| 1. |
- Iglesias, José Pedro Lopes, 1994, et al.
(författare)
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Accurate Optimization of Weighted Nuclear Norm for Non-Rigid Structure from Motion
- 2020
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Ingår i: Computer Vision – ECCV 2020 - 16th European Conference, 2020, Proceedings. - Cham : Springer International Publishing. - 0302-9743 .- 1611-3349. - 9783030585822 ; 12372 LNCS, s. 21-37
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Konferensbidrag (refereegranskat)abstract
- Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when applying more general singular value penalties, such as weighted nuclear norm priors, direct optimization over the elements of the matrix is typically used. Due to non-differentiability of the resulting objective function, first order sub-gradient or splitting methods are predominantly used. While these offer rapid iterations it is well known that they become inefficient near the minimum due to zig-zagging and in practice one is therefore often forced to settle for an approximate solution. In this paper we show that more accurate results can in many cases be achieved with 2nd order methods. Our main result shows how to construct bilinear formulations, for a general class of regularizers including weighted nuclear norm penalties, that are provably equivalent to the original problems. With these formulations the regularizing function becomes twice differentiable and 2nd order methods can be applied. We show experimentally, on a number of structure from motion problems, that our approach outperforms state-of-the-art methods.
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| 2. |
- Palmér, Tobias, et al.
(författare)
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The Misty Three Point Algorithm for Relative Pose
- 2017
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Ingår i: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.
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Konferensbidrag (refereegranskat)abstract
- There is a significant interest in scene reconstructionfrom underwater images given its utility for oceanic researchand for recreational image manipulation. In this paperwe propose a novel algorithm for two view camera motionestimation for underwater imagery. Our method leveragesthe constraints provided by the attenuation propertiesof water and its effects on the appearance of the color todetermine the depth difference of a point with respect to thetwo observing views of the underwater cameras. Additionally,we propose an algorithm, leveraging the depth differencesof three such observed points, to estimate the relativepose of the cameras. Given the unknown underwaterattenuation coefficients, our method estimates the relativemotion up to scale. The results are represented as a generalizedcamera. We evaluate our method on both real dataand simulated data.
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