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11
Outlier removal using duality
 In CVPR 2010
, 2010
"... In this paper we consider the problem of outlier removal for large scale multiview reconstruction problems. An efficient and very popular method for this task is RANSAC. However, as RANSAC only works on a subset of the images, mismatches in longer point tracks may go undetected. To deal with this pr ..."
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In this paper we consider the problem of outlier removal for large scale multiview reconstruction problems. An efficient and very popular method for this task is RANSAC. However, as RANSAC only works on a subset of the images, mismatches in longer point tracks may go undetected. To deal with this problem we would like to have, as a post processing step to RANSAC, a method that works on the entire (or a larger) part of the sequence. In this paper we consider two algorithms for doing this. The first one is related to a method by Sim & Hartley where a quasiconvex problem is solved repeatedly and the error residuals with the largest error is removed. Instead of solving a quasiconvex problem in each step we show that it is enough to solve a single LP or SOCP which yields a significant speedup. Using duality we show that the same theoretical result holds for our method. The second algorithm is a faster version of the first, and it is related to the popular method of L1optimization. While it is faster and works very well in practice, there is no theoretical guarantee of success. We show that these two methods are related through duality, and evaluate the methods on a number of data sets with promising results. 1 1. Outliers in Multiple View Geometry Geometric reconstruction is a core problem in computer vision. Typically, feature points are first extracted from the images and then matched to corresponding points in other images. The corresponding points are used to estimate the geometry. Given correct correspondences, accurate methods to estimate the geometry often exist. However, automatic matching usually results in a number of mismatches which gives rise to outliers in the data, often degrading the accuracy of the solution. In this paper we develop methods for detecting these mismatches before computing the final reconstruction. The 1 Code available at
Global Fusion of Relative Motions for Robust, Accurate and Scalable Structure from Motion
 IEEE International Conference on Computer Vision (ICCV
, 2013
"... Multiview structure from motion (SfM) estimates the position and orientation of pictures in a common 3D coordinate frame. When views are treated incrementally, this external calibration can be subject to drift, contrary to global methods that distribute residual errors evenly. We propose a new g ..."
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Cited by 7 (0 self)
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Multiview structure from motion (SfM) estimates the position and orientation of pictures in a common 3D coordinate frame. When views are treated incrementally, this external calibration can be subject to drift, contrary to global methods that distribute residual errors evenly. We propose a new global calibration approach based on the fusion of relative motions between image pairs. We improve an existing method for robustly computing global rotations. We present an efficient a contrario trifocal tensor estimation method, from which stable and precise translation directions can be extracted. We also define an efficient translation registration method that recovers accurate camera positions. These components are combined into an original SfM pipeline. Our experiments show that, on most datasets, it outperforms in accuracy other existing incremental and global pipelines. It also achieves strikingly good running times: it is about 20 times faster than the other global method we could compare to, and as fast as the best incremental method. More importantly, it features better scalability properties. 1.
Globally Optimal Algorithms for Stratified Autocalibration
 INT J COMPUT VIS
, 2009
"... We present practical algorithms for stratified autocalibration with theoretical guarantees of global optimality. Given a projective reconstruction, we first upgrade it to affine by estimating the position of the plane at infinity. The plane at infinity is computed by globally minimizing a least squ ..."
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Cited by 3 (0 self)
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We present practical algorithms for stratified autocalibration with theoretical guarantees of global optimality. Given a projective reconstruction, we first upgrade it to affine by estimating the position of the plane at infinity. The plane at infinity is computed by globally minimizing a least squares formulation of the modulus constraints. In the second stage, this affine reconstruction is upgraded to a metric one by globally minimizing the infinite homography relation to compute the dual image of the absolute conic (DIAC). The positive semidefiniteness of the DIAC is explicitly enforced as part of the optimization process, rather than as a postprocessing step. For each stage, we construct and minimize tight convex relaxations of the highly nonconvex objective functions in a branch and bound optimization framework. We exploit the inherent problem structure to restrict the search space for the DIAC and the plane at infinity to a small, fixed number of branching dimensions, independent of the number of views. Chirality constraints are incorporated into our convex relaxations to automatically select an initial region which is guaranteed to contain the global minimum.
