Evaluation of liver metastasis volume changes in longitudinal CT images using statistical modeling and adversarial image registration networks

• Proposes an adversarial diffeomorphic framework for liver CT registration. • Normalizes intensities via Yeo–Johnson transformation to stabilize optimization. • Improves boundary alignment near the liver and metastatic lesions. • Runs faster than conventional deformable registration approaches. • Enables volumetric monitoring beyond RECIST-based clinical assessment. Assessing treatment response and disease progression in patients with liver metastases requires accurate quantification of volumetric changes across longitudinal CT scans. Therefore, it is essential to achieve reliable registration of post-treatment volumes to their corresponding pre-treatment scans. This study proposes an adversarial diffeomorphic image registration framework that integrates the Gaussianization transformation for statistical normalization of liver intensities. Because liver CT data often exhibit skewed and heavy-tailed intensity distributions, the Gaussianization transformation maps voxel intensities into an approximately Gaussian distribution, thereby improving conformity with the Gaussian noise assumptions of probabilistic registration models. By incorporating this step within a generative adversarial training pipeline, the model learns to produce accurate and anatomically consistent deformation fields. Experiments on 128 longitudinal CT scans from 64 patients, with external validation on the Liver DIR Landmark dataset, demonstrated that Gaussianization substantially enhanced registration accuracy and convergence stability. The method achieved a mean target registration error of 1.586 ± 0.729 mm, normalized mutual information of 1.229 ± 0.018, and boundary HD95 of 2.756 ± 0.293 voxels (all P < 0.02), while reducing inference time from 120 ± 33 s to 30 ± 9 s per volume (≈75% faster). Application to volumetric analysis showed results consistent with RECIST 1.1 partial response classification. These findings demonstrate that intensity Gaussianization combined with adversarial diffeomorphic registration provides accurate, efficient, and anatomically coherent alignment for quantitative longitudinal liver CT analysis.