FEM-based evaluation of deformable image registration for radiation therapy

This paper presents a new concept to automatically detect the neighborhood in an image where deformable registration is mis-performing. Specifically, the displacement vector field (DVF) from a deformable image registration is substituted into a finite-element-based elastic framework to calculate unbalanced energy in each element. The value of the derived energy indicates the quality of the DVF in its neighborhood. The new voxel-based evaluation approach is compared with three other validation criteria: landmark measurement, a finite element approach and visual comparison, for deformable registrations performed with the optical-flow-based 'demons' algorithm as well as thin-plate spline interpolation. This analysis was performed on three pairs of prostate CT images. The results of the analysis show that the four criteria give mutually comparable quantitative assessments on the six registration instances. As an objective concept, the unbalanced energy presents no requirement on boundary constraints in its calculation, different from traditional mechanical modeling. This method is automatic, and at voxel level suitable to evaluate deformable registration in a clinical setting.