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 further study of the recovery and purification of surfactin from fermentation broth by membrane filtration

Surfactin is a bacterial lipopeptide produced by Bacillus subtilis and is a powerful surfactant, having also antiviral, antibacterial and antitumor properties. The recovery and purification of surfactin from complex fermentation broths is a major obstacle to its commercialization; therefore, a two-step membrane filtration process was developed using a lab scale tangential flow filtration (TFF) unit with 10 kDa MWCO regenerated cellulose (RC) and polyethersulfone (PES)membranes at three different transmembrane pressure (TMP) of 1.5 bar, 2.0 bar and 2.5 bar. Two modes of filtrations were studied, with and without cleaning of membranes prior to UF-2. In a first step of ultrafiltration (UF-1), surfactin was retained effectively by membranes at above its critical micelle concentration (CMC); subsequently in UF-2, the retentate micelles were disrupted by addition of 50% (v/v) methanol solution to allow recovery of surfactin in the permeate. Main protein contaminants were effectively retained by the membrane in UF-2. Flux of permeates, rejection coefficient (R) of surfactin and proteinwere measured during the filtrations. Overall the three different TMPs applied have no significant effect in the filtrations and PES is the more suitable membrane to selectively separate surfactin from fermentation broth, achieving high recovery and level of purity. In addition this two-step UF process is scalable for larger volume of samples without affecting the original functionality of surfactin, although membranes permeability can be affected due to exposure to methanolic solution used in UF-2.