Minimal-Delay Distance Transform for Neighborhood-Sequence Distances in 2D and 3D

Nicolas Normand (1) , Robin Strand (2) , Pierre Evenou (1) , Aurore Arlicot (1)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 CBA - Centre for Image Analysis

This paper presents a path-based distance where local displacement costs vary both according to the displacement vector and with the travelled distance. The corresponding distance transform algorithm is similar in its form to classical propagation-based algorithms, but the more variable distance incre- ments are either stored in look-up-tables or computed on-the-fly. These distances and distance trans- form extend neighborhood-sequence distances, chamfer distances and generalized distances based on Minkowski sums. We introduce algorithms to compute a translated version of a neighborhood sequence distance map both for periodic and aperiodic sequences and a method to derive the centered distance map. A decomposition of the grid neighbors, in ℤ² and ℤ³, allows to significantly decrease the number of displacement vectors needed for the distance transform. Overall, the distance transform can be com- puted with minimal delay, without the need to wait for the whole input image before beginning to provide the result image.

Mots clés: Neighborhood-sequence distance; Minkowski Sum; Lambek-Moser inverse; Beatty sequence; Distance transform

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Nicolas Normand, Robin Strand, Pierre Evenou, Aurore Arlicot. Minimal-Delay Distance Transform for Neighborhood-Sequence Distances in 2D and 3D. Computer Vision and Image Understanding, 2013, 117 (4), pp.409-417. ⟨10.1016/j.cviu.2012.08.015⟩. ⟨hal-00765695⟩