Matrix-free approaches for deformable image registration with large-scale and real-time applications in medical imaging

In this thesis, we propose a novel computational approach to fast and memory-efficient deformable image registration. We demonstrate the relevance of the proposed methodin three real-world medical applications with very different requirements, ranging from processing of large datasets to registration with real-time constraints. The approach builds on a variational image registration model. In this model, finding a transformation which provides a reasonable image alignment is performed by minimizingan objective function. In the utilized discretize-then-optimize approach, the minimizationis realized by using derivative-based optimization methods. Here, the objective function derivatives are typically the computationally most expensive operations, both in terms of runtime and memory requirements. Therefore, we analyze the matrix structure for all derivative components. Based on the analysis, we derive equivalent, fully matrix-freeclosed-form expressions for gradient computations as well as the Hessian-vector multiplication, enabling the use of matrix-free computations for both L-BFGS and Gauss-Newton optimization schemes. The matrix-free computations completely eliminate the need for storing intermediate results and the cost of sparse matrix arithmetic. The expressions are fully parallelizable and the memory complexity for the derivative computations is reduced from linear to constant. We show that all important matrix-free derivative computations scale virtually linear, allowing to fully benefit from parallel execution. In comparison with matrix-based algorithms, the proposed approach is several orders of magnitude faster. The generic formulation of the matrix-free approach enables the implementation on different platforms. Besides multi-core CPUs, we present a GPU implementation which achieves a substantial, additional speedup. In order to justify the effort for deriving the matrix-free computations, we additionally implement the registration algorithm using an automatic differentiation framework. This method automatically computes optimized, analytically exact derivatives and allows for seamless execution on GPUs. In comparison with matrix-based methods, the automatic differentiation-based approach achieves comparable runtimes, making it a well-suited alternative for rapid prototyping and algorithm development. In the second part of the thesis, we utilize the matrix-free registration in three clinical applications. First, in an application from oncology, we present an automatic pipeline for registration of follow-up thorax-abdomen CT scans. We evaluate the algorithm on a large number of datasets, achieving clinically feasible runtimes. Second, we consider registration of CT and cone-beam CT images in radiotherapy. To achieve physically plau-sible deformations, we introduce an additional local rigidity constraint. In comparison to a commercial registration method, we achieve comparable accuracy, while obtaining physically more plausible deformations within a clinically suitable runtime. Third, we use the registration in real-time liver ultrasound tracking in order to determine respiratory motion. For this, we integrate the matrix-free registration in a tracking scheme with a moving-window strategy. In a public benchmark, we achieve real-time performance with the lowest mean tracking error of all participants. In each of these applications, the matrix-free methods allow the use of registration in scenarios where it would not be possible otherwise, due to run-time or memory constraints. Thus, the matrix-free registration can contribute to further increasing the use of image registration in clinical practice.