Distance measures and algorithms for feature-based and intensity-based non-rigid registration

Anand Rangarajan
Dept. of Computer & Information Science and Engineering

Non-rigid registration is an important subfield within medical imaging
with particular relevance to brain mapping. Approaches to non-rigid
registration are typically classified as feature-based or
intensity-based. Within the class of feature-based approaches, the
actual features used range from points to surfaces. When unordered and
unlabeled points are used, the correspondence problem between two
point-sets looms. We have developed frameworks and algorithms for
jointly solving for point correspondences and the non-rigid spatial
mapping between two sets of point features. Our approach consists of
solving for a doubly substochastic matrix (for the correspondence) and
a thin-plate spline (for the spatial mapping). We have recently
extended this approach to the problem of estimating an atlas (or a
representative point-set) from a collection of point-sets. In
addition, where a thin-plate spline has been unsuitable, we have
estimated a diffeomorphism between unlabeled point-sets. The
application area is the matching of cortical and subcortical
structures extracted from anatomical 3D MRI.  

Since the extraction of point features from medical imaging modalities
is frequently cumbersome, we have recently looked at intensity-based
distance measures for non-rigid registration. We show that the
ubiquitous mutual-information distance measure (with an added
deformation penalty) can be reformulated as a Bayesian MAP objective
function. We prove that the infimum of the Bayesian MAP objective
function is identical to the infimum of the true mutual information
provided a restriction is placed on the number of allowed
configurations of the displacement field. In addition, since the raw
intensity may not be the ideal feature for registration, we show that a
normalized mutual information criterion can be used to find the best
transformation of the intensities for matching purposes. The
application area is brain MRI registration from different modalities
(T1, T2 and PD).