An approach to estimate of 2D-3D motion of surfaces: the frequency domain technique

Phase correlation is one of the robustest methods for estimating planar translations: it is a global approach because it operates in the frequency domain using the whole image information and not just a selected subset of the image as the feature-based methods do. The good characteristics of phase correlation for estimating planar translations were found to be a strong motivation for its extension to the estimation of planar rotations. An original algorithm for estimating planar rotations inspired by phase correlation is presented in this work. Practical experimentation on real imagery confirm the expected robustness of the method. Furthermore, a natural extension of the proposed algorithm will be also presented for 3D shapes motion estimation. Free-form 3-D surfaces registration is a fundamental problem in 3-D imaging, tipi-cally approached by extensions or variations of the ICP algorithm [2,10]. In this paper an alternative procedure for 3-D motion estimation wiil be suggested, based on the Fourier transform of the 3-D intensity function, implicitly described by the registered time-sequences of range data. As the proposed method is very suitable for 2D and 3D modeling of cultural heritages, some examples and results of its application to Madonna of Donatello, located in the Basilica of St. Anthony in Padua, will be also presented.