A linear-time algorithm for Euclidean feature transform sets

Hesselink, Wim H.

doi:10.1016/j.ipl.2006.12.005

Cited by 11 publications

(5 citation statements)

References 13 publications

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“…Computational algorithms for the exact Euclidean distance transform (EDT) appeared later [4,[8][9][10][11][12][13][14], and several linear-time algorithms are now known. Current research focuses on providing simpler algorithms, now that we have a better understanding of the properties of the EDT, and on extending the distance transform to a more general setting [6,10,[13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

New sequential exact Euclidean distance transform algorithms based on convex analysis

Lucet

2009

Image and Vision Computing

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Section: Introductionmentioning

confidence: 99%

New sequential exact Euclidean distance transform algorithms based on convex analysis

Lucet

2009

Image and Vision Computing

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“…In the following, we focus on the restricted Voronoi map computation and we may omit the word restricted for the sake of clarity. Interested readers may refer to (Couprie et al, 2007;Hesselink, 2007) for separable algorithms to compute the complete Voronoi map of Definition 1.…”

Section: Metric Space and Distance Transformationmentioning

confidence: 99%

Efficient distance transformation for path-based metrics

Cœurjolly

Sivignon

2020

Computer Vision and Image Understanding

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In many applications, separable algorithms have demonstrated their efficiency to perform high performance volumetric processing of shape, such as distance transformation or medial axis extraction. In the literature, several authors have discussed about conditions on the metric to be considered in a separable approach. In this article, we present generic separable algorithms to efficiently compute Voronoi maps and distance transformations for a large class of metrics. Focusing on path-based norms (chamfer masks, neighborhood sequences), we propose efficient algorithms to compute such volumetric transformation in dimension n. We describe a new O(n • N n • log N • (n + log f)) algorithm for shapes in a N n domain for chamfer norms with a rational ball of f facets (compared to O(f n 2 • N n) with previous approaches). Last we further investigate a more elaborate algorithm with the same worst-case complexity, but reaching a complexity of O(n • N n • log f • (n + log f)) experimentally, under assumption of regularity distribution of the mask vectors.

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“…Several algorithms [39,46,54,64,173,238,112] were introduced to compute the Euclidean Distance Transform (EDT), and the performance of some of them were recently compared [79]. Recent research focuses on simplifying the algorithms while still achieving linear-time complexity.…”

Section: Network Flowmentioning

confidence: 99%

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

Lucet¹

2010

SIAM Rev.

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Abstract. Computational Convex Analysis algorithms have been rediscovered several times in the past by researchers from different fields. To further communications between practitioners, we review the field of Computational Convex Analysis, which focuses on the numerical computation of fundamental transforms arising from convex analysis. Current models use symbolic, numeric, and hybrid symbolic-numeric algorithms. Our objective is to disseminate widely the most efficient numerical algorithms useful for applications in image processing (computing the distance transform, the generalized distance transform, and mathematical morphology operators), partial differential equations (solving Hamilton-Jacobi equations, and using differential equations numerical schemes to compute the convex envelope), max-plus algebra (computing the equivalent of the Fast Fourier Transform), multi-fractal analysis, etc. The fields of applications include, among others, computer vision, robot navigation, thermodynamics, electrical networks, medical imaging, and network communication.

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A linear-time algorithm for Euclidean feature transform sets

Cited by 11 publications

References 13 publications

New sequential exact Euclidean distance transform algorithms based on convex analysis

New sequential exact Euclidean distance transform algorithms based on convex analysis

Efficient distance transformation for path-based metrics

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

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