# HV Geometry for Signal Comparison

arXiv: https://arxiv.org/abs/2304.11538 · HTML: https://mlsanity.com/paper/2304.11538/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [HV Metric For Time-Domain Full Waveform Inversion](https://mlsanity.com/paper/2508.17122/) (2025)

## Abstract (arXiv)

In order to compare and interpolate signals, we investigate a Riemannian geometry on the space of signals. The metric allows discontinuous signals and measures both horizontal (thus providing many benefits of the Wasserstein metric) and vertical deformations. Moreover, it allows for signed signals, which overcomes the main deficiency of optimal transportation-based metrics in signal processing. We characterize the metric properties of the space of signals and establish the regularity and stability of geodesics. Furthermore, we introduce an efficient numerical scheme to compute the geodesics and present several experiments which highlight the nature of the metric.