Conventional spatial imaging of the same object at different times or with different sensing modalities often requires the identification of corresponding points within a solid object. A mathematically similar problem occurs in the remote hyperspectral imaging of one scene at two widely separated time intervals. In both cases the information can be interpreted using linear vector spaces, and the differences in sensed signals can be modeled with linear transformations of these spaces. Here we explore first, how much can be deduced about the transformations based solely on the multivariate statistics of the two data sets. Then we solve application-specific models for each of conventional and hyperspectral applications.