TL;DR
This paper introduces a new variant of the continuous Fréchet distance that can be computed efficiently and produces more natural, noise-tolerant morphings between curves, improving practical applications.
Contribution
It presents a novel algorithm for a non-monotone Fréchet distance variant, enabling near-linear time computation and more natural morphings, with practical implementations and experiments.
Findings
Near-linear time computation on many inputs
More natural and noise-tolerant morphings
Open-source Julia and Python packages
Abstract
We show that a variant of the continuous Frechet distance between polygonal curves can be computed using essentially the same algorithm used to solve the discrete version. The new variant is not necessarily monotone, but this shortcoming can be easily handled via refinement. Combined with a Dijkstra/Prim type algorithm, this leads to a realization of the Frechet distance (i.e., a morphing) that is locally optimal (aka locally correct), that is both easy to compute, and in practice, takes near linear time on many inputs. The new morphing has the property that the leash is always as short as possible. These matchings/morphings are more natural and are better than the ones computed by standard algorithms -- in particular, they handle noise more graciously. This approach should make the Frechet distance more useful for real-world applications. We implemented the new algorithm and…
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