Composition of Transformations in the Registration of Sets of Points or Oriented Points

Registration of point sets in medical imaging applications may in some cases benefit from application-specific rather than general models of deformation by which to transform the model point set to the target. Further, including orientation data with the points may improve accuracy. To facilitate this, we propose an algorithm to register sets of points or oriented points through arbitrarily composed sets of transformations, so as to allow the construction of context-specific deformation spaces. The algorithm is generic with respect to the choice of transformations, requiring only that each constituent has a known solution to a particular standard form of equation. Our approach is framed in the mixture model framework, and constitutes a generalized expectation maximization algorithm. We present experimental results for two models—a 2D model of a cardiac ventricle, and a 3D model of a bug—testing the algorithm’s robustness to noise and outliers, and comparing the accuracy when using points or oriented points. The results suggest the algorithm is quite robust to both noise and outliers, with inclusion of orientation data consistently resulting in more accurate registrations.