<title>Variable size block matching motion estimation with minimal error</title>

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Block matching type motion compensation is relatively simple to implement, and thus widely adopted in image sequence coding. Most techniques use fixed-size blocks, and their success relies on the assumption that the motion within each block is uniform. This is not necessarily true, especially if the block size is increased to reduce the number of motion vectors. One solution is to use variable-sized blocks, and a number of schemes have been suggested. The success of variable-size block matching (VSBM) is dependent on an appropriate selection of different size blocks to cover the entire image. Given a fixed number of blocks, in order to obtain the best frame prediction it is necessary to select that set of variable-sized blocks which, when matched with similar blocks in the previous frame, results in the minimum total error. This requirement is difficult to satisfy. Two advances are reported. Firstly an algorithm is described which, based on a quad-tree structure, results in the optimal selection of variable-sized square blocks. It is applied in a VSBM scheme in which the total mean squared error (MSE) is minimized. This provides the best-achievable performance for a quad-tree based VSBM technique. Although it is computationally demanding and hence impractical for real-time codecs, it does provide a yardstick by which the performance of other VSBM techniques can be measured. Secondly, a new VSBM algorithm which adopts a `bottom-up'' approach is described. The technique starts by computing sets of `candidate'' motion vectors for fixed-size small blocks. Blocks are then effectively merged in a quad-tree manner if they have similar motion vectors. The result is a computationally-efficient VSBM technique which performs very well when compared with the optimal algorithm.