Computing global minimizers to a constrained B-spline image registration problem from optimal l1 perturbations to block match data.
OBJECTIVE
Block matching is a well-known strategy for estimating corresponding voxel locations between a pair of images according to an image similarity metric. Though robust to issues such as image noise and large magnitude voxel displacements, the estimated point matches are not guaranteed to be spatially accurate. However, the underlying optimization problem solved by the block matching procedure is similar in structure to the class of optimization problem associated with B-spline based registration methods. By exploiting this relationship, the authors derive a numerical method for computing a global minimizer to a constrained B-spline registration problem that incorporates the robustness of block matching with the global smoothness properties inherent to B-spline parameterization.


METHODS
The method reformulates the traditional B-spline registration problem as a basis pursuit problem describing the minimall1-perturbation to block match pairs required to produce a B-spline fitting error within a given tolerance. The sparsity pattern of the optimal perturbation then defines a voxel point cloud subset on which the B-spline fit is a global minimizer to a constrained variant of the B-spline registration problem. As opposed to traditional B-spline algorithms, the optimization step involving the actual image data is addressed by block matching.


RESULTS
The performance of the method is measured in terms of spatial accuracy using ten inhale/exhale thoracic CT image pairs (available for download atwww.dir-lab.com) obtained from the COPDgene dataset and corresponding sets of expert-determined landmark point pairs. The results of the validation procedure demonstrate that the method can achieve a high spatial accuracy on a significantly complex image set.


CONCLUSIONS
The proposed methodology is demonstrated to achieve a high spatial accuracy and is generalizable in that in can employ any displacement field parameterization described as a least squares fit to block match generated estimates. Thus, the framework allows for a wide range of image similarity block match metric and physical modeling combinations.
Department of Radiation Physics, University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Unit 56 Houston, Texas 77030 and Department of Computational and Applied Mathematics, Rice University, 6100 Main MS-134, Houston, Texas 77005.
Edward
E
Castillo
Department of Radiation Physics, University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Unit 56 Houston, Texas 77030.
Richard
R
Castillo
Department of Imaging Physics, University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Unit 1902 Houston, Texas 77030.
David
D
Fuentes
Department of Radiation Oncology, University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Unit 56 Houston, Texas 77030 and Department of Computational and Applied Mathematics, Rice University, 6100 Main MS-134, Houston, Texas 77005.
Thomas
T
Guerrero
D000465:Algorithms; D045853:Exhalation; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D001239:Inhalation; D013902:Radiography, Thoracic / Q000379:methods*; D014057:Tomography, X-Ray Computed / Q000379:methods*