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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… (More)

In many computer vision applications, a desired model of some type is computed by minimizing a cost function based on several measurements. Typically, one may compute the model that minimizes the L2 cost, that is the sum of squares of measurement errors with respect to the model. However, the Lq solution which minimizes the sum of the qth power of errors… (More)

This paper presents a method for finding an L q-closest-point to a set of affine subspaces, that is a point for which the sum of the q-th power of orthogonal distances to all the subspaces is minimized, where 1 ≤ q < 2. We give a theoretical proof for the convergence of the proposed algorithm to a unique L q minimum. The proposed method is motivated by the… (More)

This paper presents a method for finding an $$L_q$$ L q -closest-point to a set of affine subspaces, that is a point for which the sum of the q-th power of orthogonal distances to all the subspaces is minimized, where $$1 \le q < 2$$ 1 ≤ q < 2 . We give a theoretical proof for the convergence of the proposed algorithm to a unique $$L_q$$ L q minimum. The… (More)

- Khurrum Aftab, Richard Hartley, Jochen Trumpf
- 2012

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