A pseudoinverse deformation vector field generator and its applications

PURPOSE: To present, implement, and test a self-consistent pseudoinverse displacement vector field (PIDVF) generator, which preserves the location of information mapped back-and-forth between image sets. METHODS: The algorithm is an iterative scheme based on nearest neighbor interpolation and a subsequent iterative search. Performance of the algorithm is benchmarked using a lung 4DCT data set with six CT images from different breathing phases and eight CT images for a single prostrate patient acquired on different days. A diffeomorphic deformable image registration is used to validate our PIDVFs. Additionally, the PIDVF is used to measure the self-consistency of two nondiffeomorphic algorithms which do not use a self-consistency constraint: The ITK Demons algorithm for the lung patient images and an in-house B-Spline algorithm for the prostate patient images. Both Demons and B-Spline have been QAed through contour comparison. Self-consistency is determined by using a DIR to generate a displacement vector field (DVF) between reference image R and study image S (DVF(R-S)). The same DIR is used to generate DVF(S-R). Additionally, our PIDVF generator is used to create PIDVF(S-R). Back-and-forth mapping of a set of points (used as surrogates of contours) using DVF(R-S) and DVF(S-R) is compared to back-and-forth mapping performed with DVF(R-S) and PIDVF(S-R). The Euclidean distances between the original unmapped points and the mapped points are used as a self-consistency measure. RESULTS: Test results demonstrate that the consistency error observed in back-and-forth mappings can be reduced two to nine times in point mapping and 1.5 to three times in dose mapping when the PIDVF is used in place of the B-Spline algorithm. These self-consistency improvements are not affected by the exchanging of R and S. It is also demonstrated that differences between DVF(S-R) and PIDVF(S-R) can be used as a criteria to check the quality of the DVF. CONCLUSIONS: Use of DVF and its PIDVF will improve the self-consistency of points, contour, and dose mappings in image guided adaptive therapy.