We propose a deterministic and a probabilistic extension of classical diffusion tensor imaging (DTI) tractography algorithms based on a sharp fiber orientation distribution function (ODF) reconstruction from Q-Ball Imaging (QBI). An important contribution of the paper is the integration of some of the latest state-of-the-art high angular resolution diffusion imaging (HARDI) data processing methods to obtain accurate and convincing results of complex fiber bundles with crossing, fanning and branching configurations. First, we develop a new deconvolution \emph{sharpening} transformation from diffusion ODF (dODF) to fiber ODF (fODF). We show that this sharpening transformation improves angular resolution and fiber detection of QBI and thus greatly improves tractography results. The angular resolution of QBI is in fact improved by approximately 20$^\circ$ and the fODF is shown to behave very similarly of the fiber orientation density (FOD) estimated from the spherical deconvolution method of Tournier et al. Another major contribution of the paper is the extensive comparison study on human brain datasets of our new deterministic and probabilistic tracking algorithms. As an application, we show how the reconstruction of transcallosal fiber connections intersecting with the corona radiata and the superior longitudinal fasciculus can be improved with the fODF in a group of 8 subjects. Current DTI based methods neglect these fibers, which might lead to wrong interpretations of the brain functions.