Research Of Discrete Cosine Transform And Compression Based On Hexagonal Sampling Grid

Image as material representations of human visual perception is no stranger to us who live in the information age. Image with a lot of information is vivid and it is the important carrier for human being who obtains abundant information. With the development and maturation of computer technology and 3G communication technology, image and video as an important carrier of multimedia information have been widely used in various fields of people's lives. The data quantity of image and video that is not compressed is very large, which requires extremely high for storage capacity and transmission bandwidth. At present, the ordinary computer can not meet such high requirements for mass data of image and video. Therefore, the compression technology plays an important role in storage and transmission of image and video.Traditionally, the image sampling is based on rectangular lattice. Medical research shows that the arrangement of human retinal cells is hexagonal structure. Therefore, hexagonal sampling scheme is more consistent with human visual characteristics and it can produce better visual effects. Hexagonal sampling is the optimal sampling scheme for continuous images which are band limited over a circular region of Fourier plane. In the sense that hexagonal sampling requires 13.4% fewer samples than rectangular sampling if we reconstruct the original image exactly. The efficiency of hexagonal sampling is higher with the increase of dimensions. Hexagonal sampling requires 29.5% fewer samples when the data are three-dimensional and the reduction of samples is up to 50.1% when the data are four-dimensional. So the dimensions of the processed data are higher, the advantages of hexagonal sampling are more obvious. Compared with the rectangular sampling scheme, there are many other advantages with the hexagonal sampling scheme. Among these advantages are higher degree of circular symmetry, uniform connectivity, greater angular resolution, and a reduced need of storage and computation in image processing operations. Therefore, the hexagonal sampling scheme applied to the field of image coding can improve the coding efficiency.The main content of this paper is the study of color image and video coding based on hexagonal discrete cosine transform. Hexagonal sampling is applied to color image and video compression in this paper. The paper in detail discusses the hexagonal discrete Fourier transform (HDFT) and the resultant hexagonal discrete cosine transform (HDCT). At present, all image capturing and displaying devices are based on rectangular grid structure. We need to convert the rectangular sampled image to hexagonal sampled image first in order to apply the HDCT to image coding. The rectangular sampled image is converted to hexagonal sampled image by interpolation according to the sampling matrix. The re-sampling image is partitioned into hexagonal sub-images and then the HDCT is applied to these hexagonal sub-images for color image coding.Generally, the RGB signals are converted to YUV signals first when color image is coded. Then gray image coding method is applied to each component separately. There is great correlation between RGB components since they come from the same physical model. The various redundancy and correlation between RGB components of color image are not utilized fully if each component is coded independently. This problem also exists in the frames of video data. In order to take use of correlation between color components of color image and correlation between frames of video, the paper presents a 3D discrete cosine transform based on hexagonal sampling and verifies the performance of energy concentration. In order to take use of 3D transform, the 3D data representation and block segmentation method of color image and video are given in this paper according to characteristics of color image and video. During the transformation, the RGB components of color image and successive frames of video can be considered as a whole and based on the same model. The transform coefficients obtained are coded by lossless compression technology in order to compress the color image and video.Finally, the effectiveness of algorithms in this paper is verified by simulation results and the conceptions are presented according to the deficiency and the future research direction of this paper. All algorithms are programmed by C language in this paper.