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二维旋转不变U变换及其应用

陈伟

陈伟. 二维旋转不变U变换及其应用. 自动化学报, 2016, 42(9): 1380-1388. doi: 10.16383/j.aas.2016.c150630
引用本文: 陈伟. 二维旋转不变U变换及其应用. 自动化学报, 2016, 42(9): 1380-1388. doi: 10.16383/j.aas.2016.c150630
CHEN Wei. 2D Rotation-invariant U Transform and Its Application. ACTA AUTOMATICA SINICA, 2016, 42(9): 1380-1388. doi: 10.16383/j.aas.2016.c150630
Citation: CHEN Wei. 2D Rotation-invariant U Transform and Its Application. ACTA AUTOMATICA SINICA, 2016, 42(9): 1380-1388. doi: 10.16383/j.aas.2016.c150630

二维旋转不变U变换及其应用

doi: 10.16383/j.aas.2016.c150630
基金项目: 

浙江大学CAD & CG国家重点实验室开放课题 A1609

中央高校基本科研业务费专项资金 JUSRP11416

国家自然科学基金 61170320

国家自然科学基金 61602213

国家自然科学基金 61402201

国家科技支撑计划 2015BAH54F00

详细信息
    作者简介:

    陈伟江南大学数字媒体学院讲师.2013年获得澳门科技大学理学博士学位.主要研究方向为计算机图形学和图像处理.E-mail:wchen_jdsm@163.com

2D Rotation-invariant U Transform and Its Application

Funds: 

the Open Project Program of the State Key Laboratory of CAD & CG of Zhejiang University A1609

Fundamental Research Funds for the Central Universities of China JUSRP11416

National Natural Science Foundation of China 61170320

National Natural Science Foundation of China 61602213

National Natural Science Foundation of China 61402201

National Science and Technology Support Program 2015BAH54F00

More Information
    Author Bio:

    Lecturer at the School of Digital Medial, Jiangnan University. He received his Ph. D. degree from Macau University of Science and Technology in 2013. His research interest covers computer graphics and image processing

  • 摘要: U-系统是一类L2[0,1]上的正交分段多项式函数系,为了将其推广到二维情形,传统的L2[0,1]2上张量积形式的U变换并不具有旋转不变性.本文提出了一类二维旋转不变U变换(Rotation-invariant U transform,RIUT). RIUT将U-系统函数与调和函数相结合,使得图像的旋转转化为相位的平移而模保持不变.与经典的正交旋转不变矩(如Zernike矩)相比,RIUT具有诸多特别的性质,从而在图像特征提取中具有良好的潜力.本文将RIUT应用到二值图像检索中的实验结果表明,RIUT具有更高的检索精度.
  • 图  1  1次U-系统的前16个基函数生成过

    Fig.  1  The first sixteen basis functions in U-system of degree one

    图  2  L2[0, 1]2上张量积形式的二维U-系统(k=1)

    Fig.  2  2D tensor product U-system on L2[0, 1]2(k=1)

    图  3  U-调和基函数图像

    Fig.  3  U-harmonic basis functions

    图  4  U-调和基函数的径向基

    Fig.  4  The radial kernels of U-harmonic basis functions

    图  5  Zernike多项式函数支撑

    Fig.  5  The suppression of Zernike polynomials

    图  6  图像的RIUT描述子

    Fig.  6  RIUT descriptor

    图  7  Lena图像旋转示例

    Fig.  7  Rotation examples of Lena image

    图  8  旋转图像的MSE

    Fig.  8  The MSE of rotated images

    图  9  CE2-A2库中图像示例

    Fig.  9  Images in CE2-A2 data set

    图  10  CE2-A4库中图像示例

    Fig.  10  Images in CE2-A4 data set

    图  11  CE2-B库中商标图像示例

    Fig.  11  Images in CE2-B data set

    表  1  各方法检索精度(CE2-A2图像库)(%)

    Table  1  Retrieval precision of different methods (CE2-A2 image data set) (%)

    检索精度 ZM PZM OFMM RIUT
    BEP 97.96 92.86 97.96 98.57
    下载: 导出CSV

    表  2  各方法检索精度(CE2-A4图像库) (%)

    Table  2  Retrieval precision of different methods (CE2-A4 image data set) (%)

    检索精度 ZM PZM OFMM RIUT
    BEP 70.39 58.87 70.66 76.97
    下载: 导出CSV

    表  3  CE2-B库中前10组相似商标数目

    Table  3  The similar trademarks number for the first ten groups in CE2-B data set

    组号 1 2 3 4 5 6 7 8 9 10
    数目 68 244 22 28 17 22 45 145 45 42
    下载: 导出CSV

    表  4  每组商标的检索精度(%)

    Table  4  Retrieval precision for each group (%)

    组号 1 2 3 4 5 6 7 8 9 10
    ZM 37.37 54.94 38.43 42.98 27.34 28.72 24.79 42.00 37.83 26.59
    PZM 22.45 52.99 33.88 23.60 40.48 26.45 17.23 41.02 44.00 30.22
    OFMM 25.65 49.41 30.37 38.90 33.22 22.31 26.27 45.65 29.23 22.90
    RIUT 31.55 53.33 38.84 41.74 47.40 20.04 30.72 52.12 33.93 28.29
    下载: 导出CSV

    表  5  平均检索精度(%)

    Table  5  The average retrieval precision (%)

    检索精度 ZM PZM OFMM RIUT
    BEP 36.10 33.23 32.39 37.79
    下载: 导出CSV
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出版历程
  • 收稿日期:  2015-10-12
  • 录用日期:  2016-03-10
  • 刊出日期:  2016-09-01

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