Nonparametric Curve Alignment
This work addresses curve alignment for applications like image and 3D data processing, but it is incremental as it extends an existing method to a new data type.
The paper tackles the problem of aligning curve data by enhancing the congealing framework with a parameterized set of nonlinear transformations, achieving positive results on synthetic and real datasets.
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.