We present a novel unified framework for explicitly param- eterizing white fiber tracts. The coor... more We present a novel unified framework for explicitly param- eterizing white fiber tracts. The coordinates of tracts are parameterized using a Fourier series expansion. For an arbitrary tract, a 19 degree co- sine 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 com- bination 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.
We present a novel unified framework for explicitly param- eterizing white fiber tracts. The coor... more We present a novel unified framework for explicitly param- eterizing white fiber tracts. The coordinates of tracts are parameterized using a Fourier series expansion. For an arbitrary tract, a 19 degree co- sine 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 com- bination 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.
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Papers by Nicholas Lange