title: Efficient methods for implementation of multi-level nonrigid mass-preserving image registration on GPUs and multi-threaded CPUs.
abstract: OBJECTIVE
  Faster and more accurate methods for registration of images are important for research involved in conducting population-based studies that utilize medical imaging, as well as improvements for use in clinical applications. We present a novel computation- and memory-efficient multi-level method on graphics processing units (GPU) for performing registration of two computed tomography (CT) volumetric lung images.
  
  
  METHODS
  We developed a computation- and memory-efficient Diffeomorphic Multi-level B-Spline Transform Composite (DMTC) method to implement nonrigid mass-preserving registration of two CT lung images on GPU. The framework consists of a hierarchy of B-Spline control grids of increasing resolution. A similarity criterion known as the sum of squared tissue volume difference (SSTVD) was adopted to preserve lung tissue mass. The use of SSTVD consists of the calculation of the tissue volume, the Jacobian, and their derivatives, which makes its implementation on GPU challenging due to memory constraints. The use of the DMTC method enabled reduced computation and memory storage of variables with minimal communication between GPU and Central Processing Unit (CPU) due to ability to pre-compute values. The method was assessed on six healthy human subjects.
  
  
  RESULTS
  Resultant GPU-generated displacement fields were compared against the previously validated CPU counterpart fields, showing good agreement with an average normalized root mean square error (nRMS) of 0.044±0.015. Runtime and performance speedup are compared between single-threaded CPU, multi-threaded CPU, and GPU algorithms. Best performance speedup occurs at the highest resolution in the GPU implementation for the SSTVD cost and cost gradient computations, with a speedup of 112 times that of the single-threaded CPU version and 11 times over the twelve-threaded version when considering average time per iteration using a Nvidia Tesla K20X GPU.
  
  
  CONCLUSIONS
  The proposed GPU-based DMTC method outperforms its multi-threaded CPU version in terms of runtime. Total registration time reduced runtime to 2.9min on the GPU version, compared to 12.8min on twelve-threaded CPU version and 112.5min on a single-threaded CPU. Furthermore, the GPU implementation discussed in this work can be adapted for use of other cost functions that require calculation of the first derivatives.
authors.affiliation: IIHR-Hydroscience & Engineering, The University of Iowa, Iowa City, IA 52242, United States. Electronic address: nathan.ellingwood@gmail.com.
authors.forename: Nathan D
authors.initials: ND
authors.lastname: Ellingwood
authors.affiliation: Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, IA 52242, United States. Electronic address: youbing.yin@gmail.com.
authors.forename: Youbing
authors.initials: Y
authors.lastname: Yin
authors.affiliation: National Cheng Kung University, Tainan City, Taiwan. Electronic address: msmith@mail.ncku.edu.tw.
authors.forename: Matthew
authors.initials: M
authors.lastname: Smith
authors.affiliation: IIHR-Hydroscience & Engineering, The University of Iowa, Iowa City, IA 52242, United States; Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, IA 52242, United States; Department of Applied Mathematical and Computational Sciences, The University of Iowa, Iowa City, IA 52242, United States. Electronic address: ching-long-lin@uiowa.edu.
authors.forename: Ching-Long
authors.initials: CL
authors.lastname: Lin
mesh_terms: D003201:Computers; D006801:Humans; D008168:Lung / Q000000981:diagnostic imaging; D014057:Tomography, X-Ray Computed
keywords: GPU; Lungs; Mass-preserving image registration; Multi-level