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.