Registration of Multiple Temporally Related Point Sets Using a Novel Variant of the Coherent Point Drift Algorithm: Application to Coronary Tree Matching

We present a novel algorithm for the registration of multiple temporally related point sets. Although our algorithm is derived in a general setting, our primary motivating application is coronary tree matching in multi-phase cardiac spiral CT. Our algorithm builds upon the fast, outlier-resistant Coherent Point Drift (CPD) algorithm, but incorporates temporal consistency constraints between the point sets, resulting in spatiotemporally smooth displacement fields. We preserve the speed and robustness of the CPD algorithm by using the technique of separable surrogates within an EM (Expectation-Maximization) optimization framework, while still minimizing a global registration cost function employing both spatial and temporal regularization. We demonstrate the superiority of our novel temporally consistent group-wise CPD algorithm over a straightforward pair-wise approach employing the original CPD algorithm, using coronary trees derived from both simulated and real cardiac CT data. In all the tested configurations and datasets, our method presents lower average error between tree landmarks compared to the pairwise method. In the worst case, the difference is around few micrometers but in the better case, our method divides by two the error from the pairwise method. This improvement is especially important for a dataset with numerous outliers. With a fixed set of parameter that has been tuned automatically, our algorithm yields better results than the original CPD algorithm which shows the capacity to register without a priori information on an unknown dataset.