Composition of Transformations in Feature-Based Registration
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Accurate registration of medical images is crucial to the successful deployment of computer assisted interventions or surgical navigation systems. Nonrigid registration techniques are important when considering soft tissues or other deformable anatomies, inter-individual registration, or the use of atlases or template objects; however, nonrigid transformations must be constrained in order to ensure that the resulting mappings are anatomically feasible. Application-specific models of deformation---designed to capture statistical relationships, or functional constraints of the anatomy of interest---are one way of constraining nonrigid deformations while maintaining the generalizability of the model. In most cases however, the use of these application-specific models is complicated by the need for customized registration algorithms. This work facilitates the use of application-specific models of deformation by proposing a general algorithm to allow sets of points or oriented points to be registered through arbitrarily composed sets of transformations. Simple transformations can, in principle, be combined into more complex models specific to the anatomy under consideration. The algorithm is designed to be modular: by leveraging the power of modern statistical framings of the point set registration problem, arbitrarily composed sets of transformations can be optimized, requiring only that each transformation has a known solution to a particular standard form of equation. The basic approach is developed first in the context of an actual medical imaging problem: the registration of intraoperative cardiac ultrasound, and preoperative CT scans. The ultrasound images are processed by registering a model through a hierarchical transformation using a novel generalized expectation-maximization approach. This approach is extended to a general algorithm for the registration of point or oriented point sets through arbitrarily composed transformations, and a class of heuristic modifications are proposed and experimentally examined. The algorithm is shown to produce promising results in both synthetic data experiments examining robustness to noise and outliers, and in an application to actual cardiac imaging data. Ultimately, it is hoped that this work can aid researchers in constructing application-specific solutions to the problems they face and help improve registration accuracy in a variety of difficult medical imaging problems.