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| 2. |
- Berglund, Tomas, et al.
(författare)
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An obstacle-avoiding minimum variation B-spline problem
- 2003
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Ingår i: Proceedings. - Los Alamitos, Calif : IEEE Communications Society. - 0769519857 ; , s. 156-161
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 3. |
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| 4. |
- Berglund, Tomas, et al.
(författare)
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Epi-convergence of minimum curvature variation B-splines
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 5. |
- Berglund, Tomas, et al.
(författare)
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Estimation of curl in paper : an industrial application combining shape measurement and least squares modeling
- 2000
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Ingår i: Proceedings / International Conference on Trends in Optical Nondestructive Testing. - Lugano : Ecole Polytechnique Fédérale de Lausanne. ; , s. 23-33
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Konferensbidrag (refereegranskat)abstract
- If a sheet of paper is subjected to humidity changes and have structural variations through its thickness such as gradients of fibre orientation, density and filler content, the sheet will curl and hence assume a cylindrical shape. Curl is a quality problem that makes the paper less suitable for printing. We propose a method to measure curl that can be used for automated analysis of the paper quality. The shape of the curled paper is measured from the perspective difference in a stereoscopic camera system, which is viewing an irregular pattern that is projected onto the specimen. The perspective difference is calculated by a correlation algorithm, a technique often referred to as digital speckle photography. The most interesting quality parameters are the magnitude of curl, which is defined as the inverse of the radius of curvature and also the orientation of the curled paper. These parameters are estimated by performing a least squares fit of a cylindrical shape to the three-dimension...
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| 7. |
- Berglund, Tomas, et al.
(författare)
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Planning smooth and obstacle-avoiding b-spline paths for autonomous mining vehicles
- 2010
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Ingår i: IEEE Transactions on Automation Science and Engineering. - 1545-5955 .- 1558-3783. ; 7:1, s. 167-172
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 8. |
- Berglund, Tomas, et al.
(författare)
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The problem of computing an obstacle-avoiding minimum variation B-spline
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 9. |
- 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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| 10. |
- Bergström, Per, et al.
(författare)
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Fitting NURBS using separable least squares techniques
- 2012
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Ingår i: International Journal of Mathematical Modelling and Numerical Optimisation. - 2040-3607 .- 2040-3615. ; 3:4, s. 319-334
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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