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Image registration is an inherently ill-posed problem that lacks the constraints needed for a unique mapping between voxels of the two images being registered. As such, one must regularize the registration to achieve physically meaningful transforms. The regularization penalty is usually a function of derivatives of the displacement-vector field and can be calculated either analytically or numerically. The numerical approach, however, is computationally expensive depending on the image size, and therefore a computationally efficient analytical framework has been developed. Using cubic B-splines as the registration transform, we develop a generalized mathematical framework that supports five distinct regularizers: diffusion, curvature, linear elastic, third-order, and total displacement. We validate our approach by comparing each with its numerical counterpart in terms of accuracy. We also provide benchmarking results showing that the analytic solutions run significantly faster-up to two orders of magnitude-than finite differencing based numerical implementations., (© 2021 IOP Publishing Ltd.)

Image registration is inherently ill-posed, and lacks a unique solution. In the context of medical applications, it is desirable to avoid solutions that describe physically unsound deformations within the patient anatomy. Among the accepted methods of regularizing non-rigid image registration to provide solutions applicable to medical practice is the penalty of thin-plate bending energy. In this paper, we develop an exact, analytic method for computing the bending energy of a three-dimensional B-spline deformation field as a quadratic matrix operation on the spline coefficient values. Results presented on ten thoracic case studies indicate the analytic solution is between 61-1371x faster than a numerical central differencing solution.

Spline-based deformable registration methods are quite popular within the medical-imaging community due to their flexibility and robustness. However, they require a large amount of computing time to obtain adequate results. This paper makes two contributions towards accelerating B-spline-based registration. First, we propose a grid-alignment scheme and associated data structures that greatly reduce the complexity of the registration algorithm. Based on this grid-alignment scheme, we then develop highly data parallel designs for B-spline registration within the stream-processing model, suitable for implementation on multi-core processors such as graphics processing units (GPUs). Particular attention is focused on an optimal method for performing analytic gradient computations in a data parallel fashion. CPU and GPU versions are validated for execution time and registration quality. Performance results on large images show that our GPU algorithm achieves a speedup of 15 times over the single-threaded CPU implementation whereas our multi-core CPU algorithm achieves a speedup of 8 times over the single-threaded implementation. The CPU and GPU versions achieve near-identical registration quality in terms of RMS differences between the generated vector fields.

This paper shows how to significantly accelerate cone-beam CT reconstruction and 3D deformable image registration using the stream-processing model. We describe data-parallel designs for the Feldkamp, Davis and Kress (FDK) reconstruction algorithm, and the demons deformable registration algorithm, suitable for use on a commodity graphics processing unit. The streaming versions of these algorithms are implemented using the Brook programming environment and executed on an NVidia 8800 GPU. Performance results using CT data of a preserved swine lung indicate that the GPU-based implementations of the FDK and demons algorithms achieve a substantial speedup--up to 80 times for FDK and 70 times for demons when compared to an optimized reference implementation on a 2.8 GHz Intel processor. In addition, the accuracy of the GPU-based implementations was found to be excellent. Compared with CPU-based implementations, the RMS differences were less than 0.1 Hounsfield unit for reconstruction and less than 0.1 mm for deformable registration.