Reinterpreting the Transformation Posterior in Probabilistic Image Registration

TL;DR

This paper critically examines the traditional interpretation of transformation posteriors in probabilistic image registration, proposing ensemble fields as a new way to represent and utilize uncertainty more faithfully.

Contribution

It introduces ensemble fields as a novel data type to better encode and interpret the variability in transformation posteriors in image registration.

Findings

Conventional methods may misrepresent registration uncertainty.

Ensemble fields provide a more faithful representation of transformation variability.

Pilot examples demonstrate the potential of ensemble fields.

Abstract

Probabilistic image registration methods estimate the posterior distribution of transformation. The conventional way of interpreting the transformation posterior is to use the mode as the most likely transformation and assign its corresponding intensity to the registered voxel. Meanwhile, summary statistics of the posterior are employed to evaluate the registration uncertainty, that is the trustworthiness of the registered image. Despite the wide acceptance, this convention has never been justified. In this paper, based on illustrative examples, we question the correctness and usefulness of conventional methods. In order to faithfully translate the transformation posterior, we propose to encode the variability of values into a novel data type called ensemble fields. Ensemble fields can serve as a complement to the registered image and a foundation for developing advanced methods to characterize the uncertainty in registration-based tasks. We demonstrate the potential of ensemble fields by pilot examples