A Newton method for pose refinement of 3D models

Different optimization methods can be employed to optimize a numerical estimate for the match between an instantiated object model and an image. In order to take advantage of gradient-based optimization methods, perspective inversion must be used in this context. We show that convergence can be very fast by extrapolating to maximum goodness-of-fit with Newton's method. This approach is related to methods which either maximize a similar goodness-of-fit measure without use of gradient information, or else minimize distances between projected model lines and image features. Newton's method combines the accuracy of the former approach with the speed of convergence of the latter.

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

A benchmark method for global optimization problems in structure determination from powder diffraction data

Quasi-Newton-Raphson minimization and conjugate gradient minimization have been used to solve the crystal structures of famotidine form B and capsaicin from X-ray powder diffraction data and characterize the chi(2) agreement surfaces. One million quasi-Newton-Raphson minimizations found the famotidine global minimum with a frequency of ca 1 in 5000 and the capsaicin global minimum with a frequency of ca 1 in 10 000. These results, which are corroborated by conjugate gradient minimization, demonstrate the existence of numerous pathways from some of the highest points on these chi(2) agreement surfaces to the respective global minima, which are passable using only downhill moves. This important observation has significant ramifications for the development of improved structure determination algorithms.

Detection of polycyclic aromatic hydrocarbons using quartz crystal microbalances

A chemically coated piezoelectric sensor has been developed for the determination of PAHs in the liquid phase. An organic monolayer attached to the surface of a gold electrode of a quartz crystal microbalance (QCM) via a covalent thiol-gold link complete with an ionically bound recognition element has been produced. This study has employed the PAH derivative 9-anthracene carboxylic acid which, once bound to the alkane thiol, functions as the recognition element. Binding of anthracene via pi-pi interaction has been observed as a frequency shift in the QCM with a detectability of the target analyte of 2 ppb and a response range of 0-50 ppb. The relative response of the sensor altered for different PAHs despite pi-pi interaction being the sole communication between recognition element and analyte. It is envisaged that such a sensor could be employed in the identification of key marker compounds and, as such, give an indication of total PAH flux in the environment.

Enantioselective detection of L-serine

An acoustic wave sensor coated with an artificial biomimetic recognition element has been developed to selectively detect the amino acid L-serine. A highly specific non-covalently imprinted polymer was cast on one electrode of a quartz crystal microbalance (QCM) as a thin permeable film. Selective rebinding of the L-serine was observed as a frequency shift in the QCM with a detection limit of 2 ppb and for concentrations up to 0.4 ppm. The sensor binding is shown to be capable of discrimination between L- and D-stereoisomers of serine as a result of the enantioselectivity of the imprinted binding sites. (C) 2002 Elsevier Science B.V. All rights reserved.

A fast identification algorithm for Box-Cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.