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Söderkvist, Inge
Publications (10 of 33) Show all publications
Bergström, P., Edlund, O. & Söderkvist, I. (2012). Efficient computation of the Gauss-Newton direction when fitting NURBS using ODR (ed.). Paper presented at . BIT Numerical Mathematics, 52(3), 571-588
Open this publication in new window or tab >>Efficient computation of the Gauss-Newton direction when fitting NURBS using ODR
2012 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 52, no 3, p. 571-588Article in journal (Refereed) Published
Abstract [en]

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.

Keywords
Mathematics, numerik, Matematik
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-8758 (URN)10.1007/s10543-012-0371-7 (DOI)000308234600004 ()2-s2.0-84865746930 (Scopus ID)74aec6df-c813-471b-a9b5-df74c969c19b (Local ID)74aec6df-c813-471b-a9b5-df74c969c19b (Archive number)74aec6df-c813-471b-a9b5-df74c969c19b (OAI)
Note
Validerad; 2012; 20120130 (berper)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Bergström, P. & Söderkvist, I. (2012). Fitting NURBS using separable least squares techniques (ed.). International Journal of Mathematical Modelling and Numerical Optimisation, 3(4), 319-334
Open this publication in new window or tab >>Fitting NURBS using separable least squares techniques
2012 (English)In: International Journal of Mathematical Modelling and Numerical Optimisation, ISSN 2040-3607, E-ISSN 2040-3615, Vol. 3, no 4, p. 319-334Article in journal (Refereed) Published
Abstract [en]

We consider the problem of fitting a non-uniform rational B-spline (NURBS) curve to a set of data points by determining the control points and the weights using techniques aimed for solving separable least squares problems. The main technique under consideration is the variable projection method which utilises that the NURBS model depends linearly on its control points but non-linearly on the weights. The variable projection method can be used with the Gauss-Newton algorithm but also with Newton's algorithm. We investigate the efficiency of the different algorithms when fitting NURBS and observe that the variable projection methods do not perform as well as reported for its use on, e.g., exponential fitting problems.

National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-13914 (URN)10.1504/IJMMNO.2012.049600 (DOI)2-s2.0-84878299784 (Scopus ID)d3a4e548-e5bf-44d7-a9f9-81f18b8ad21f (Local ID)d3a4e548-e5bf-44d7-a9f9-81f18b8ad21f (Archive number)d3a4e548-e5bf-44d7-a9f9-81f18b8ad21f (OAI)
Note

Validerad; 2012; 20120314 (ingsor)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Bergström, P., Edlund, O. & Söderkvist, I. (2011). Repeated surface registration for on-line use (ed.). Paper presented at . The International Journal of Advanced Manufacturing Technology, 54(5-8), 677-689
Open this publication in new window or tab >>Repeated surface registration for on-line use
2011 (English)In: The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, E-ISSN 1433-3015, Vol. 54, no 5-8, p. 677-689Article in journal (Refereed) Published
Abstract [en]

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.

Keywords
Manufacturing engineering and work sciences - Manufacturing engineering, Produktion och arbetsvetenskap - Produktionsteknik
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-10134 (URN)10.1007/s00170-010-2950-6 (DOI)000290164500022 ()2-s2.0-79955666988 (Scopus ID)8e1867e0-d523-11df-8b36-000ea68e967b (Local ID)8e1867e0-d523-11df-8b36-000ea68e967b (Archive number)8e1867e0-d523-11df-8b36-000ea68e967b (OAI)
Note
Validerad; 2011; 20101011 (berper)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Berglund, T., Brodnik, A., Jonsson, H., Staffansson, M. & Söderkvist, I. (2010). Planning smooth and obstacle-avoiding b-spline paths for autonomous mining vehicles (ed.). IEEE Transactions on Automation Science and Engineering, 7(1), 167-172
Open this publication in new window or tab >>Planning smooth and obstacle-avoiding b-spline paths for autonomous mining vehicles
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2010 (English)In: IEEE Transactions on Automation Science and Engineering, ISSN 1545-5955, E-ISSN 1558-3783, Vol. 7, no 1, p. 167-172Article in journal (Refereed) Published
Abstract [en]

We study the problem of automatic generation of smooth and obstacle-avoiding planar paths for efficient guidance of autonomous mining vehicles. Fast traversal of a path is of special interest. We consider four-wheel four-gear articulated vehicles and assume that we have an a priori knowledge of the mine wall environment in the form of polygonal chains. Computing quartic uniform B-spline curves, minimizing curvature variation, staying at least at a proposed safety margin distance from the mine walls, we plan high speed paths.

