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