An L&lt;sub&gt;&amp;#x0221E;&lt;/sub&gt; approach to structure and motion problems in ID-vision

Åström, Kalle; Enquist, Olof; Kahl, Fredrik; Hartley, Richard

doi:10.1109/iccv.2007.4408914

Cited by 12 publications

(6 citation statements)

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“…In recent years, the convex optimization theory [8] has been applied to computer vision problems and useful results have been attained [9], [10], [11], [7], [12], [13], [14], [15], [16], [17].…”

Section: Related Workmentioning

confidence: 99%

Multiview triangulation with uncertain data

Zhang

Chen

et al. 2013

2013 IEEE International Conference on Robotics and Biomimetics (ROBIO)

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The traditional triangulation algorithms in multiview geometry problems have the drawback that its solution is locally optimal. Robust Optimization is a specific and relatively novel methodology for handling optimization problems with uncertain data. The key idea of robust optimization is to find the best possible performance in the worst case. In this paper, we propose a novel approach which solves the triangulation problems with perturbational data employing robust optimization. The main advantage of this method is global optimality under the perturbational data. Good performance has been demonstrated by experimental results for synthetic and real data, respectively.

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Section: Related Workmentioning

confidence: 99%

Multiview triangulation with uncertain data

Zhang

Chen

et al. 2013

2013 IEEE International Conference on Robotics and Biomimetics (ROBIO)

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“…18. 19 Although latest developments for L ∞ based norms vision optimization could provide accurate and global minimum solutions, the technique used is computationally heavy. In Ref.…”

Section: Related Workmentioning

confidence: 99%

Robust L∞ homography estimation using reduced image feature covariances from an RGB image

Imran

Aouf

2012

J. Electron. Imaging

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Image features are regularly used in computer and machine vision applications to solve problems pertaining to image geometry. The effectiveness of techniques used rely on how accurately corresponding features are located in two (or more) images. Current techniques define a feature as a variation in intensity within a pixel neighborhood. The greater the change, the more pronounced a feature becomes, and is thus more accurately located. The remaining uncertainty is characterized via a covariance matrix, which is used to weight the influence of each feature on model estimation. As our first contribution, we propose a novel technique to decrease feature location uncertainty. Considering uncertainty information from all three channels of an RGB image, we employ covariance intersection (CI) to reduce measurement errors leading to a decrease in homography (H) estimation error. Our second contribution is to use an L ∞ filter capable of dealing with system uncertainties to estimate H. By feeding the feature location uncertainty information into our filter, we observe significantly improved estimates of the homography. Our filtering approach outperforms covariance weighted optimization techniques proposed in literature shown through a number of examples.

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“…It has been used for various problems such as triangulation, inter-image homography, camera resectioning, structure and motion with known rotation [6,8,7]. Recent publications include motion estimation [16], robot application [2], non-rigid surface tracking [14], outliers removal [17,9,10], increasing the speed of computation [15,1], the pseudo-convexity of the re-projection error function [11], etc.…”

Section: Introductionmentioning

confidence: 99%