An inexact matching approach for the comparison of plane curves with general elastic metrics
This work addresses a domain-specific problem in computational geometry for curve comparison, but it appears incremental as it builds on existing transforms and metrics.
The paper tackles the problem of computing distances and geodesics between planar curves by introducing a new mathematical formulation and numerical approach that combines a simplifying transform with a relaxation of matching constraints, leading to a simple optimization problem and flexibility for noisy data, as illustrated in preliminary numerical results.
This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic metrics that was recently introduced by Kurtek and Needham, together with a relaxation of the matching constraint using parametrization-invariant fidelity metrics. The main advantages of this formulation are that it leads to a simple optimization problem for discretized curves, and that it provides a flexible approach to deal with noisy, inconsistent or corrupted data. These benefits are illustrated via a few preliminary numerical results.