| 1. |
- Arslan, O., et al.
(författare)
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Algorithms to compute CM - and S-estimates for regression
- 2003
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Ingår i: International Conference on Robust Statistics. - : Physica-Verlag Rudolf Liebig GmbH. - 3790815187 ; , s. 62-76
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Konferensbidrag (refereegranskat)abstract
- Constrained M-estimators for regression were introduced by Mendes and Tyler in 1995 as an alternative class of robust regression estimators with high breakdown point and high asymptotic efficiency. To compute the CM-estimate, the global minimum of an objective function with an inequality constraint has to be localized. To find the S-estimate for the same problem, we instead restrict ourselves to the boundary of the feasible region. The algorithm presented for computing CM-estimates can easily be modified to compute S-estimates as well. Testing is carried out with a comparison to the algorithm SURREAL by Ruppert
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| 2. |
- Bergström, Per, et al.
(författare)
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Efficient computation of the Gauss-Newton direction when fitting NURBS using ODR
- 2012
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 52:3, s. 571-588
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Tidskriftsartikel (refereegranskat)abstract
- We consider a subproblem in parameter estimation using the Gauss-Newton algorithm with regularization for NURBS curve fitting. The NURBS curve is fitted to a set of data points in least-squares sense, where the sum of squared orthogonal distances is minimized. Control-points and weights are estimated. The knot-vector and the degree of the NURBS curve are kept constant. In the Gauss-Newton algorithm, a search direction is obtained from a linear overdetermined system with a Jacobian and a residual vector. Because of the properties of our problem, the Jacobian has a particular sparse structure which is suitable for performing a splitting of variables. We are handling the computational problems and report the obtained accuracy using different methods, and the elapsed real computational time. The splitting of variables is a two times faster method than using plain normal equations.
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| 3. |
- Bergström, Per, et al.
(författare)
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Repeated surface registration for on-line use
- 2011
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Ingår i: The International Journal of Advanced Manufacturing Technology. - : Springer Science and Business Media LLC. - 0268-3768 .- 1433-3015. ; 54:5-8, s. 677-689
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of matching sets of 3D points from a measured surface to the surface of a corresponding computer-aided design (CAD) object. The problem arises in the production line where the shape of the produced items is to be compared on-line with its pre-described shape. The involved registration problem is solved using the iterative closest point (ICP) method. In order to make it suitable for on-line use, i.e., make it fast, we pre-process the surface representation of the CAD object. A data structure for this purpose is proposed and named Distance Varying Grid tree. It is based on a regular grid that encloses points sampled from the CAD surfaces. Additional finer grids are added to the vertices in the grid that are close to the sampled points. The structure is efficient since it utilizes that the sampled points are distributed on surfaces, and it provides fast identification of the sampled point that is closest to a measured point. A local linear approximation of the surface is used for improving the accuracy. Experiments are done on items produced for the body of a car. The experiments show that it is possible to reach good accuracy in the registration and decreasing the computational time by a factor 700 compared with using the common kd-tree structure.
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| 4. |
- Bergström, Per, et al.
(författare)
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Robust registration of point sets using iteratively reweighted least squares
- 2014
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Ingår i: Computational optimization and applications. - : Springer Science and Business Media LLC. - 0926-6003 .- 1573-2894. ; 58:3, s. 543-561
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Tidskriftsartikel (refereegranskat)abstract
- Registration of point sets is done by finding a rotation and translation that produces a best fit between a set of data points and a set of model points. We use robust M-estimation techniques to limit the influence of outliers, more specifically a modified version of the iterative closest point algorithm where we use iteratively re-weighed least squares to incorporate the robustness. We prove convergence with respect to the value of the objective function for this algorithm. A comparison is also done of different criterion functions to figure out their abilities to do appropriate point set fits, when the sets of data points contains outliers. The robust methods prove to be superior to least squares minimization in this setting.
