Cosine series representation of 3D curves and its application to white matter fiber bundles in diffusion tensor imaging

We present a novel cosine series representation for encoding fiber bundles consisting of multiple 3D curves. The coordinates of curves are parameterized as coefficients of cosine series expansion. We address the issue of registration, averaging and statistical inference on curves in a unified Hilbert space framework. Unlike traditional splines, the proposed method does not have internal knots and explicitly represents curves as a linear combination of cosine basis. This simplicity in the representation enables us to design statistical models, register curves and perform subsequent analysis in a more unified statistical framework than splines. The proposed representation is applied in characterizing abnormal shape of white matter fiber tracts passing through the spleniurn of the corpus callosum in autistic subjects. For an arbitrary tract, a 19 degree expansion is usually found to be sufficient to reconstruct the tract with 60 parameters.