Longitudinal reproducibility is an essential concern in automated medical image segmentation, yet has proven to be an elusive objective as manual brain structure tracings have shown more than 10% variability. To improve reproducibility, longitudinal segmentation (4D) approaches have been investigated to reconcile temporal variations with traditional 3D approaches. In the past decade, multi-atlas label fusion has become a state-of-the-art segmentation technique for 3D image and many efforts have been made to adapt it to a 4D longitudinal fashion. However, the previous methods were either limited by using application specified energy function (e.g., surface fusion and multi model fusion) or only considered temporal smoothness on two consecutive time points (t and t+1) under sparsity assumption. Therefore, a 4D multi-atlas label fusion theory for general label fusion purpose and simultaneously considering temporal consistency on all time points is appealing. Herein, we propose a novel longitudinal label fusion algorithm, called 4D joint label fusion (4DJLF), to incorporate the temporal consistency modeling via non-local patch-intensity covariance models. The advantages of 4DJLF include: (1) 4DJLF is under the general label fusion framework by simultaneously incorporating the spatial and temporal covariance on all longitudinal time points. (2) The proposed algorithm is a longitudinal generalization of a leading joint label fusion method (JLF) that has proven adaptable to a wide variety of applications. (3) The spatial temporal consistency of atlases is modeled in a probabilistic model inspired from both voting based and statistical fusion. The proposed approach improves the consistency of the longitudinal segmentation while retaining sensitivity compared with original JLF approach using the same set of atlases. The method is available online in open-source.