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- Börlin, Niclas, 1968-, et al.
(författare)
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A globally convergent gauss-newton algorithm for the bundle adjustment problem with functional constraints
- 2003
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Ingår i: Optical 3-D measurement techniques. - : Wichmann-Verlag. ; , s. 269-276
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This paper describes a Gauss-Newton-based algorithm for the bundle adjustment problem with functional constraints (GNC). The GNC algorithm has superior theoretical convergence properties compared to the conventional bundle algorithm. Both algorithms were applied to simulated measurements of a sphere with 2-3 cameras and 4-9 points. For 2 cameras and 4-5 points, the GNC converged in substantially more cases. For the other configurations, the convergence properties were similar. The added cost for the GNC algorithm was less than 0.01 iterations on average. The GNC algorithm need to be evaluated on real-world problems, but the results suggest that the algorithm will be more reliable for minimum data problems and have a minimal overhead for easy problems.
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- Börlin, Niclas, 1968-
(författare)
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Adaptive least squares matching as a non-linear least squares optimization problem
- 2002
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Ingår i: Proceedings SSAB 2002.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Adaptive Least Squares Matching (ALSM) is a powerful technique for precisely locating objects in digital images. The method was introduced to the photogrammetric community by Gruen in 1985 and has since been developed further. The purpose of this paper is to study the basic ALSM formulation from a least squares optimization point of view. It turns out that it is possible to describe the basic algorithm as a variation of the Gauss-Newton method for solving weighted non-linear least squares optimization problems. This opens the possibility of applying optimization theory on the ALSM problem. The line-search algorithm for obtaining global convergence is especially described and illustrated
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- Börlin, Niclas
(författare)
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Comparison of resection : intersection algorithms and projection geometries in radiostereometry
- 2002
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Ingår i: ISPRS journal of photogrammetry and remote sensing (Print). - : Elsevier. - 0924-2716 .- 1872-8235. ; 56:5-6, s. 390-400
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Tidskriftsartikel (refereegranskat)abstract
- Three resection-intersection algorithms were applied to simulated projections and clinical data from radiostereometric patients. On simulated data, the more advanced bundle-adjustment-based algorithms outperformed the classical Selvik algorithm, even if the error reductions were small for some parameters. On clinical data, the results were inconclusive. The two different projection geometries had a much larger influence on the error size and distribution. For the biplanar configuration, the position and motion errors were small and almost isotropic. For the uniplanar configuration, the position errors were comparably high and anisotropic, but still resulted in a high accuracy for some motion parameters at the expense of others. The simplified resection-intersection algorithm by Selvik may still be considered a good and robust algorithm for radiostereometry. More studies will have to be performed to find out how the theoretical advantages of the bundle methods can be utilized in clinical radiostereometry. (C) 2002 Elsevier Science B.V. All rights reserved.
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- Börlin, Niclas, 1968-
(författare)
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Improving the robustness of least squares template matching with a line-search algorithm
- 2002
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Ingår i: Close-range imaging, long-range vision. - : ISPRS. ; , s. 7-11
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The Adaptive Least Squares Matching (ALSM) problem of Gruen is conventionally described as a statistical estimation problem. This paper shows that the ALSM problem may also be interpreted as a weighted non-linear least squares problem. This enables optimization theory to be applied to the ALSM problem. The ALSM algorithm may be interpreted as an instance of the well-known Gauss-Newton algorithm. A problem-independent termination criteria is introduces based on angles in high-dimensional vector spaces. The line-search modification of the Gauss-Newton method is explained and applied to the ALSM problem. The implications of the line-search modification is an increased robustness, reduced oscillations, and increased pull-in range. A potential drawback is the increased number of convergences toward side minima in images with repeating patterns.
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- Börlin, Niclas, 1968-, et al.
(författare)
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Pros and cons of constrained and unconstrained formulation of the bundle adjustment problem
- 2004
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Ingår i: ISPRS Congress Istanbul 2004, Proceedings of Commission III. - : ISPRS. ; , s. 589-594
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Two implementations of the bundle adjustment problem were applied to a subset of the Zurich City Hall reference data set. One implementation used the standard Euler angle parameterisation of the rotation matrix. The second implementation used all nine elements of the rotation matrix as unknowns and six functional constraints. The second formulation was constructed to reduce the non-linearity of the optimisation problem. The hypothesis was that a lower degree of non-linearity would lead to faster convergence. Furthermore, each implementation could optionally use the line search damping technique known from optimisation theory. The algorithms were used to solve the relative orientation problem for a varying number of homologous points from 33 different camera pairs. The results show that the constrained formulation has marginally better convergence properties, with or without damping. However, damping alone halves the number of convergence failures at a minor computational cost. The conclusion is that except to avoid the singularities associated with the Euler angles, the preferred use of the constrained formulation remains an open question. However, the results strongly suggest that the line search damping technique should be included in standard implementations of the bundle adjustment algorithm.
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- Börlin, Niclas, 1968-, et al.
(författare)
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The precision of radiostereometric measurements : manual vs. digital measurements
- 2002
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Ingår i: Journal of Biomechanics. - : Elsevier. - 0021-9290 .- 1873-2380. ; 35:1, s. 69-79
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Tidskriftsartikel (refereegranskat)abstract
- The precision of digital vs. manual radiostereometric measurements in total hip arthroplasty was evaluated using repeated stereoradiographic exposures with an interval of 10–15 min. Ten Lubinus SP2 stems cemented into bone specimens and 12 patients with the same stem design were used to evaluate the precision of stem translations and rotations. The precision of translations and rotations of the cup and femoral head penetration was studied in 12 patients with whole polyethylene cups.The use of a measurement method based on digitised radiographs improved the precision for some of the motion parameters, whereas many of them did not change. A corresponding pattern was observed for both the intra- and interobserver error. Of the wear parameters, the most pronounced improvements were the 3D wear and in the proximal-distal direction, although the anterior-posterior precision was also improved. The mean errors of rigid body and elliptic fitting decreased in all evaluations but one, consistent with a more reproducible identification of the markers centres and the edge of the femoral head.Increased precision of radiostereometric measurements may be used to increase the statistical power of future randomised studies and to study new fields in orthopaedics requiring higher precision than has been available with RSA based on manual measurements.
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