| With the development of the computer and network technique, information is increasing at a dramatic speed. If one wants to use it effectively, then it is necessary to compress it. The main type of information people get is image and video. But the mount of data of digital image and video is huge. Due to the limitation of current computer technique and network bandwidth, it is impossible to store and transmit it directly. Since there exist visual, statistical, structural and knowledge redundancies in image and video, it is possible to compress it at a high compression ratio. From the first generation to the second generation of coding technique, video coding develops rapidly. Some new video coding techniques and new standards have been proposed in recent years, among witch the most famous are H.26x and MPEG. Object-oriented coding is the main trend under research. And it is consistent with people's perceptional characteristics. This paper proposed an object-oriented coding algorithm of color video based on multidimensional matrix theories. In the current segmentation algorithms, the ones based on spatial features can achieve accurate contour. But the segmented regions usually have no semantic meanings. Since the motion features of regions in a semantic object are usually the same, the algorithm based on motion can get the main part of a semantic object. But the contour achieved in this algorithm is rough. Therefore, spatial-temporal segmentation algorithm combining spatial features and motion features can derive accurate semantic object. A spatial-temporal segmentation is used in this paper. The multidimensional matrix transform theories we proposed can get rid of correlation in spatial, temporal and spectral dimensions. Multidimensional matrix theories are expanded and improved in this paper. Some key definitions are given, including point multiplication of multidimensional matrix and two-dimensional matrix, matrix multiplication of multidimensional matrices, matrix division of multidimensional matrices, and zero plane. In addition, primary transform of multidimensional matrix is introduced. We construct a four-dimensional matrix model for color video sequence, which includes two spatial dimensions, one spectral dimension and one temporal dimension. Directly applying transformation to the four-dimensional matrix is unsuitable for computation or for getting rid of the correlation in the matrix. So it is necessary to partition the matrix, and submatrices of size 8×8×3×8 are achieved. Then four-dimensional matrix DCT(4D-MDCT) is performed to get rid of the correlation between pixels in the submatrix. Four subscripts of the submatrix construct a vector. Norm 2 is used to denote the distance between the subscript vector and zero vector. After transformation, larger coefficients lie on those pixels with smaller distance according to the zero vector. After the coefficients are quantized by a four-dimensional quantization matrix, most of them equal 0, and thus many zero planes appear in the submatrix. Therefore, we proposed an omitting zero plane coding scheme, which greatly increases the efficiency of coding. In the subsequent coding, traditional run-length coding and Huffman coding are used. Though 4D-MDCT can get rid of the correlation between pixels in the submatrix, it can not get rid of the correlation between the submatrices. Research indicates that there is still much correlation between the submatrices in most of the color video sequences, especially the less textured color video. So 4D-MDCT coding of color video based on prediction and compensation is proposed. First, it detects whether the current quantized submatrix is the same as the previous temporal one, and denotes with a flag. If they are different, then the previous one is used to predict the current one, and calculate the compensation coefficients. Search submatrices with the same compensation coefficients in the current temporal position. Only the first one of the submatrices with same compensation coefficients...
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