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Multi-view video coding exploits inter-view redundancies to compress the video streams and their associated depth information. These techniques utilize disparity estimation techniques to obtain disparity vectors (DVs) across different views. However, these methods contribute to the majority of the computational power needed for multi-view video encoding. This paper proposes a solution for fast disparity estimation based on multi-view geometry and depth information. A DV predictor is first calculated followed by an iterative or a fast search estimation process which finds the optimal DV in the search area dictated by the predictor. Simulation results demonstrate that this predictor is reliable enough to determine the area of the optimal DVs to allow a smaller search range. Furthermore, results show that the proposed approach achieves a speedup of 2.5 while still preserving the original rate-distortion performance.