Translation Invariant Fréchet Distance Queries

02/11/2021

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by   Joachim Gudmundsson, et al.

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The Fréchet distance is a popular similarity measure between curves. For some applications, it is desirable to match the curves under translation before computing the Fréchet distance between them. This variant is called the Translation Invariant Fréchet distance, and algorithms to compute it are well studied. The query version, however, is much less well understood. We study Translation Invariant Fréchet distance queries in a restricted setting of horizontal query segments. More specifically, we prepocess a trajectory in O(n^2 log^2 n) time and space, such that for any subtrajectory and any horizontal query segment we can compute their Translation Invariant Fréchet distance in O(polylog n) time. We hope this will be a step towards answering Translation Invariant Fréchet queries between arbitrary trajectories.