  In image-guided neurosurgery, current commercial systems usually provide only
rigid registration, partly because it is harder to predict, validate and
understand non-rigid registration error. For instance, when surgeons see a
discrepancy in aligned image features, they may not be able to distinguish
between registration error and actual tissue deformation caused by tumor
resection. In this case, the spatial distribution of registration error could
help them make more informed decisions, e.g., ignoring the registration where
the estimated error is high. However, error estimates are difficult to acquire.
Probabilistic image registration (PIR) methods provide measures of registration
uncertainty, which could be a surrogate for assessing the registration error.
It is intuitive and believed by many clinicians that high uncertainty indicates
a large error. However, the monotonic association between uncertainty and error
has not been examined in image registration literature. In this pilot study, we
attempt to address this fundamental problem by looking at one PIR method, the
Gaussian process (GP) registration. We systematically investigate the relation
between GP uncertainty and error based on clinical data and show empirically
that there is a weak-to-moderate positive monotonic correlation between
point-wise GP registration uncertainty and non-rigid registration error.
