A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model

We propose a new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2-phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In Scale-Space'99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141–151) and T. Chan and L. Vese (2001. IEEE-IP, 10(2):266–277). The multiphase level set formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlap; it needs only log n level set functions for n phases in the piecewise constant case; it can represent boundaries with complex topologies, including triple junctions; in the piecewise smooth case, only two level set functions formally suffice to represent any partition, based on The Four-Color Theorem. Finally, we validate the proposed models by numerical results for signal and image denoising and segmentation, implemented using the Osher and Sethian level set method.     

31P magnetic resonance spectroscopy of the liver in an infant with galactosaemia

Sequential studies of the liver of an infant with galactosaemia were made by phosphorus magnetic resonance spectroscopy (31P MRS). A peak attributable to galactose 1-phosphate (gal 1-P) was seen in early liver spectra. This peak diminished during dietary therapy in the early months of life, corresponding to a falling level of gal 1-P in red blood cells.     

Assessing renewable energy research and development

Probabilistic decision analysis is employed to calculate the economic benefits from research and development. The ability to use uncertain data gives advantages over non-probabilistic assessment methods.Nine renewable energy technologies currently under consideration in the United Kingdom are assessed. Results suggest that despite the technical and economic uncertainties surrounding their use, the development of several of the renewable energy technologies represents a worthwhile national investment.     

Component placement through graph partitioning in computer-aided printed-wiring-board design

The partitioning of the abstract graph representing an electronic circuit has been applied to the placement of components on a printed wiring board. Results obtained from a computer program exhibit a marked degree of similarity to placements produced by a skilled draughtsman, for a very low processing cost.     

Fattening up for the market? Higher electricity prices and the value of the CEGB

A mathematical model of the evolution of the electricity supply industry to beyond the end of the century is used to forecast the cost and revenues of electricity generation after privatization. Subracting the costs from the revenues gives a time profile of profits that is discounted back to the date privatization to give a valuation of the Central Electricity Generating Board (CEGB). The model shows that every 1% rise in the price of electricity before privatization adds between 2.2% and 3.3% to the value of the CEGB. The exact increase depends mainly on whether the price rises are permanent, or are clawed back after privatization by price cuts until turn of the century. The tougher financial targets for the industry announced by the Department of Energy in 1987 are expected to add about 7% in real terms to the price of electricity before privatization. The government's proceeds from the sale of the CEGB should receive a 15–20% boost as a result.     

Recursive subdivision without the convex hull property

Recursive subdivision is a standard technique in computer aided geometric design for intersecting and rendering curves and surfaces. The convergence of recursive subdivision is critical for its effective use. Bézier and B-spline curves and surfaces have recursive subdivision algorithms that are known to converge. We show more generally that if a recursive subdivision algorithm exists for a given curve or surface type, then convergence is guaranteed if the blending functions are continuous, form a partition of unity, and are linearly independent. Thus, convergence of recursive subdivision does not depend on the convex hull property. We also show that even in the absence of the convex hull property, it is possible to define termination tests based on the flatness of control polygons, and to construct intersection algorithms based on recursive subdivision. Examples are given of polynomial curves to which our theorems apply.     

Using modified strong copper extractants to treat sulfidic ores

This article summarizes the evolution of modified strong copper extractants, focusing on the fairly recent requirement to effectively extract copper from high-concentration aqueous feeds derived from the hydrometallurgical processing of sulfidic copper ores. For more information contact Charles Maes at Avecia, 3259 E. Harbor Drive, Suite 100, Phoenix, Arizona, 85034; (602) 470-1446; fax (602) 470-5030; e-mail Charles.Maes@avecia.com.