A Linear Euclidean Distance Transform Algorithm Based on the Linear-Time Legendre Transform

Authors:
Yves Lucet
Affiliations:
University of British Columbia - Okanagan Campus, Okanagan University College, Canada
Venue:
CRV '05 Proceedings of the 2nd Canadian conference on Computer and Robot Vision
Year:
2005

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Abstract

We introduce a new exact Euclidean distance transform algorithm for binary images based on the Linear-time Legendre Transform algorithm. The three-step algorithm uses dimension reduction and convex analysis results on the Legendre-Fenchel transform to achieve linear-time complexity. First, computation on a grid (the image) is reduced to computation on a line, then the convex envelope is computed, and finally the squared Euclidean distance transform is obtained. Examples and an extension to non-binary images are provided.