  Estimating the uncertainty in (probabilistic) image registration enables,
e.g., surgeons to assess the operative risk based on the trustworthiness of the
registered image data. If surgeons receive inaccurately calculated registration
uncertainty and misplace unwarranted confidence in the alignment solutions,
severe consequences may result. For probabilistic image registration (PIR), the
predominant way to quantify the registration uncertainty is using summary
statistics of the distribution of transformation parameters. The majority of
existing research focuses on trying out different summary statistics as well as
a means to exploit them. Distinctively, in this paper, we study two rarely
examined topics: (1) whether those summary statistics of the transformation
distribution most informatively represent the registration uncertainty; (2)
Does utilizing the registration uncertainty always be beneficial. We show that
there are two types of uncertainties: the transformation uncertainty, Ut, and
label uncertainty Ul. The conventional way of using Ut to quantify Ul is
inappropriate and can be misleading. By a real data experiment, we also share a
potentially critical finding that making use of the registration uncertainty
may not always be an improvement.
