A Matrix-Free Approach to Parallel and Memory-Efficient Deformable Image Registration

Abstract

We present a novel computational approach to fast and memory-efficient deformable image registration. In the variational registration model, the computation of the objective function derivatives is the computationally most expensive operation, both in terms of runtime and memory requirements. In order to target this bottleneck, we analyze the matrix structure of gradient and Hessian computations for the case of the normalized gradient fields distance measure and curvature regularization. Based on this analysis, we derive equivalent matrix-free closed-form expressions for derivative computations, eliminating the need for storing intermediate results and the costs of sparse matrix arithmetic. This has further benefits: (1) matrix computations can be fully parallelized, (2) memory complexity for derivative computation is reduced from linear to constant, and (3) overall computation times are substantially reduced.In comparison with an optimized matrix-based reference implementation, the CPU implementation achieves speedup factors between 3.1 and 9.7, and we are able to handle substantially higher resolutions. Using a GPU implementation, we achieve an additional speedup factor of up to 9.2.Furthermore, we evaluated the approach on real-world medical datasets. On ten publicly available lung CT images from the DIR-Lab 4DCT dataset, we achieve the best mean landmark error of 0.93 mm compared to other submissions on the DIR-Lab website, with an average runtime of only 9.23 s. Complete non-rigid registration of full-size 3D thorax-abdomen CT volumes from oncological follow-up is achieved in 12.6 s. The experimental results show that the proposed matrix-free algorithm enables the use of variational registration models also in applications which were previously impractical due to memory or runtime restrictions.

Multimodal image registration for liver radioembolization planning and patient assessment

“…However, the comparison seems unfair, as our method was not specifically adapted to lung image registration. A performance evaluation on the DIR-Lab dataset with adjusted parameters to the demands of lung image registration (e.g., , ) was presented in [ 18 ] and an average landmark error of 0.93 mm was reported there.…”

Fully-Deformable 3D Image Registration in Two Seconds

“…Regarding the model, we follow [2]: We seek a three-dimensional deformation vector field y ∈ R 3m y , m y := m y x m y y m y z , discretized on a deformation grid with dimensions m y x ×m y y ×m y z , which deforms a template image T ∈ R m to be similar to a reference image R ∈ R m , m := m x m y m z , both discretized on an image grid with dimensions m x ×m y ×m z .…”

“…The chain rule yields ∇D NGF (y) = ∂ψ ∂T ∂T ∂P ∂P ∂y with the reduction function ψ : R m → R. Evaluating the gradient using the chain rule by computing the gradient parts and multiplying step-by-step is expensive in terms of (intermediate) memory required. We avoid this by relying on the matrix-free methods introduced by [2].…”

“…Towards reducing runtime, the authors of [1,2] propose a highly accurate nonrigid registration model with applications in follow-up imaging in radiology and liver ultrasound tracking, and introduce a parallel algorithm for the CPU. They also include a preliminary GPU implementation for the 2D case provided by [3].…”

Learning Deformable Image Registration with Structure Guidance Constraints for Adaptive Radiotherapy

“…Aside from that, flexible organs, such as bladder or rectum, can introduce extreme deformations, complicating an accurate registration. Conventional DIR algorithms such as [11] tend to underestimate large deformations, which is why extended DIR approaches were presented [9,14]. These so-called structure guided approaches include information about corresponding anatomical delineations on the images in order to guide the registration.…”