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Motion segmentation and motion estimation are important topics in computer vision. Tensor Voting is a process that addresses both issues simultaneously; but running time is a challenge. We propose a novel approach which can yield both the motion segmentation and the motion estimation in the presence of discontinuities. This method is a combination of a non-iterative boosted-speed voting process in sparse space in a first stage, and a Graph-Cuts framework for boundary refinement in a second stage. Here, we concentrate on the motion segmentation problem. After initially choosing a sparse space by sampling the original image, we represent each of these pixels as 4-D tensor points and apply the voting framework to enforce local smoothness of motion. Afterwards, the boundary refinement is obtained by using the Graph-Cuts image segmentation. Our results attained in different types of motion show that the method outperforms other Tensor Voting approaches in speed, and the results are comparable with other methodologies in motion segmentation.