Ice velocity observations available on-line or on-demand at intra-annual resolutions still contain gaps, noise, and artifacts, especially in mountain areas. There is a need to fuse the available multi-temporal and multi-sensor velocity observations to be able to study intra-annual glacier dynamics. The proposed approach includes an inversion based on the temporal closure of displacement observation networks and a temporal interpolation. It reconstructs velocity time series between consecutive dates at a regular temporal sampling (called Regular Leap Frog (RLF) time series) inferred from all the velocity observations without a prori knowledge on the displacement behavior. The RLF time series can be reconstructed for different temporal sampling. Root Mean Square Error (RMSE) over stable areas and Velocity Vector Coherence (VVC) over fast moving areas are proposed to select a temporal sampling allowing a compromise between uncertainty and temporal resolution. This study focuses on the Fox glacier, in the Southern Alps of New Zealand. It shows that RMSE over stable areas is decreased from 78% for a temporal sampling of 5 days to 40% for a temporal sampling of 60 days. Thus, using this approach, we obtain a velocity time series with complete temporal coverage and reduced uncertainty for a regular and optimal temporal sampling. The results highlight the large seasonal variability of the flow of Fox Glacier that fluctuates by more than 30% between spring and autumn.