Computer Vision, Graphics, and Image Processing
Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological methods in image and signal processing
Morphological methods in image and signal processing
A note on “distance transformations in digital images"
Computer Vision, Graphics, and Image Processing
Decomposition of gray-scale morphological structuring elements
Pattern Recognition
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance
Journal of the ACM (JACM)
Digital Picture Processing
A mathematical morphology approach to Euclidean distance transformation
IEEE Transactions on Image Processing
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A distance transformation converts a digital binary image that consists of object (foreground) and nonobject (background) pixels into a gray-level image in which all object pixels have a value corresponding to the minimum distance from the background. Computing the distance from a pixel to a set of background pixels is in principle a global operation that is often prohibitively costly. The Euclidean distance measurement is very useful in object recognition and inspection because of the metric accuracy and rotation invariance. However, its global operation is difficult to decompose into small neighborhood operations because of the nonlinearity of Euclidean distance computation. This paper presents three algorithms for Euclidean distance transformation in digital images by the use of the grayscale morphological erosion with the squared Euclidean distance structuring element. The optimal algorithm requires only four erosions by small structuring components and is independent of the object size. It can be implemented in parallel and is very efficient in computation because only the integer is used until the last step of a square-root operation.