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Affine SPHARM Registration - Neural Estimation of Affine Transformation in Spherical Domain

In this work we propose an algorithm to perform the affine 3D surface registration using the shape modeling based on SPHerical HARMonic: called SPHARM. In the existing SPHARM registration algorithms the alignment is obtained using the rotation properties, that allows to perform the 3D surface rotation transforming only the spherical coefficients. The major limit is that this approach aligns the surface only by rotation. We propose a method to generalize this solution without lose the advantage to perform whole the registration process in the spherical domain. An estimation of the coefficients transformation that guarantees an affinity in the spatial domain is obtained by regression, using a set of RBF networks. The description of the 3D surface with the spherical harmonic coefficients is brief but comprehensive and provides directly a metric of the shape similarity. Therefore, the registration is obtained aligning the SPHARM model thought the minimization of the root mean square distance between the coefficients vectors. Many experiments are performed to test the affine SPHARM registration algorithm which appears efficient and effective compared with a standard registration algorithm in the spatial domain.