Self-Similarity Based Time Warping
This addresses alignment challenges in applications like MOCAP to video synchronization, offering a general solution that eliminates manual cropping, though it appears incremental as it builds on existing dynamic time warping concepts.
The paper tackles the problem of aligning time-ordered point clouds that are spatially transformed and re-parameterized, such as in cross-modal time series synchronization, by introducing a method that uses self-similarity matrices to sidestep spatial alignment, resulting in a simple algorithm called IBDTW that lower bounds the L1 Gromov-Hausdorff distance.
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.