algorithms, and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Euclidean distance transformation in two scans using a 3 × 3 neighborhood
Computer Vision and Image Understanding
Signed Distance Transform Using Graphics Hardware
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
3D Distance Fields: A Survey of Techniques and Applications
IEEE Transactions on Visualization and Computer Graphics
2D Euclidean distance transform algorithms: A comparative survey
ACM Computing Surveys (CSUR)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Information Geometry for Landmark Shape Analysis: Unifying Shape Representation and Deformation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Distance transforms for three-dimensional grids with non-cubic voxels
Computer Vision and Image Understanding
Parallel Banding Algorithm to compute exact distance transform with the GPU
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
Distance-Driven Skeletonization in Voxel Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Euclidean distance transform using perpendicular bisector segmentation
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
The efficient algorithms for achieving Euclidean distance transformation
IEEE Transactions on Image Processing
A mathematical morphology approach to Euclidean distance transformation
IEEE Transactions on Image Processing
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In this paper, we propose an efficient algorithm, i.e., PBEDT, for short, to compute the exact Euclidean distance transform (EDT) of a binary image in arbitrary dimensions. The PBEDT is based on independent scan and implemented in a recursive way, i.e., the EDT of a d-dimensional image is able to be computed from the EDTs of its (d-1)-dimensional sub-images. In each recursion, all of the rows in the current dimensional direction are processed one by one. The points in the current processing row and their closest feature points in (d-1)-dimensional sub-images can be shown in a Euclidean plane. By using the geometric properties of the perpendicular bisector, the closest feature points of (d-1)-dimensional sub-images are easily verified so as to lead to the EDT of a d-dimensional image after eliminating the invalid points. The time complexity of the PBEDT algorithm is linear in the amount of both image points and dimensions with a small coefficient. Compared with the state-of-the-art EDT algorithms, the PBEDT algorithm is much faster and more stable in most cases.