Comments on: Shape-based functional data analysis

The discussion focuses on the different choices that are made by the user in carrying out shape-based functional data analysis. First, there is the choice of an additional warping penalty that can be included in the procedure. An object-oriented data analysis approach can be useful for selecting such a warping penalty, and an example from monitoring peatland is given. Also, there is a choice to be made about whether the analysis is in a quotient manifold or an ambient space. There are advantages and disadvantages to either strategy, but in many examples, the results are similar due to a Laplace approximation. The final comment states that the authors provide plenty of convincing approaches with many useful insights. It is clear that the square root velocity function (SRVF) and transported SRVF methods will give solutions to many more problems in the future.