@inproceedings{1b4e20557da447ec8dc14a4dae14746a,

title = "L1 rotation averaging using the weiszfeld algorithm",

abstract = " We consider the problem of rotation averaging under the L 1 norm. This problem is related to the classic Fermat-Weber problem for finding the geometric median of a set of points in IR n . We apply the classical Weiszfeld algorithm to this problem, adapting it iteratively in tangent spaces of SO(3) to obtain a provably convergent algorithm for finding the L 1 mean. This results in an extremely simple and rapid averaging algorithm, without the need for line search. The choice of L 1 mean (also called geometric median) is motivated by its greater robustness compared with rotation averaging under the L 2 norm (the usual averaging process). We apply this problem to both single-rotation averaging (under which the algorithm provably finds the global L 1 optimum) and multiple rotation averaging (for which no such proof exists). The algorithm is demonstrated to give markedly improved results, compared with L 2 averaging. We achieve a median rotation error of 0.82 degrees on the 595 images of the Notre Dame image set.",

author = "Richard Hartley and Khurrum Aftab and Jochen Trumpf",

year = "2011",

doi = "10.1109/CVPR.2011.5995745",

language = "English",

isbn = "9781457703942",

series = "Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition",

publisher = "IEEE Computer Society",

pages = "3041--3048",

booktitle = "2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011",

address = "United States",

}