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3D imaging techniques have the potential to establish a future mass-market in the fields of entertainment and communications. Integral imaging, which can capture true 3D color images with only one camera, has been seen as the right technology to offer stress-free viewing to audiences of more than one person. Just like any digital video, 3D video sequences must also be compressed in order to make it suitable for consumer domain applications. However, ordinary compression techniques found in state-of-the-art video coding standards such as H.264, MPEG-4 and MPEG-2 are not capable of producing enough compression while preserving the 3D clues. Fortunately, a huge amount of redundancies can be found in an integral video sequence in terms of motion and disparity. This paper discusses a novel approach to use both motion and disparity information to compress 3D integral video sequences. We propose to decompose the integral video sequence down to viewpoint video sequences and jointly exploit motion and disparity redundancies to maximize the compression. We further propose an optimization technique based on evolutionary strategies to minimize the computational complexity of the joint motion- disparity estimation. Experimental results demonstrate that Joint Motion and Disparity Estimation can achieve over 1 dB objective quality gain over normal motion estimation. Once combined with Evolutionary strategy, this can achieve up to 94% computational cost saving.