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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.Abstract: U-system is a class of orthogonal piecewise-polynomial function system in L2[0, 1], and its generalized U-system in L2[0, 1]2 with tensor-product form is not rotation-invariant. In this paper, we present a novel 2D transform named rotation-invariant U transform (RIUT). The construction of RIUT combines U-system functions with harmonic functions so that the object's rotation is transformed into its phase's translation and the modulus keeps unchanged. Compared with the classical rotation-invariant moments, such as Zernike moment, RIUT has many special properties, suggesting an applying potential in image feature extraction. The experiment results for binary image retrieval show that RIUT method has a higher retrieval precision.
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Key words:
- Rotation-invariant /
- U-system /
- Zernike moment /
- binary image retrieval
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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
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 
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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
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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
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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
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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
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