Comparing object alignment algorithms with appearance variation: Forward-additive vs inverse-composition

A common problem that affects object alignment algorithms is when they have to deal with objects with unseen intra-class appearance variation. Several variants based on gradient-decent algorithms, such as the Lucas-Kanade (or forward-additive) and inverse-compositional algorithms, have been proposed to deal with this issue by solving for both alignment and appearance simultaneously. In [1], Baker and Matthews showed that without appearance variation, the inverse-compositional (IC) algorithm was theoretically and empirically equivalent to the forward-additive (FA) algorithm, whilst achieving significant improvement in computational efficiency. With appearance variation, it would be intuitive that a similar benefit of the IC algorithm would be experienced over the FA counterpart. However, to date no such comparison has been performed. In this paper we remedy this situation by performing such a comparison. In this comparison we show that the two algorithms are not equivalent due to the inclusion of the appearance variation parameters. Through a number of experiments on the MultiPIE face database, we show that we can gain greater refinement using the FA algorithm due to it being a truer solution than the IC approach.