MEMBER, IEEE, United Technologies Research Center, East Hart-ford, CT 06108.
IEEE Trans Pattern Anal Mach Intell. 1983 Feb;5(2):191-9. doi: 10.1109/tpami.1983.4767371.
A modified Mellin transform for digital implementation is developed and applied to range radar profiles of naval vessels. The scale invariance property of the Mellin transform provides a means for extracting features from the profiles which are insensitive to the aspect angle of the radar. Past implementations of the Mellin transform based on the FFT have required exponential sampling, interpolation, and the computation of a correction term, all of which introduce errors into the transform. In addition, exponential sampling results in a factor of ln N increase in the number of data points. An alternate implementation, developed in the paper, utilizes a direct expansion of the Mellin integral definition. This direct Mellin transform (DMT) eliminates the implementation problems associated with the FFT approach, and does not increase the number of samples. A scale and translation invariant transform is developed from a modification of the DMT. The MDMT applied to the FFT of the radar profiles results in the desired insensitivity without having the low-pass filtering characteristic that exists in other Fourier-Mellin implementations.
为数字实现开发了一种改进的 Mellin 变换，并将其应用于舰船雷达的距离剖面。Mellin 变换的尺度不变性为从剖面中提取对雷达方位角不敏感的特征提供了一种方法。基于 FFT 的 Mellin 变换的过去实现需要指数采样、插值和计算校正项，所有这些都会给变换带来误差。此外，指数采样会导致数据点数量增加因子 ln N。本文中开发的一种替代实现方法利用了 Mellin 积分定义的直接展开。这种直接 Mellin 变换（DMT）消除了与 FFT 方法相关的实现问题，并且不会增加采样数量。从 DMT 的修改中开发了一种具有尺度和平移不变性的变换。将 MDMT 应用于雷达剖面的 FFT 会得到所需的不敏感性，而不存在其他傅里叶-Mellin 实现中存在的低通滤波特性。
