A Unified Parametric Model of White Matter Fiber Tracts University of Wisconsin , Madison Department of Biostatistics and Medical Informatics Technical Report

We present a novel unified framework for explicitly parameterizing white fiber tracts. The coordinates of tracts are parameterized using a Fourier series expansion. For an arbitrary tract, a 19 degree cosine expansion is found to be sufficient to reconstruct the tract with an error of about 0.26 mm. By adding specific periodic constraints to open tracts, we can avoid using the sine basis. Then each tract is fully parameterized with 60 parameters, which results in a substantial data reduction. Unlike available spline models, the proposed method does not have internal knots and explicitly represents the tract as a linear combination of basis functions. This simplicity in the representation enables us to design statistical models, register tracts and segment tracts in a unified Hilbert space formulation.