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.
The method reformulates the traditional B-spline registration problem as a basis pursuit problem describing the minimall 1-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.
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.
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.
We wish to thank the COPDgene Ancillary Studies Committee and Executive Committee who approved this study. This work was partially funded by the National Institutes of Health through an NIH Director's New Innovator Award DP2OD007044 and an NIH Research Supplement to Promote Diversity in Health Related Research 3DP2OD007044-01S1. Richard Castillo was partially supported by an NIH Research Scientist Development Award K01CA181292.
II. B-SPLINE AND BLOCK MATCHING DIR AS NONLINEAR LEAST SQUARES PROBLEMS
III. A CONSTRAINED NONLINEAR LEAST SQUARES FORMULATION FOR B-SPLINE DIR
IV. MINIMAL l 1 PERTURBATION TO BLOCK MATCH DATA
V. BLOCK MATCH FILTERING FROM MINIMAL l 1 PERTURBATION
VI. NUMERICAL IMPLEMENTATION
VII. NUMERICAL EXPERIMENTS AND RESULTS
- Medical imaging
- Spatial analysis
- Spatial dimensions
- Computed tomography
Data & Media loading...
Article metrics loading...
Full text loading...