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In order to study the anatomical variability of the uterus induced by pregnancy, a parametrization of gravid uterine geometry based on principal component analysis (PCA) is proposed. Corresponding meshes used for PCA are created by a ray description technique applied to a reference mesh. A smoothed voxel-based methodology is applied to determine the reference mesh from a database of 11 real shapes produced by the FEMONUM project. The ray-based correspondence technique is compared to two existing methods (He, Giessen) as well as a proposed mixed method. Principal component analysis results are based on a database of 11 existing shapes. Results of the parametrization show that 90% of the total variance of the database can be represented with four new shape parameters and that a wide spectrum of shapes can be generated. Graphical Abstract Proposed correspondence technique compared to existing methods., (© 2021. International Federation for Medical and Biological Engineering.)