With the increasing application of robots, stable and efficient Visual Odometry (VO) algorithms are becoming more and more important. Based on the Fourier Mellin Transformation (FMT) algorithm, the extended Fourier Mellin Transformation (eFMT) is an image registration approach that can be applied to downward-looking cameras, for example on aerial and underwater vehicles. eFMT extends FMT to multi-depth scenes and thus more application scenarios. It is a visual odometry method which estimates the pose transformation between three overlapping images. On this basis, we develop an optimized eFMT algorithm that improves certain aspects of the method and combines it with back-end optimization for the small loop of three consecutive frames. For this we investigate the extraction of uncertainty information from the eFMT registration, the related objective function and the graph-based optimization. Finally, we design a series of experiments to investigate the properties of this approach and compare it with other VO and SLAM (Simultaneous Localization and Mapping) algorithms. The results show the superior accuracy and speed of our o-eFMT approach, which is published as open source.

翻译：随着机器人应用的日益增多，稳定高效的视觉里程计算法（VO）变得愈发重要。基于傅里叶梅林变换（FMT）算法，扩展傅里叶梅林变换（eFMT）是一种适用于下视摄像头（例如空中和水下飞行器）的图像配准方法。eFMT将FMT扩展至多深度场景，从而适用于更多应用场景。它是一种视觉里程计方法，通过估计三幅重叠图像之间的位姿变换来实现定位。在此基础上，我们开发了一种优化的eFMT算法，改进了该方法的部分环节，并将其与后端优化结合，用于连续三帧的小回路处理。为此，我们研究了从eFMT配准中提取不确定信息的方法、相关目标函数以及基于图优化的技术。最后，我们设计了一系列实验来探究该方法的特性，并将其与其他VO和SLAM（同时定位与地图构建）算法进行了比较。结果表明，我们的o-eFMT方法具有卓越的精度和速度，并已作为开源代码发布。