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| 5. |
- Bergström, Per, et al.
(författare)
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Robust registration of surfaces using a refined iterative closest point algorithm with a trust region approach
- 2017
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Ingår i: Numerical Algorithms. - : Springer. - 1017-1398 .- 1572-9265. ; 74:3, s. 755-779
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Tidskriftsartikel (refereegranskat)abstract
- The problem of finding a rigid body transformation, which aligns a set of data points with a given surface, using a robust M-estimation technique is considered. A refined iterative closest point (ICP) algorithm is described where a minimization problem of point-to-plane distances with a proposed constraint is solved in each iteration to find an updating transformation. The constraint is derived from a sum of weighted squared point-to-point distances and forms a natural trust region, which ensures convergence. Only a minor number of additional computations are required to use it. Two alternative trust regions are introduced and analyzed. Finally, numerical results for some test problems are presented. It is obvious from these results that there is a significant advantage, with respect to convergence rate of accuracy, to use the proposed trust region approach in comparison with using point-to-point distance minimization as well as using point-to-plane distance minimization and a Newton- type update without any step size control.
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| 6. |
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| 7. |
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| 8. |
- Edlund, Ove
(författare)
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A software package for sparse orthogonal factorization and updating
- 2002
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Ingår i: ACM Transactions on Mathematical Software. - : Association for Computing Machinery (ACM). - 0098-3500 .- 1557-7295. ; 28:4, s. 448-482
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Tidskriftsartikel (refereegranskat)abstract
- Although there is good software for sparse QR factorization, there is little support for updating and downdating, something that is absolutely essential in some linear programming algorithms, for example. This article describes an implementation of sparse LQ factorization, including block triangularization, approximate minimum degree ordering, symbolic factorization, multifrontal factorization, and updating and downdating. The factor Q is not retained. The updating algorithm expands the nonzero pattern of the factor L, which is reflected in the dynamic representation of L. The block triangularization is used as an `ordering for sparsity' rather than as a prerequisite for block backward substitution. In symbolic factorization, something called `element counters' is introduced to reduce the overestimation of the number of nonzeros that the commonly used methods do. Both the approximate minimum degree ordering and the symbolic factorization are done without explicitly forming the nonzero pattern of the symmetric matrix in the corresponding normal equations. Tests show that the average time used for a single update or downdate is essentially the same as the time used for a single forward or backward substitution. Other parts of the implementation show the same range of performance as existing code, but cannot be replaced because of the special character of the systems that are solved.
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| 9. |
- Edlund, Ove, et al.
(författare)
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Algorithms for non-linear M-estimation
- 1997
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Ingår i: Computational statistics (Zeitschrift). - 0943-4062 .- 1613-9658. ; 12:3, s. 373-383
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Tidskriftsartikel (refereegranskat)
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| 10. |
- Edlund, Ove, et al.
(författare)
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Algorithms for robustified error-in-variables problems
- 1998
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Ingår i: COMPSTAT [1998]. - Heidelberg : Physica-Verlag Rudolf Liebig GmbH. - 3790811319 ; , s. 293-298
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Konferensbidrag (refereegranskat)abstract
- From the introduction: We consider the problem of fitting a model of the form $y=f(x,\beta)$ to a set of points $(x_i,y_i)$, $i=1,\dots,n$. If there are measurement or observation errors in $x$ as well as in $y$, we have the so-called errors-in-variables-problem with model equation $$y_i=f(x_i+\delta_i,\beta)+\varepsilon_i,\ i=1,\dots,n,\tag 1$$ where $\delta_i\in\bbfR^m$, $i=1,\dots,n$, are the errors in $x_i\in\bbfR^m$. Then the problem is to find a vector of parameters $\beta\in\bbfR^p$ that minimizes the errors $\varepsilon_i$ and $\delta_i$ in some loss function subject to (1). We present algorithms using more robust alternatives to the least squares criterion.\par We will further discuss, from
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