Céline Fouard

Weighted distance transforms generalized to modules and their computation on point lattices

This paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices. The first part is dedicated to formalization of definitions and properties (distance, metric, norm) of weighted distances on modules. It resumes tools found in literature to express the weighted distance of any point of a module and to compute optimal weights in the general case to get rotation invariant distances. The second part of this paper proves that, for any point lattice, the sequential two-scan chamfer algorithm produces correct distance maps. Finally, the definitions and computation of weighted distances are applied to the face-centered cubic (FCC) and body-centered cubic (BCC) grids.

An objective comparison between gray weighted distance transforms and weighted distance transforms on curved spaces

In this paper, we compare two different definitions of distance transform for gray level images: the Gray Weighted Distance Transform (GWDT), and the Weighted Distance Transform On Curved Space (WDTOCS) We show through theoretical and experimental comparisons the differences, the strengths and the weaknesses of these two distances.

Generating distance maps with neighbourhood sequences

A sequential algorithm for computing the distance map using distances based on neighbourhood sequences (of any length) in the 2D square grid; and 3D cubic, face-centered cubic, and body-centered cubic grids is presented Conditions for the algorithm to produce correct results are derived using a path-based approach Previous sequential algorithms for this task have been based on algorithms that compute the digital Euclidean distance transform It is shown that the latter approach is not well-suited for distances based on neighbourhood sequences.