System and method for quantifying the quality of motion correction in image registration

摘要

A method of evaluating the quality of a deformation field includes providing a deformation field from a first domain to a second domain, where a deformation field Φ=(φ_x,φ_y,φ_z) that transforms a point (x,y,z) in the first domain to a point (X,Y,Z) in the second domain is defined by; $$ \{\begin{array}{c}X={\varphi }_x\left(x,y,z\right)=x+u_x\left(x,y,z\right)\\ Y={\varphi }_y\left(x,y,z\right)=y+u_y\left(x,y,z\right)\\ Z={\varphi }_z\left(x,y,z\right)=z+u_z\left(x,y,z\right)\end{array},$$where u_x, u_y, u_z are displacement fields, and calculating a quality factor as a function of the of the displacement fields and the Jacobian matrix DΦ(x,y,z) of the deformation fields. The quality factor is a measure of the quality of said deformation field.