In functional Magnetic Resonance Imaging (fMRI) data analysis, normalization of time series is an important and sometimes necessary preprocessing step in many widely used methods. The space of normalized time series with n time points is the unit sphere S^{n-2}, named the functional space. Riemannian framework on the sphere, including the geodesic, the exponential map, and the logarithmic map, has been well studied in Riemannian geometry. In this paper, by introducing the Riemannian framework in the functional space, we propose a novel nonparametric robust method, namely Mean Shift Functional Detection (MSFD), to explore the functional space. The first merit of the MSFD is that it does not need many assumptions on data which are assumed in many existing method, e.g. linear addition (GLM, PCA, ICA), uncorrelation (PCA), independence (ICA), the number and the shape of clusters (FCM). Second, MSFD takes into account the spatial information and can be seen as a multivariate extension of the functional connectivity analysis method. It is robust and works well for activation detection in task study even with a biased activation reference. It is also able to find the functional networks in resting-state study without a user-selected "seed" region. Third, it can enhance the boundary between different functional networks. Experiments were conducted on synthetic and real data to compare the performance of the proposed method with GLM and ICA. The experimental results validated the accuracy and robustness of MSFD, not only for activation detection in task study but also for functional network exploration in resting-state study.