Efficient Distance Transformation for Path-based Metrics
Résumé
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 $O(n\cdot N^n\cdot\log{N}\cdot(n+\log f))$
algorithm for shapes in a $N^n$ domain
for chamfer norms with a rational ball of $f$ facets (compared to
$O(f^{\lfloor\frac{n}{2}\rfloor}\cdot N^n)$ with previous
approaches). Last we further investigate an even more elaborate
algorithm with the same worst-case complexity, but reaching a
complexity of $O(n\cdot N^n\cdot\log{f}\cdot(n+\log f))$ experimentally,
under assumption of regularity distribution of the mask vectors.
Origine : Fichiers produits par l'(les) auteur(s)
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