Rejoinder to 'multivariate functional outlier detection'

First of all we would like to thank the editor, Professor Andrea Cerioli, for inviting us to submit our work and for requesting comments from some esteemed colleagues. We were surprised by the number of invited comments and grateful to their contributing authors, all of whom raised important points and/or offered valuable suggestions. We are happy for the opportunity to rejoin the discussion. Rather than addressing the comments in turn we will organize our rejoinder by topic, starting with comments directly related to concepts we proposed in the paper and continuing with some extensions.