# Data-Driven, Soft Alignment of Functional Data Using Shapes and Landmarks

arXiv: https://arxiv.org/abs/2203.14810 · HTML: https://mlsanity.com/paper/2203.14810/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 33 references that are in the map.
- First posted on arXiv 22 Mar 2022.

## Builds on (most cited first, 6 of 6)

- [Functional Data Analysis of Amplitude and Phase Variation](https://mlsanity.com/paper/1512.03216/) (2015)
- [Bayesian registration of functions and curves](https://mlsanity.com/paper/1311.2105/) (2013)
- [Landmark-Guided Elastic Shape Analysis of Human Character Motions](https://mlsanity.com/paper/1502.07666/) (2015)
- [A Geometric Approach to Pairwise Bayesian Alignment of Functional Data Using Importance Sampling](https://mlsanity.com/paper/1505.06954/) (2015)
- [Distribution on Warp Maps for Alignment of Open and Closed Curves](https://mlsanity.com/paper/1708.04891/) (2017)
- [Multimodal Bayesian Registration of Noisy Functions using Hamiltonian Monte Carlo](https://mlsanity.com/paper/2005.14372/) (2020)

## Abstract (arXiv)

Alignment or registration of functions is a fundamental problem in statistical analysis of functions and shapes. While there are several approaches available, a more recent approach based on Fisher-Rao metric and square-root velocity functions (SRVFs) has been shown to have good performance. However, this SRVF method has two limitations: (1) it is susceptible to over alignment, i.e., alignment of noise as well as the signal, and (2) in case there is additional information in form of landmarks, the original formulation does not prescribe a way to incorporate that information. In this paper we propose an extension that allows for incorporation of landmark information to seek a compromise between matching curves and landmarks. This results in a soft landmark alignment that pushes landmarks closer, without requiring their exact overlays to finds a compromise between contributions from functions and landmarks. The proposed method is demonstrated to be superior in certain practical scenarios.