  In this work, we explore the problem of aligning two time-ordered point
clouds which are spatially transformed and re-parameterized versions of each
other. This has a diverse array of applications such as cross modal time series
synchronization (e.g. MOCAP to video) and alignment of discretized curves in
images. Most other works that address this problem attempt to jointly uncover a
spatial alignment and correspondences between the two point clouds, or to
derive local invariants to spatial transformations such as curvature before
computing correspondences. By contrast, we sidestep spatial alignment
completely by using self-similarity matrices (SSMs) as a proxy to the
time-ordered point clouds, since self-similarity matrices are blind to
isometries and respect global geometry. Our algorithm, dubbed "Isometry Blind
Dynamic Time Warping" (IBDTW), is simple and general, and we show that its
associated dissimilarity measure lower bounds the L1 Gromov-Hausdorff distance
between the two point sets when restricted to warping paths. We also present a
local, partial alignment extension of IBDTW based on the Smith Waterman
algorithm. This eliminates the need for tedious manual cropping of time series,
which is ordinarily necessary for global alignment algorithms to function
properly.
