Robust point matching (RPM) jointly estimates correspondences and non-rigid warps between unstructured
point-clouds. RPM does not, however, utilize information of the topological structure or group memberships of
the data it is matching. In numerous medical imaging applications, each extracted point can be assigned group
membership attributes or labels based on segmentation, partitioning, or clustering operations. For example,
points on the cortical surface of the brain can be grouped according to the four lobes. Estimated warps should
enforce the topological structure of such point-sets, e.g. points belonging to the temporal lobe in the two
point-sets should be mapped onto each other.
We extend the RPM objective function to incorporate group membership labels by including a Label Entropy
(LE) term. LE discourages mappings that transform points within a single group in one point-set onto points
from multiple distinct groups in the other point-set. The resulting Labeled Point Matching (LPM) algorithm
requires a very simple modification to the standard RPM update rules.
We demonstrate the performance of LPM on coronary trees extracted from cardiac CT images. We partitioned
the point sets into coronary sections without a priori anatomical context, yielding potentially disparate labelings
(e.g. [1,2,3] → [a,b,c,d]). LPM simultaneously estimated label correspondences, point correspondences, and a
non-linear warp. Non-matching branches were treated wholly through the standard RPM outlier process akin to
non-matching points. Results show LPM produces warps that are more physically meaningful than RPM alone.
In particular, LPM mitigates unrealistic branch crossings and results in more robust non-rigid warp estimates.