An efficient stochastic approach to groupwise non-rigid image registration

The groupwise approach to non-rigid image registration, solving the dense correspondence problem, has recently been shown to be a useful tool in many applications, in- cluding medical imaging, automatic construction of statis- tical models of appearance and analysis of facial dynam- ics. Such an approach overcomes limitations of traditional pairwise methods but at a cost of having to search for the solution (optimal registration) in a space of much higher dimensionality which grows rapidly with the number of ex- amples (images) being registered. Techniques to overcome this dimensionality problem have not been addressed suffi- ciently in the groupwise registration literature. In this paper, we propose a novel, fast and reliable, fully unsupervised stochastic algorithm to search for optimal groupwise dense correspondence in large sets of unmarked images. The efficiency of our approach stems from novel di- mensionality reduction techniques specific to the problem of groupwise image registration and from comparative insen- sitivity of the adopted optimisation scheme (Simultaneous Perturbation Stochastic Approximation (SPSA)) to the high dimensionality of the search space. Additionally, our algo- rithm is formulated in way readily suited to implementation on graphics processing units (GPU). In evaluation of our method we show a high robust- ness and success rate, fast convergence on various types of test data, including facial images featuring large degrees of both inter- and intra-person variation, and show consid- erable improvement in terms of accuracy of solution and speed compared to traditional methods