Nonparametric Curve Alignment

TL;DR

This paper extends the congealing framework to effectively align curve data using a new set of nonlinear transformations, demonstrating positive results on synthetic and real datasets and discussing future extensions.

Contribution

It introduces a parameterized nonlinear transformation set enabling congealing to be applied to curve data, expanding its applicability.

Findings

Successful alignment of synthetic curve datasets

Effective alignment of real-world curve data

Discussion on extending to simultaneous alignment and clustering

Abstract

Congealing is a flexible nonparametric data-driven framework for the joint alignment of data. It has been successfully applied to the joint alignment of binary images of digits, binary images of object silhouettes, grayscale MRI images, color images of cars and faces, and 3D brain volumes. This research enhances congealing to practically and effectively apply it to curve data. We develop a parameterized set of nonlinear transformations that allow us to apply congealing to this type of data. We present positive results on aligning synthetic and real curve data sets and conclude with a discussion on extending this work to simultaneous alignment and clustering.