  The inevitable noise in real measurements motivates the problem to
continuously quantify the similarity between rigid objects such as periodic
time series and proteins given by ordered points and considered up to isometry
maintaining inter-point distances. The past work produced many Hausdorff-like
distances that have slow or approximate algorithms due to minimizations over
infinitely many isometries. For finite and 1-periodic sequences under isometry
in any high-dimensional Euclidean space, we introduce continuous metrics with
faster algorithms. The key novelty in the periodic case is the continuity of
new metrics under perturbations that change the minimum period.
