薛帅, 王光霞, 郭建忠, 余文涛, 徐新伟. 顾及最大绝对误差的频率域矢量数据压缩算法[J]. 武汉大学学报 ( 信息科学版), 2018, 43(9): 1438-1444. DOI: 10.13203/j.whugis20160452
引用本文: 薛帅, 王光霞, 郭建忠, 余文涛, 徐新伟. 顾及最大绝对误差的频率域矢量数据压缩算法[J]. 武汉大学学报 ( 信息科学版), 2018, 43(9): 1438-1444. DOI: 10.13203/j.whugis20160452
XUE Shuai, WANG Guangxia, GUO Jianzhong, YU Wentao, XU Xinwei. Vector Map Data Compression of Frequency Domain with Consideration of Maximum Absolute Error[J]. Geomatics and Information Science of Wuhan University, 2018, 43(9): 1438-1444. DOI: 10.13203/j.whugis20160452
Citation: XUE Shuai, WANG Guangxia, GUO Jianzhong, YU Wentao, XU Xinwei. Vector Map Data Compression of Frequency Domain with Consideration of Maximum Absolute Error[J]. Geomatics and Information Science of Wuhan University, 2018, 43(9): 1438-1444. DOI: 10.13203/j.whugis20160452

顾及最大绝对误差的频率域矢量数据压缩算法

Vector Map Data Compression of Frequency Domain with Consideration of Maximum Absolute Error

  • 摘要: 针对传统的基于离散余弦变换(discrete cosine transform,DCT)的矢量数据压缩算法局部误差较大和计算复杂度高的问题,提出了一种顾及矢量数据最大绝对误差的快速近似DCT压缩方法。首先,结合现有矢量数据拓扑关系,构造矢量数据块;其次,根据近似DCT变换正交性的特点,计算约定矩阵的最优化解,将计算复杂度最低的解设为近似DCT变换的转换矩阵;最后,结合矢量数据近似DCT变换和精确DCT变换的总能量差,计算重构数据的最大绝对误差,对超过误差阈值的数据进行三次样条插值,最大限度地保证矢量数据精度。实验结果表明,该方法计算复杂度较低,压缩速度快,在降低压缩率的同时,能较好地保持空间数据的拓扑关系和数据精度。

     

    Abstract: In this paper, taking the maximum absolute error for vector data into account, we propose an approximate DCT compression method, which is designed for controlling the maximum absolute error and the high arithmetic complexity, aimed at traditional local compression algorithm for vector data based on discrete cosine transform. First of all, we construct vector data blocks on the basis of vector data topology. Secondly, we calculate the optimization solution of the agreed matrix in accor-dance with the orthogonality of approximate DCT transform, and then set the solution which has the minimum computational complexity as the conversion matrix for approximate DCT transform to ma-ximally guarantee the precision of vector data. Finally, we combine the total energy between the DCT transform and accurate approximate DCT transform of vector data with maximum absolute error of the reconstructed data, and use three spline interpolation function for data which exceeds thresholds of error to ensure maximum accuracy. Experimental results show that the proposed method has low computational complexity and high speed compression, it can keep the topological relation of the spatial data and the accuracy of the data while reducing the compression rate.

     

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