Robust similarity registration technique for volumetric shapes represented by characteristic functions

This paper proposes a novel similarity registration technique for volumetric shapes implicitly represented by characteristic functions (CFs). Here, the calculation of rotation parameters is considered as a spherical cross-correlation problem and the solution is therefore found using the standard phase correlation technique facilitated by principal components analysis (PCA). Thus, fast Fourier transform (FFT) is employed to vastly improve efficiency and robustness. Geometric moments are then used for shape scale estimation which is independent from rotation and translation parameters. It is numerically demonstrated that our registration method is able to handle shapes with various topologies and robust to noise and initial poses. Further validation of our method is performed by registering a lung database. HighlightsWe propose a similarity registration method that registers volumetric shapes.The method naturally handles shapes with topological differences.The method is validated by registering a lung database.The method can be applied to shape-based image segmentation.