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We propose an integral concept for tractography to describe crossing and splitting fibre bundles based on the fibre orientation distribution function (ODF) estimated from high angular resolution diffusion imaging (HARDI). We show that in order to perform accurate probabilistic tractography, one needs to use a fibre ODF estimation and not the diffusion ODF. We use a new fibre ODF estimation obtained from a sharpening deconvolution transform (SDT) of the diffusion ODF reconstructed from q-ball imaging (QBI). This SDT provides new insight into the relationship between the HARDI signal, the diffusion ODF, and the fibre ODF. We demonstrate that the SDT agrees with classical spherical deconvolution and improves the angular resolution of QBI. Another important contribution of this paper is the development of new deterministic and new probabilistic tractography algorithms using the full multidirectional information obtained through use of the fibre ODF. An extensive comparison study is performed on human brain datasets comparing our new deterministic and probabilistic tracking algorithms in complex fibre crossing regions. Finally, as an application of our new probabilistic tracking, we quantify the reconstruction of transcallosal fibres intersecting with the corona radiata and the superior longitudinal fasciculus in a group of eight subjects. Most current diffusion tensor imaging (DTI)-based methods neglect these fibres, which might lead to incorrect interpretations of brain functions.