Abstract

Temporal alignment of human motion has been a topic of recent interest due to its applications in animation, telerehabilitation and activity recognition among others. This paper presents generalized time warping (GTW), an extension of dynamic time warping (DTW) for temporally aligning multi-modal sequences from multiple subjects performing similar activities. GTW solves three major drawbacks of existing approaches based on DTW: (1) GTW provides a feature weighting layer to adapt different modalities (e.g., video and motion capture data), (2) GTW extends DTW by allowing a more flexible time warping as combination of monotonic functions, (3) unlike DTW that typically incurs in quadratic cost, GTW has linear complexity. Experimental results demonstrate that GTW can efficiently solve the multi-modal temporal alignment problem and outperforms state-of-the-art DTW methods for temporal alignment of time series within the same modality.

Highlights

  • Alignment of time series is an important unsolved problem in many scientific disciplines

  • canonical time warping (CTW) and dynamic manifold warping (DMW) have three main limitations due to reliance in dynamic time warping (DTW): (1) Their computational complexity is quadratic in space and time; (2) They address the problem of aligning two sequences, and it is unclear how to extend it to the alignment of multiple sequences; (3) They compute the temporal alignment using DTW, which relies on dynamic programming to find the optimal path; it is unclear how to adaptively constrain the temporal warping

  • There are three major limitations of using DTW to align multi-modal and multi-dimensional time series: (1) DTW relies on dynamic programming (DP) to exhaustively search over all possible warping paths

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Summary

Introduction

Alignment of time series is an important unsolved problem in many scientific disciplines. CTW and DMW have three main limitations due to reliance in DTW: (1) Their computational complexity is quadratic in space and time; (2) They address the problem of aligning two sequences, and it is unclear how to extend it to the alignment of multiple sequences; (3) They compute the temporal alignment using DTW, which relies on dynamic programming to find the optimal path; it is unclear how to adaptively constrain the temporal warping To overcome these limitations, this paper proposes generalized time warping (GTW), which allows an efficient and flexible alignment between two or more multi-dimensional time series of different modalities.

Previous work
Dynamic time warping
Generalized time warping
Objective function
Experiments
Synthetic dataset
Findings
Conclusions
Full Text
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