When two 1D signals are compared, they must be represented in the same reference system. In most cases, biological signals present a big interindividual variability that should be eliminated in order to compare them properly. This variability can be erased by aligning the signals. A robust variational setting is proposed for 1D signal registration and applied to the computation of shape geodesics for shape classification issues. For validation purposes, experiments are carried out on real signals and shapes issued from marine biological archives which depict a high interindividual variability such that registration-based approaches are of particular interest.