Volume 27, 2021
|Number of page(s)||25|
|Published online||03 March 2021|
Average-distance problem with curvature penalization for data parameterization: regularity of minimizers
Department of Mathematics and Statistics, Lakehead University,
ON P7B5E1, Canada.
2 Department of Mathematical Sciences, McGill University, Montréal, QC H3A0B9, Canada.
3 Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
* Corresponding author: email@example.com
Accepted: 28 December 2020
We propose a model for finding one-dimensional structure in a given measure. Our approach is based on minimizing an objective functional which combines the average-distance functional to measure the quality of the approximation and penalizes the curvature, similarly to the elastica functional. Introducing the curvature penalization overcomes some of the shortcomings of the average-distance functional, in particular the lack of regularity of minimizers. We establish existence, uniqueness and regularity of minimizers of the proposed functional. In particular we establish C1,1 estimates on the minimizers.
Mathematics Subject Classification: 49Q20 / 49Q10 / 35B65
Key words: Average-distance problem / elastica functional / Willmore energy / curve fitting
© EDP Sciences, SMAI 2021
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