Manifold embedding for curve registration

TL;DR

This paper introduces a manifold-based approach for curve registration, estimating a common pattern from warped random curves using geodesic distances on a manifold, and compares it to traditional methods.

Contribution

It develops a novel manifold framework for curve registration and proposes an estimation method based on geodesic distances, advancing existing techniques.

Findings

The manifold approach effectively captures the common pattern among warped curves.

The proposed method outperforms classical registration techniques in experiments.

Geodesic distance approximation improves the robustness of pattern estimation.

Abstract

We focus on the problem of finding a good representative of a sample of random curves warped from a common pattern f. We first prove that such a problem can be moved onto a manifold framework. Then, we propose an estimation of the common pattern f based on an approximated geodesic distance on a suitable manifold. We then compare the proposed method to more classical methods.