Average Curve of n Digital Curves

  • Isabelle SivignonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)


Building on [23], we investigate the problem of defining and computing the average of digital curves. Given n digital curves that satisfy compatibility conditions, a set - called the gap - in which the average curve is looked for, is defined. The proposed definition rewrites the classical arithmetic mean for curves by (i) defining the distance between each point of the gap and its projection on each curve and (ii) computing the points that minimize the sum of squared deviations. We show that, algorithmically speaking, computing such projections comes down to computing a distance transform with visibility constraints. We propose a fast algorithm to compute a good approximation of these distance maps and finally show that the average curve can be obtained using classical watershed algorithm.


Digital curves Arithmetic mean Distance transform Visibility 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-LabGrenobleFrance

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