Images with Uncertainty: Efficient Algorithms for Shift, Rotation, Scaling, and Registration, and their Applications to Geosciences

In geosciences, we often need to combine two or images of the same area: in data fusion, we must combine, e.g., data from satellite images with a radar image in analyzing the effect of an earthquake, we must compare the before and after images, etc. Compared images are often obtained from slightly different angles, from a slightly different position. Therefore, in order to compare these images, we must register them, i.e., find the shift, rotation, and scaling after which these images match the best, and then apply these transformations to the original images. There exist efficient algorithms for registration and for the corresponding transformations, but these algorithms are only effective when we know these images with high accuracy. In many real-life situation - e.g., when comparing pre- and post-earthquake image - the accuracy with which we determine these images is of the same order of magnitude as the desired different between the compared images. In this paper, we describe how we can generalize the existing techniques to the case of low accuracy images, and how the resulting algorithms can be efficiently applied in geosciences