The 2nd Canadian Conference on Computer and Robot Vision (CRV'05)
A Linear Euclidean Distance Transform Algorithm Based on the Linear-Time Legendre Transform
The University of Victoria, Victoria, British Columbia, Canada
May 09-May 11
ISBN: 0-7695-2319-6
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.