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- Richard I. Hartley, Khurrum Aftab, Jochen Trumpf
- CVPR
- 2011

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)

- Khurrum Aftab, Richard I. Hartley, Jochen Trumpf
- IEEE Transactions on Pattern Analysis and Machine…
- 2015

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 L<sub>2</sub> cost, that is the sum of squares of measurement errors with respect to the model. However, the L<sub>q</sub> solution which minimizes the sum of the… (More)

- Khurrum Aftab, Richard I. Hartley
- 2015 IEEE Winter Conference on Applications of…
- 2015

This paper presents a way of using the Iteratively Reweighted Least Squares (IRLS) method to minimize several robust cost functions such as the Huber function, the Cauchy function and others. It is known that IRLS (otherwise known as Weiszfeld) techniques are generally more robust to outliers than the corresponding least squares methods, but the full range… (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)

- Khurrum Aftab, Richard I. Hartley
- 2015 IEEE International Conference on Image…
- 2015

In this paper we propose a method to solve for an L<sub>q</sub> solution of bundle adjustment, a non-linear parameter estimation problem. Given a set of images of a scene, bundle adjustment simultaneously estimates camera parameters and 3D structure of the scene. Generally, a least squares criterion is minimized by using the Levenberg-Marquardt (LM) method,… (More)

In next generation global communication networks, satellite networks are expected to complement terrestrial networks where they best serve communication needs of users. Weight and power constraints place severe limitations on satellite on-board resources which includes the number of transponders that a satellite can carry and on-board processing… (More)

- Khurrum Aftab, Richard I. Hartley, Jochen Trumpf
- International Journal of Computer Vision
- 2014

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 I. Hartley
- 2013 International Conference on Digital Image…
- 2013

We propose a method to find the L<sub>q</sub> mean of a set of symmetric positive-definite (SPD) matrices, for 1 ≤ q ≤ 2. Given a set of points, the L<sub>q</sub> mean is defined as a point for which the sum of q-th power of distances to all the given points is minimum. The L<sub>q</sub> mean, for some value of q, has an advantage of being… (More)

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