A Complexity-Distortion Approach to Joint Pattern Alignment

Image Congealing (IC) is a non-parametric method for the joint alignment of a col- lection of images affected by systematic and unwanted deformations. The method attempts to undo the deformations by minimizing a measure of complexity of the image ensemble, such as the averaged per-pixel entropy. This enables alignment without an explicit model of the aligned dataset as required by other methods (e.g. transformed component analysis). While IC is simple and general, it may intro- duce degenerate solutions when the transformations allow minimizing the com- plexity of the data by collapsing them to a constant. Such solutions need to be explicitly removed by regularization. In this paper we propose an alternative formulation which solves this regulariza- tion issue on a more principled ground. We make the simple observation that alignment should simplify the data while preserving the useful information car- ried by them. Therefore we trade off fidelity and complexity of the aligned en- semble rather than minimizing the complexity alone. This eliminates the need for an explicit regularization of the transformations, and has a number of other useful properties such as noise suppression. We show the modeling and computa- tional benefits of the approach to the some of the problems on which IC has been demonstrated.