While motion estimation has been extensively studied in the computer vision literature, the inherent information redundancy in an image sequence has not been well utilised. In particular as many as \frac{{N(N - 1)}}{2} pairwise relative motions can be estimated efficiently from a sequence of N images. This highly redundant set of observations can be efficiently averaged resulting in fast motion estimation algorithms that are globally consistent. In this paper we demonstrate this using the underlying Lie-group structure of motion representations. The Lie-algebras of the Special Orthogonal and Special Euclidean groups are used to define averages on the Lie-group which in turn gives statistically meaningful, efficient and accurate algorithms for fusing motion information. Using multiple constraints also controls the drift in the solution due to accumulating error. The performance of the method in estimating camera motion is demonstrated on image sequences.