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The computation of optical flow in video sequences is a challenging task in most camera based scene interpretation systems. In the past, most optical flow computation algorithms has been either implemented in software running on general purpose processors or designed as an application specific hardware. However, these implementations either cannot support real-time processing requirements or result in excessive inaccuracies in the computed velocity values. In this work, we propose a efficient VLSI system architecture for computing the optical flow in video sequences using the Lucas-Kanade (L-K) algorithm. The algorithm is converted into high speed RTL implementation by exploiting the inherent paralellism in the data flow graph. Clever pipelining strategies has been used throughout the design to further improve the speedup of velocity computation. We have mapped the RTL design on a Xilinx Virtex II XUPV2P FPGA board. Experimental results of our proposed design showed significant improvements in accuracy with a speedup of five times when compared with other recent hardware implementations.