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This study proposes two efficient block matching algorithms for fast motion estimation using a histogram ordering model in order to reduce the computational cost of video coding. Since the representative pixels that consist of edge or texture mainly contribute to the block matching criterion, it is important to analyse the details of the current block. To analyse the characteristics of the block with low complexity, the pixel histogram is used for the observation of the block. Based on this pixel histogram for the current block, an optimal block matching order is determined for the lossless fast matching algorithm. In addition, adaptive partial block matching algorithm for lossy fast motion estimation using histogram-based block matching ordering is also presented to further reduce the complexity of block matching. By capturing the representative pixels, block matching distortion is maximised soon enough during the block matching. For this reason, partial block matching is available instead of full block matching, which is also known as a full search algorithm. Our experimental results show that the proposed algorithm not only reduces the computational complexity of block matching criterion, but also tends to maintain the image quality when compared to the conventional fast matching algorithms.