Abstract: Extraction of image rotation invariant feature is an important application in image processing and pattern recognition. The orthogonal moment function in polar coordinate is the primary method of extracting feature information. The decomposition and reconstruction error of image is the standard of measuring its feature extraction accuracy. To improve the performance of orthogonal moment function in image reconstruction, it proposes a new orthogonal moment function based on trigonometric functions, and a new measure method based on function error analysis, and applies the new measure method and the traditional method which needs error statistics in a large number of image reconstructions to make a comparison between the new orthogonal moment function and the other two orthogonal moment functions which have the best performance in feature extraction. The result of experiment demonstrates the effectiveness of the new measure method and also concludes that the new orthogonal moment function has better effect in image reconstruction.

Key words: error analysis, error prediction, image reconstruction, rotation invariant

摘要： 提取图像中旋转不变特征是图像处理和模式识别中重要的应用。在极坐标下的正交矩函数则是提取这种特征信息的主要方法。正交矩函数在图像分解和重建过程中的误差是衡量其特征提取精确度的标准。为了提高正交矩函数在图像重建中的性能，提出了一种新的基于三角函数的正交矩函数和一种基于函数误差分析的新的衡量方法，并分别应用新的衡量方法和传统的在大量图像中进行重建误差统计的方法对新的正交矩函数以及另外两种在特征提取方面表现最好的正交矩函数进行了比较。实验结果验证了新的衡量方法的有效性并得到了新的正交矩函数的重建效果更好的结论。

关键词: 误差分析, 误差预测, 图像重建, 旋转不变