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Image registration consists in estimating geometric and photometric transformations that align two images as best as possible. The direct approach consists in minimizing the discrepancy in the intensity or color of the pixels. The inverse compositional algorithm has been recently proposed by Baker et al. for the direct estimation of groupwise geometric transformations. It is efficient in that it performs several computationally expensive calculations at a pre-computation phase. Photometric transformations act on the value of the pixels. They account for effects such as lighting change. Jointly estimating geometric and photometric transformations is thus important for many tasks such as image mosaicing. We propose an algorithm to jointly estimate groupwise geometric and photometric transformations while preserving the efficient pre-computation based design of the original inverse compositional algorithm. It is called the dual inverse compositional algorithm. It uses different approximations than the simultaneous inverse compositional algorithm and handles groupwise geometric and global photometric transformations. Its name stems from the fact that it uses an inverse compositional update rule for both the geometric and the photometric transformations. We demonstrate the proposed algorithm and compare it to previous ones on simulated and real data. This shows clear improvements in computational efficiency and in terms of convergence.