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.

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.

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.

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.

This paper describes how to use the Matlab software package CMregr, and also gives some limited information on the CM-estimation problem itself. For detailed information on the algorithms used in CMregr as well as extensive testings, please refer to Arslan, Edlund & Ekblom (2002) and Edlund & Ekblom (2004).

This thesis is devoted to algorithms for solving two optimization problems, using linear M-estimation methods, and their implementation. First, an algorithm for the non-linear M-estimation problem ...

We consider the problem of fitting a model of the form y = f (x, β) to a set of points (x i , y i ), i = 1,..., 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 (1) $$ {y_i} = f\left( {{x_i} + {\delta _i},\beta } \right) + {\varepsilon _i},\left( {i = 1, \ldots ,n} \right) $$ where δ i ∈ ℝm, i = 1,..., n are the errors in x i ∈ ℝm. Then the problem is to find a vector of parameters β ∈ ℝ p that minimizes the errors ε i and δ i in some loss function subject to (1). We will present algorithms using more robust alternatives to the least squares criterion. Figure 1 gives examples where the least squares (L2), the least absolute deviation (L1) and the Huber criteria are used.

A subproblem in the trust region algorithm for non-linear M-estimation by Ekblom and Madsen is to find the restricted step. It is found by calculating the M-estimator of the linearized model, subject to an L(2)-norm bound on the variables. In this paper it is shown that this subproblem can be solved by applying Hebden-iterations to the minimizer of the Lagrangian function. The new method is compared with an Augmented Lagrange implementation.

Gamma-irradiated monoclinic single crystals and powders of LiH 3 (SeO 3 ) 2 and LiD 3 (SeO 3 ) 2 have been investigated at room temperature by ESR in both the X and the Q band. Twelve species consisting of six pairs of inequivalent radicals have all been identified as SeO 2 − -type radicals pairwise located in two different sites. The origin of the difference in the principal values of the g-tensors for the radicals is attributed to a difference between the SeO bond lengths, which in fact gives a lower symmetry of the radicals. The generation of the radicals has been explained as a rupture of a SeO bond, which can occur in six different ways due to the crystal structure. The orientations of the radicals in the crystal are different compared to corresponding SeO 2 groups in the host crystal, and this phenomenon presumably depends either on a reorientation of the radicals or on a radical reaction. One extra splitting of peaks originating from two of the radicals in LiH 3 (SeO 3 ) 2 is absent in LiD 3 (SeO 3 ) 2 , thus indicating hydrogen bonding to the radicals.

Trimethylenemethane was generated by γ-irradiating polycrystalline methylenecyclopropane, and studied by EPR at various temperatures. The zero-field splitting constant, D, was observed to change from 0.0260 cm−1 at 4 K to 0.0212 cm−1 at 126 K, though the hyperfine coupling showed little temperature dependence.

Proton hyperfine coupling constants of monoprotonated p-benzosemiquinone, durosemiquinone, 2,6-dimethyl-p-benzosemiquinone, 2,5-dimethyl-p-benzosemiquinone and methyl-p-benzosemiquinone radicals were determined from ESR spectra during photolysis of the corresponding quinones under identical conditions, i.e., in ethanol and at about 20 °C. By considering all these constants together, the ESR spectra were assigned and following results obtained: (1) the hydroxyl groups were at the oxygen atom further from the methyl substituents, (2) the coupling constant was generally −1.86–−1.65 G for the hydroxylic protons, (3) the absolute value of the coupling constant for both ring and methyl protons was in the range 0–0.7 G for ortho-positions and 4.3–5.2 G for meta-positions relative to the hydroxyl group, and (4) the hydroxylic proton of durosemiquinone had an exceptionally small coupling constant because of steric hindrance of the methyl groups. The temperature dependence of the coupling constants in p-benzosemiqu...

Chemischer InformationsdienstVolume 6, Issue 20 Physical Organic Chemistry ChemInform Abstract: ESR-SPECTRA OF MONOPROTONATED SEMIQUINONE RADICALS FORMED DURING PHOTOLYSIS OF P-BENZOQUINONE AND ITS METHYL DERIVATIVES TETSUO WARASHINA, TETSUO WARASHINASearch for more papers by this authorOVE EDLUND, OVE EDLUNDSearch for more papers by this authorHIROSHI YOSHIDA, HIROSHI YOSHIDASearch for more papers by this author TETSUO WARASHINA, TETSUO WARASHINASearch for more papers by this authorOVE EDLUND, OVE EDLUNDSearch for more papers by this authorHIROSHI YOSHIDA, HIROSHI YOSHIDASearch for more papers by this author First published: May 20, 1975 https://doi.org/10.1002/chin.197520060AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume6, Issue20May 20, 1975 RelatedInformation

Benzene/silica gel has been irradiated at 77°K. with 60Co γ-rays at a dose rate of 300-350 krads/hour. At a low benzene content the monomeric benzene cation is observed, while at higher concentrations the singly charged dimer is predominant. Cyclohexadienyl is formed from hydrogen atoms, radiolytically liberated from surface hydroxyl groups. The ions are created at other sites. At higher temperatures radical reactions occur between benzene and cyclohexadienyl or the positive ion. The dependency of the yields on the dose shows that only a limited number of sites, 7 X 1014 per sq. meter. Brunauer-Emmett-Teller (BET) surface, is available for the oxidation of benzene. Cyclohexadienyl yields do not saturate to the same extent. The magnitude of energy transfer is estimated.