Information geometric measurements of generalisation

Neural networks can be regarded as statistical models, and can be analysed in a Bayesian framework. Generalisation is measured by the performance on independent test data drawn from the same distribution as the training data. Such performance can be quantified by the posterior average of the information divergence between the true and the model distributions. Averaging over the Bayesian posterior guarantees internal coherence; Using information divergence guarantees invariance with respect to representation. The theory generalises the least mean squares theory for linear Gaussian models to general problems of statistical estimation. The main results are: (1)~the ideal optimal estimate is always given by average over the posterior; (2)~the optimal estimate within a computational model is given by the projection of the ideal estimate to the model. This incidentally shows some currently popular methods dealing with hyperpriors are in general unnecessary and misleading. The extension of information divergence to positive normalisable measures reveals a remarkable relation between the dlt dual affine geometry of statistical manifolds and the geometry of the dual pair of Banach spaces Ld and Ldd. It therefore offers conceptual simplification to information geometry. The general conclusion on the issue of evaluating neural network learning rules and other statistical inference methods is that such evaluations are only meaningful under three assumptions: The prior P(p), describing the environment of all the problems; the divergence Dd, specifying the requirement of the task; and the model Q, specifying available computing resources.

Developments in contact lens measurement:a comparative study of industry standard geometric inspection and optical coherence tomography

Purpose: The aim of this study was to compare a developmental optical coherence tomography (OCT) based contact lens inspection instrument to a widely used geometric inspection instrument (Optimec JCF), to establish the capability of a market focused OCT system. Methods: Measurements of 27 soft spherical contact lenses were made using the Optimec JCF and a new OCT based instrument, the Optimec is830. Twelve of the lenses analysed were specially commissioned from a traditional hydrogel (Contamac GM Advance 49%) and 12 from a silicone hydrogel (Contamac Definitive 65), each set with a range of back optic zone radius (BOZR) and centre thickness (CT) values. Three commercial lenses were also measured; CooperVision MyDay (Stenfilcon A) in −10D, −3D and +6D powers. Two measurements of BOZR, CT and total diameter were made for each lens in temperature controlled saline on both instruments. Results: The results showed that the is830 and JCF measurements were comparable, but that the is830 had a better repeatability coefficient for BOZR (0.065 mm compared to 0.151 mm) and CT (0.008 mm compared to 0.027 mm). Both instruments had similar results for total diameter (0.041 mm compared to 0.044 mm). Conclusions: The OCT based instrument assessed in this study is able to match and improve on the JCF instrument for the measurement of total diameter, back optic zone radius and centre thickness for soft contact lenses in temperature controlled saline.

Malmquist indexes using a geometric distance function (GDF)

Traditional approaches to calculate total factor productivity change through Malmquist indexes rely on distance functions. In this paper we show that the use of distance functions as a means to calculate total factor productivity change may introduce some bias in the analysis, and therefore we propose a procedure that calculates total factor productivity change through observed values only. Our total factor productivity change is then decomposed into efficiency change, technological change, and a residual effect. This decomposition makes use of a non-oriented measure in order to avoid problems associated with the traditional use of radial oriented measures, especially when variable returns to scale technologies are to be compared.

Malmquist indexes using a geometric distance function (GDF):application to a sample of Portuguese bank branches

Traditional approaches to calculate total factor productivity (TFP) change through Malmquist indexes rely on distance functions. In this paper we show that the use of distance functions as a means to calculate TFP change may introduce some bias in the analysis, and therefore we propose a procedure that calculates TFP change through observed values only. Our total TFP change is then decomposed into efficiency change, technological change, and a residual effect. This decomposition makes use of a non-oriented measure in order to avoid problems associated with the traditional use of radial oriented measures, especially when variable returns to scale technologies are to be compared. The proposed approach is applied in this paper to a sample of Portuguese bank branches.

Modeling geometric rules in object based models:an XML / GML approach

Most object-based approaches to Geographical Information Systems (GIS) have concentrated on the representation of geometric properties of objects in terms of fixed geometry. In our road traffic marking application domain we have a requirement to represent the static locations of the road markings but also enforce the associated regulations, which are typically geometric in nature. For example a give way line of a pedestrian crossing in the UK must be within 1100-3000 mm of the edge of the crossing pattern. In previous studies of the application of spatial rules (often called 'business logic') in GIS emphasis has been placed on the representation of topological constraints and data integrity checks. There is very little GIS literature that describes models for geometric rules, although there are some examples in the Computer Aided Design (CAD) literature. This paper introduces some of the ideas from so called variational CAD models to the GIS application domain, and extends these using a Geography Markup Language (GML) based representation. In our application we have an additional requirement; the geometric rules are often changed and vary from country to country so should be represented in a flexible manner. In this paper we describe an elegant solution to the representation of geometric rules, such as requiring lines to be offset from other objects. The method uses a feature-property model embraced in GML 3.1 and extends the possible relationships in feature collections to permit the application of parameterized geometric constraints to sub features. We show the parametric rule model we have developed and discuss the advantage of using simple parametric expressions in the rule base. We discuss the possibilities and limitations of our approach and relate our data model to GML 3.1. © 2006 Springer-Verlag Berlin Heidelberg.