National Category
Computational Mathematics Computer Sciences
Research subject
Scientific Computing; Dependable Communication and Computation Systems
Identifiers
urn:nbn:se:ltu:diva-5437 (URN)10.1109/TASE.2009.2015886 (DOI)000273133300017 ()2-s2.0-73849111744 (Scopus ID)38ae9f20-38bf-11dd-8721-000ea68e967b (Local ID)38ae9f20-38bf-11dd-8721-000ea68e967b (Archive number)38ae9f20-38bf-11dd-8721-000ea68e967b (OAI)
Note

Validerad; 2010; Bibliografisk uppgift: Paper id:: T-ASE-2008-162; 20080612 (tb)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Eriksson, J., Wedin, P. A., Gulliksson, M. E. & Söderkvist, I. (2005). Regularization methods for uniformly rank-deficient nonlinear least-squares problems (ed.). Paper presented at . Journal of Optimization Theory and Applications, 127(1), 1-26
Open this publication in new window or tab >>Regularization methods for uniformly rank-deficient nonlinear least-squares problems
2005 (English)In: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 127, no 1, p. 1-26Article in journal (Refereed) Published
Abstract [en]

In solving the nonlinear least-squares problem of minimizing ||f(x)||22, difficulties arise with standard approaches, such as the Levenberg-Marquardt approach, when the Jacobian of f is rank-deficient or very ill-conditioned at the solution. To handle this difficulty, we study a special class of least-squares problems that are uniformly rank-deficient, i.e., the Jacobian of f has the same deficient rank in the neighborhood of a solution. For such problems, the solution is not locally unique. We present two solution tecniques: (i) finding a minimum-norm solution to the basic problem, (ii) using a Tikhonov regularization. Optimality conditions and algorithms are given for both of these strategies. Asymptotical convergence properties of the algorithms are derived and confirmed by numerical experiments. Extensions of the presented ideas make it possible to solve more general nonlinear least-squares problems in which the Jacobian of f at the solution is rank-deficient or ill-conditioned.

National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-10119 (URN)10.1007/s10957-005-6389-0 (DOI)000232059800001 ()2-s2.0-25444435351 (Scopus ID)8ddebe40-a530-11db-8975-000ea68e967b (Local ID)8ddebe40-a530-11db-8975-000ea68e967b (Archive number)8ddebe40-a530-11db-8975-000ea68e967b (OAI)
Note
Validerad; 2005; 20070116 (evan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Berglund, T., Brodnik, A., Jonsson, H., Mrozek, K., Staffansson, M. & Söderkvist, I. (2004). Minimum curvature variation B-splines: validation of a path-planning model (ed.). Paper presented at . Ljubljana, Slovenia: Institute for Mathematics, Physics and Mechanics
Open this publication in new window or tab >>Minimum curvature variation B-splines: validation of a path-planning model
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2004 (English)Report (Other academic)
Place, publisher, year, edition, pages
Ljubljana, Slovenia: Institute for Mathematics, Physics and Mechanics, 2004. p. 19
Series
Preprint series, Institute for Mathematics, Physics and Mechanics, Ljubljana ; IMFM-(2004)-PS-917
National Category
Computational Mathematics Computer Sciences
Research subject
Scientific Computing; Dependable Communication and Computation Systems
Identifiers
urn:nbn:se:ltu:diva-22977 (URN)51c9ea90-38bb-11dd-8721-000ea68e967b (Local ID)51c9ea90-38bb-11dd-8721-000ea68e967b (Archive number)51c9ea90-38bb-11dd-8721-000ea68e967b (OAI)
Note

Godkänd; 2004; 20080612 (tb)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approved
Osborne, M. R. & Söderkvist, I. (2004). V-invariant methods, generalised least squares problems, and the Kalman filter (ed.). Paper presented at . ANZIAM journal (Print), 45(Part C), 232-247
Open this publication in new window or tab >>V-invariant methods, generalised least squares problems, and the Kalman filter
2004 (English)In: ANZIAM journal (Print), ISSN 1446-1811, E-ISSN 1446-8735, Vol. 45, no Part C, p. 232-247Article in journal (Refereed) Published
Abstract [en]

V-invariant methods for the generalised least squares problem extend the techniques based on orthogonal factorization for ordinary least squares to problems with multiscaled, even singular covariances. These methods are summarised briefly here, and the ability to handle multiple scales indicated. An application to a class of Kalman filter problems derived from generalised smoothing splines is considered. Evidence of severe illconditioning of the covariance matrices is demonstrated in several examples. This suggests that this is an appropriate application for the V-invariant techniques.

