Constructing Hilbert Curve Of Any Size For Image And Video Compression

With the development of information and hardware technology and the rapid rise of short video multimedia industry,the amount of image and video data dissemination and preservation is increasing at a geometric rate.It is difficult to support such a large amount of data by hardware technology alone to expand storage equipment and upgrade transmission equipment bandwidth.Based on the above reasons,image compression technology emerges as the times require,and has a considerable application prospect.When the two-dimensional image coefficient and the three-dimensional video coefficient are compressed,both the two-dimensional or three-dimensional coefficients need to be scanned into one-dimensional data through the scanning curve,so as to facilitate the subsequent processing.Most of the previous compression methods used relatively simple line-by-line scanning or zigzag scanning curves.However,compared with these two scanning curves,Hilbert curves can better preserve the correlation between image and video coefficients.Most of the previous studies on the construction method of Hilbert curve path stay in the construction of square curve with side length of 2⁹).Similar to two-dimensional,the traditional scanning method of three-dimensional Hilbert curve path should satisfy the cube structure with a side length of 2⁹).Since the two-dimensional and three-dimensional Hilbert curves can only take some fixed values because of the side length,the application of Hilbert curves is greatly limited.In view of the above problems,a method of constructing arbitrary scale Hilbert curve is proposed and applied to image compression,which improves the compression performance to a certain extent.Among them,the idea of two-dimensional Hilbert curve construction is to divide any scale rectangle into sub-blocks and then construct each sub-block in turn.Similarly,the three-dimensional Hilbert curve is divided into sub-blocks by cube and constructed in turn.In the construction of two-dimensional curve,the sub-blocks divided each time should contain the largest square curve with a side length of 2⁶)in the unconstructed part,and the three-dimensional curve should construct a square shape curve with a maximum side length of 2⁶).Further,based on the largest square or square shape curve,add or delete rows in the high direction of a square or cube.According to this idea,the construction method of Hilbert curve scanning path of arbitrary scale rectangle or cube is obtained.On the basis of this method,two-dimensional Hilbert curves of arbitrary scale and three-dimensional Hilbert curve paths with width and height of arbitrary scale are constructed.Since Hilbert scan curves can retain data aggregation,two and three-dimensional Hilbert curves can be used in image and video compression at any scale.Experiments show that Hilbert curve scanning can effectively improve the image compression efficiency compared with line scanning.