2D Subquadratic Separable Distance Transformation for Path-Based Norms

David Coeurjolly 1, *
* Corresponding author
1 M2DisCo - Geometry Processing and Constrained Optimization
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : In many applications, separable algorithms have demon- strated their efficiency to perform high performance volumetric com- putations, such as distance transformation or medial axis extraction. In the literature, several authors have discussed about the 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 to path based norms (chamfer masks, neighborhood sequences, ...), we detail a subquadratic algorithm to compute such volumetric transformations in dimension 2. More precisely, we describe a O(log2 m · N2) algorithm in dimension 2 for shapes in a N × N domain with chamfer norm of size m.
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David Coeurjolly. 2D Subquadratic Separable Distance Transformation for Path-Based Norms. 18th International Conference on Discrete Geometry for Computer Imagery, Sep 2014, Siena, Italy. pp.75-87. ⟨hal-01118477⟩

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