National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-4762 (URN)2c0ea1e0-ab88-11db-aeba-000ea68e967b (Local ID)2c0ea1e0-ab88-11db-aeba-000ea68e967b (Archive number)2c0ea1e0-ab88-11db-aeba-000ea68e967b (OAI)
Note
Validerad; 2004; 20070117 (evan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approved
Berglund, T., Jonsson, H. & Söderkvist, I. (2003). An obstacle-avoiding minimum variation B-spline problem (ed.). In: (Ed.), (Ed.), Proceedings: 2003 International Conference on Geometric Modeling and Graphics, GMAG 2003 ; 16 - 18 July 2003, London, England. Paper presented at International Conference on Geometric Modeling and Graphics : 16/07/2003 - 18/07/2003 (pp. 156-161). Los Alamitos, Calif: IEEE Communications Society
Open this publication in new window or tab >>An obstacle-avoiding minimum variation B-spline problem
2003 (English)In: Proceedings: 2003 International Conference on Geometric Modeling and Graphics, GMAG 2003 ; 16 - 18 July 2003, London, England, Los Alamitos, Calif: IEEE Communications Society, 2003, p. 156-161Conference paper, Published paper (Refereed)
Abstract [en]

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the minimum variation B-spline problem, which is a linearly constrained optimization problem over curves, defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.

Place, publisher, year, edition, pages
Los Alamitos, Calif: IEEE Communications Society, 2003
National Category
Computational Mathematics Computer Sciences
Research subject
Scientific Computing; Dependable Communication and Computation Systems
Identifiers
urn:nbn:se:ltu:diva-36963 (URN)10.1109/GMAG.2003.1219681 (DOI)000184696400024 ()2-s2.0-84943595578 (Scopus ID)ad094930-c7d5-11db-98d9-000ea68e967b (Local ID)0-7695-1985-7 (ISBN)ad094930-c7d5-11db-98d9-000ea68e967b (Archive number)ad094930-c7d5-11db-98d9-000ea68e967b (OAI)
Conference
International Conference on Geometric Modeling and Graphics : 16/07/2003 - 18/07/2003
Note
Godkänd; 2003; 20070301 (evan)Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2018-07-10Bibliographically approved
Berglund, T., Strömberg, T., Jonsson, H. & Söderkvist, I. (2003). Epi-convergence of minimum curvature variation B-splines (ed.). Paper presented at . Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>Epi-convergence of minimum curvature variation B-splines
2003 (English)Report (Other academic)
Abstract [en]

We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimizers of this functional subject to additional constraints such as, for example, for the curve to avoid obstacles such as other curves. In this paper, we consider the set of smooth curves that can be written as graphs of three times continuously differentiable functions on an interval, and, in particular, we consider approximations using quartic uniform B- spline functions. We show that if quartic uniform B-spline minimizers of the curvature variation functional converge to a curve, as the number of B-spline basis functions tends to infinity, then this curve is in fact a minimizer of the curvature variation functional. In order to illustrate this result, we present an example of sequences of B-spline minimizers that converge to a cubic spiral.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2003. p. 12
Series
Technical report / Luleå University of Technology, ISSN 1402-1536 ; 2003:14
National Category
Mathematical Analysis Computer Sciences Computational Mathematics
Research subject
Mathematics; Dependable Communication and Computation Systems; Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-23274 (URN)65571df0-2bc6-11dd-8657-000ea68e967b (Local ID)65571df0-2bc6-11dd-8657-000ea68e967b (Archive number)65571df0-2bc6-11dd-8657-000ea68e967b (OAI)
Note

Godkänd; 2003; 20080527 (ysko)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approved
Berglund, T., Jonsson, H. & Söderkvist, I. (2003). The problem of computing an obstacle-avoiding minimum variation B-spline (ed.). Paper presented at . Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>The problem of computing an obstacle-avoiding minimum variation B-spline
2003 (English)Report (Other academic)
Abstract [en]

We study the problem of computing a planar curve restricted to lie between two given polygonal chains such that the integral of the square of arc- length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2003
Series
Technical report / Luleå University of Technology, ISSN 1402-1536 ; 2003:06
National Category
Computational Mathematics Computer Sciences
Research subject
Scientific Computing; Dependable Communication and Computation Systems
Identifiers
urn:nbn:se:ltu:diva-23772 (URN)859d9350-2b44-11dd-8657-000ea68e967b (Local ID)859d9350-2b44-11dd-8657-000ea68e967b (Archive number)859d9350-2b44-11dd-8657-000ea68e967b (OAI)
Note
Godkänd; 2003; 20080526 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approved
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