A 3D geometric transformation for a nonrigid image registration method

Abstract

A 3D geometric transformation is introduced for the nonrigid registration of medical images as an extension of a previous work carried out for two dimensions. A 3D spatial transformation is analyzed in order to guaranty the continuity, the differentiability and the one-to-one transformation by imposing constraints to the transformation parameters. It is also shown and analyzed the results when the fully automatic nonrigid registration method is applied to a CT-PET stack of the thorax with a spatial resolution of 80 x 80 x 80 and to a RM head stack with a spatial resolution of 128 x 128 x 128 pixels. The 3D geometric transformation has a spherical domain and it allows the continuity of the transformation in its boundary. This geometrical transformation can be applied to global or local ROIs (region of interest) up to a minimum diameter of three pixels. The nonrigid image registration method employs an evolutionary algorithm to obtain satisfactory global solutions while it maximizes the normalized mutual information (NMI). This approach has the disadvantage that the speed of convergence and the accuracy of the method depend on the population size of the evolutionary algorithm. Results show an improvement in the global similarity function between the target and source volumes throughout 73 transformations, from coarse to fine (3 levels of resolution), from 0.5017 to 0.5033, using a population size of 10 individuals. 3D surface reconstructions of the thorax are also shown before and after the nonrigid registration. In addition, a simulated experiment is carried out with a RM head stack, where a unique transformation was applied. Here, it was got an improvement in the similarity criterion from 0.5046 to 0.5218.