New sequential exact Euclidean distance transform algorithms based on convex analysis

Authors:
Yves Lucet
Affiliations:
Computer Science, I. K. Barber School of Arts and Sciences, University of British Columbia Okanagan, 3333 University Way, Kelowna, BC, Canada V1V 1V7
Venue:
Image and Vision Computing
Year:
2009

Citing 15
Cited 1

Distance transformations in digital images

Computer Vision, Graphics, and Image Processing
A fast algorithm for Euclidean distance maps of a 2-D binary image

Information Processing Letters
A fast Legendre transform algorithm and applications to the adhesion model

Journal of Scientific Computing
Fast Legendre--Fenchel Transform and Applications to Hamilton--Jacobi Equations and Conservation Laws

SIAM Journal on Numerical Analysis
A fast computational algorithm for the Legendre-Fenchel transform

Computational Optimization and Applications
Sequential Operations in Digital Picture Processing

Journal of the ACM (JACM)
Fast visualization of plane-like structures in voxel data

Proceedings of the conference on Visualization '02
Linear Time Euclidean Distance Algorithms

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Time Algorithm for Computing Exact Euclidean Distance Transforms of Binary Images in Arbitrary Dimensions

IEEE Transactions on Pattern Analysis and Machine Intelligence
Distance transformation and skeletonization of 3D pictures and their applications to medical images

Digital and image geometry
Fast Euclidean distance transformation in two scans using a 3 × 3 neighborhood

Computer Vision and Image Understanding
A Linear Euclidean Distance Transform Algorithm Based on the Linear-Time Legendre Transform

CRV '05 Proceedings of the 2nd Canadian conference on Computer and Robot Vision
Signed Distance Transform Using Graphics Hardware

Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Fast and exact signed Euclidean distance transformation with linear complexity

ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 06
An efficient euclidean distance transform

IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis

What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications

SIAM Review

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present several sequential exact Euclidean distance transform algorithms. The algorithms are based on fundamental transforms of convex analysis: The Legendre Conjugate or Legendre-Fenchel transform, and the Moreau envelope or Moreau-Yosida approximate. They combine the separability of the Euclidean distance with convex properties to achieve an optimal linear-time complexity. We compare them with a Parabolic Envelope distance transform, and provide several extensions. All the algorithms presented perform equally well in higher dimensions. They can naturally handle grayscale images, and their principles are generic enough to apply to other transforms.