Projective LeastSquares: Global Solutions with Local Optimization
"... Recent work in multiple view geometry has focused on obtaining globally optimal solutions at the price of computational time efficiency. On the other hand, traditional bundle adjustment algorithms have been found to provide good solutions even though there may be multiple local minima. In this paper ..."
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Recent work in multiple view geometry has focused on obtaining globally optimal solutions at the price of computational time efficiency. On the other hand, traditional bundle adjustment algorithms have been found to provide good solutions even though there may be multiple local minima. In this paper we justify this observation by giving a simple sufficient condition for global optimality that can be used to verify that a solution obtained from any local method is indeed global. The method is tested on numerous problem instances of both synthetic and real data sets. In the vast majority of cases we are able to verify that the solutions are optimal, in particular for smallscale problems. We also develop a branch and bound procedure that goes beyond verification. In cases where the sufficient condition does not hold, the algorithm returns either of the following two results: (i) a certificate of global optimality for the local solution or (ii) the global solution. 1.
Author manuscript, published in "ICCV, Sydney: Australia (2013)" Global Fusion of Relative Motions for Robust, Accurate and Scalable Structure from Motion
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AUTOMATIC CONTROL
, 2013
"... Technical reports from the Automatic Control group in Linköping are available from ..."
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Technical reports from the Automatic Control group in Linköping are available from
Noname manuscript No. (will be inserted by the editor) On the Length and Area Regularization for Multiphase Level Set Segmentation
"... Abstract In this paper we introduce novel regularization techniques for level set segmentation that target specifically the problem of multiphase segmentation. When the multiphase model is used to obtain a partitioning of the image in more than two regions, a new set of issues arise with respect to ..."
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Abstract In this paper we introduce novel regularization techniques for level set segmentation that target specifically the problem of multiphase segmentation. When the multiphase model is used to obtain a partitioning of the image in more than two regions, a new set of issues arise with respect to the single phase case in terms of regularization strategies. For example, if smoothing or shrinking each contour individually could be a good model in the single phase case, this is not necessarily true in the multiphase scenario. In this paper, we address these issues designing enhanced length and area regularization terms, whose minimization yields evolution equations in which each level set function involved in the multiphase segmentation can “sense ” the presence of the other level set functions and evolve accordingly. In other words, the coupling of the level set function, which before was limited to the data term (i.e. the proper segmentation driving force), is extended in a mathematically principled way to the regularization terms as well. The resulting regularization technique is more suitable to eliminate spurious regions and other kind of artifacts. An extensive experimental evaluation supports the model we introduce in this paper, showing improved segmentation performance with respect to traditional regularization techniques.
Enhanced Continuous Tabu Search for Parameter Estimation in Multiview Geometry
"... Optimization using the L ∞ norm has been becoming an effective way to solve parameter estimation problems in multiview geometry. But the computational cost increases rapidly with the size of measurement data. Although some strategies have been presented to improve the efficiency of L ∞ optimization, ..."
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Optimization using the L ∞ norm has been becoming an effective way to solve parameter estimation problems in multiview geometry. But the computational cost increases rapidly with the size of measurement data. Although some strategies have been presented to improve the efficiency of L ∞ optimization, it is still an open issue. In the paper, we propose a novel approach under the framework of enhanced continuous tabu search (ECTS) for generic parameter estimation in multiview geometry. ECTS is an optimization method in the domain of artificial intelligence, which has an interesting ability of covering a wide solution space by promoting the search far away from current solution and consecutively decreasing the possibility of trapping in the local minima. Taking the triangulation as an example, we propose the corresponding ways in the key steps of ECTS, diversification and intensification. We also present theoretical proof to guarantee the global convergence of search with probability one. Experimental results have validated that the ECTS based approach can obtain global optimum efficiently, especially for large scale dimension of parameter. Potentially, the novel ECTS based algorithm can be applied in many applications of multiview geometry. 1.