Computer aided manufacturing of geometric models

As systems for computer-aided-design and production of mechanical parts have developed, there has arisen a need for techniques for the comprehensive description of the desired part, including its 3-D shape. The creation and manipulation of shapes is generally known as geometric modelling. It is desirable that links be established between geometric modellers and machining programs. Currently, unbounded APT and some bounded geometry systems are being widely used in manufacturing industry for machining operations such as: milling, drilling, boring and turning, applied mainly to engineering parts. APT systems, however, are presently only linked to wire-frame drafting systems. The combination of a geometric modeller and APT will provide a powerful manufacturing system for industry from the initial design right through part manufacture using NC machines. This thesis describes a recently developed interface (ROMAPT) between a bounded geometry modeller (ROMULUS) and an unbounded NC processor (APT). A new set of theoretical functions and practical algorithms for the computer aided manufacturing of 3D solid geometric model has been investigated. This work has led to the development of a sophisticated computer program, ROMAPT, which provides a new link between CAD (in form of a goemetric modeller ROMULUS) and CAM (in form of the APT NC system). ROMAPT has been used to machine some engineering prototypes successfully both in soft foam material and aluminium. It has been demonstrated above that the theory and algorithms developed by the author for the development of computer aided manufacturing of 3D solid modelling are both valid and applicable. ROMAPT allows the full potential of a solid geometric modeller (ROMULUS) to be further exploited for NC applications without requiring major investment in new NC processor. ROMAPT supports output in APT-AC, APT4 and the CAM-I SSRI NC languages.

Decision-making algorithms in geometric modelling

Many of the applications of geometric modelling are concerned with the computation of well-defined properties of the model. The applications which have received less attention are those which address questions to which there is no unique answer. This thesis describes such an application: the automatic production of a dimensioned engineering drawing. One distinctive feature of this operation is the requirement for sophisticated decision-making algorithms at each stage in the processing of the geometric model. Hence, the thesis is focussed upon the design, development and implementation of such algorithms. Various techniques for geometric modelling are briefly examined and then details are given of the modelling package that was developed for this project, The principles of orthographic projection and dimensioning are treated and some published work on the theory of dimensioning is examined. A new theoretical approach to dimensioning is presented and discussed. The existing body of knowledge on decision-making is sampled and the author then shows how methods which were originally developed for management decisions may be adapted to serve the purposes of this project. The remainder of the thesis is devoted to reports on the development of decision-making algorithms for orthographic view selection, sectioning and crosshatching, the preparation of orthographic views with essential hidden detail, and two approaches to the actual insertion of dimension lines and text. The thesis concludes that the theories of decision-making can be applied to work of this kind. It may be possible to generate computer solutions that are closer to the optimum than some man-made dimensioning schemes. Further work on important details is required before a commercially acceptable package could be produced.

Computer aided geometric design of form-rolls for NC manufacture

Conventional methods of form-roll design and manufacture for Cold Roll-Forming of thin-walled metal sections have been entirely manual, time consuming and prone to errors, resulting in inefficiency and high production costs. With the use of computers, lead time can be significantly improved, particularly for those aspects involving routine but tedious human decisions and actions. This thesis describes the development of computer aided tools for producing form-roll designs for NC manufacture in the CAD/CAM environment. The work was undertaken to modernise the existing activity of a company manufacturing thin-walled sections. The investigated areas of the activity, including the design and drafting of the finished section, the flower patterns, the 10 to 1 templates, and the rolls complete with pinch-difference surfaces, side-rolls and extension-contours, have been successfully computerised by software development . Data generated by the developed software can be further processed for roll manufacturing using NC lathes. The software has been specially designed for portability to facilitate its implementation on different computers. The Opening-Radii method of forming was introduced as a subsitute to the conventional method for better forming. Most of the essential aspects in roll design have been successfully incorporated in the software. With computerisation, extensive standardisation in existing roll design practices and the use of more reliable and scientifically-based methods have been achieved. Satisfactory and beneficial results have also been obtained by the company in using the software through a terminal linked to the University by a GPO line. Both lead time and productivity in roll design and manufacture have been significantly improved. It is therefore concluded that computerisation in the design of form-rolls for automation by software development is viable. The work also demonstrated the promising nature of the CAD/CAM approach.

The geometric correction and registration of airborne line-scanned imagery for temporal thermal studies

This thesis begins by providing a review of techniques for interpreting the thermal response at the earth's surface acquired using remote sensing technology. Historic limitations in the precision with which imagery acquired from airborne platforms can be geometrically corrected and co-registered has meant that relatively little work has been carried out examining the diurnal variation of surface temperature over wide regions. Although emerging remote sensing systems provide the potential to register temporal image data within satisfactory levels of accuracy, this technology is still not widely available and does not address the issue of historic data sets which cannot be rectified using conventional parametric approaches. In overcoming these problems, the second part of this thesis describes the development of an alternative approach for rectifying airborne line-scanned imagery. The underlying assumption that scan lines within the imagery are straight greatly reduces the number of ground control points required to describe the image geometry. Furthermore, the use of pattern matching procedures to identify geometric disparities between raw line-scanned imagery and corresponding aerial photography enables the correction procedure to be almost fully automated. By reconstructing the raw image data on a truly line-by-line basis, it is possible to register the airborne line-scanned imagery to the aerial photography with an average accuracy of better than one pixel. Providing corresponding aerial photography is available, this approach can be applied in the absence of platform altitude information allowing multi-temporal data sets to be corrected and registered.

Geometric spectral accuracy of airborne remote sensing

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT