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, lon-gitudinal segmentation (4D) approaches have been investigated to reconcile tem-poral variations with traditional 3D approaches... In the past decade, multi-atlas la-bel 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 tem-poral smoothness on two consecutive time points (t and t+1) under sparsity as-sumption. 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 simul-taneously incorporating the spatial and temporal covariance on all longitudinal time points. (2) The proposed algorithm is a longitudinal generalization of a lead-ing 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 prob-abilistic model inspired from both voting based and statistical fusion. The pro-posed 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. (read more)