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We present a variational optical flow method to robustly estimate motion under varying illumination. The corresponding energy functional adopts two constancy assumptions including moments-based descriptors as well as the gradient of the brightness. We illustrate how the proposed assumptions are designed to compensate for the multiplicative and additive components of the brightness variation. The method is described within a combined local-global framework which preserves discontinuity over spatiotemporal domain. Comprehensive evaluations demonstrate the reliable results of our method under strong varying illumination as well as its robustness against random noise.