True multi-image alignment and its application to mosaicing and lens distortion correction

Multiple images of a scene are related through 2D/3D view transformations and linear and non-linear camera transformations. In all the traditional techniques to compute these transformations, especially the ones relying on direct intensity gradients, one image and its coordinate system have been assumed to be ideal and distortion free. In this paper, we present a formulation and an algorithm for true multi-image alignment that does not rely on the measurements of a reference image being distortion free. For instance, in the presence of lens distortion, none of the images can be assumed to be ideal. In our formulation, all the images are modeled as intensity measurements represented in their respective coordinate systems, each of which is related to an ideal coordinate system through an interior camera transformation and an exterior view transformation. The goal of the accompanying algorithm is to compute an image in the ideal coordinate system while solving for the transformations that relate the ideal system with each of the data images. Key advantages of the technique presented in this paper are: (i) no reliance on one distortion free image, (ii) ability to register images and compute coordinate transformations even when the multiple images are of an extended scene with no overlap between the first and last frame of the sequence, and (iii) ability to handle linear and non-linear transformations within the same framework. The new algorithm is evaluated in the context of two applications: (i) correction of lens distortion, and (ii) creation of video mosaics.