15 research outputs found
Local interpolation schemes for landmark-based image registration: a comparison
In this paper we focus, from a mathematical point of view, on properties and
performances of some local interpolation schemes for landmark-based image
registration. Precisely, we consider modified Shepard's interpolants,
Wendland's functions, and Lobachevsky splines. They are quite unlike each
other, but all of them are compactly supported and enjoy interesting
theoretical and computational properties. In particular, we point out some
unusual forms of the considered functions. Finally, detailed numerical
comparisons are given, considering also Gaussians and thin plate splines, which
are really globally supported but widely used in applications
A meshless interpolation algorithm using a cell-based searching procedure
In this paper we propose a fast algorithm for bivariate interpolation of large scattered data sets. It is based on the partition of unity method for constructing a global interpolant by blending radial basis functions as local approximants and using locally supported weight functions. The partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cell-based searching procedure. More precisely, we construct a cell structure, which partitions the domain and strictly depends on the dimension of the subdomains, thus providing a meaningful improvement in the searching process compared to the nearest neighbour searching techniques presented in Allasia et al. (2011) and Cavoretto and De Rossi (2010, 2012). In fact, this efficient algorithm and, in particular, the new searching procedure enable us a fast computation also in several applications, where the amount of data to be interpolated is often very large, up to many thousands or even millions of points. Analysis of computational complexity shows the high efficiency of the proposed interpolation algorithm. This is also supported by numerical experiments
Natural Parameterization
The objective of this project has been to develop an approach for imitating physical objects with an underlying stochastic variation. The key assumption is that a set of ânatural parametersâ can be extracted by a new subdivision algorithm so they reflect what is called the objectâs âgeometric DNAâ. A case study on one hundred wheat grain crosssections (Triticum aestivum) showed that it was possible to extract thirty-six such parameters and to reuse them for Monte Carlo simulation of ânewâ stochastic phantoms which possessthe same stochastic behavior as the âoriginalâ cross-sections
A basis for the representation, manufacturing tool path generation and scanning measurement of smooth freeform surfaces
Freeform surfaces find wide application, particularly in optics, from unique single-surface science programmes to mobile phone lenses manufactured in billions. This thesis presents research into the mathematical and algorithmic basis for the generation and measurement of smooth freeform surfaces. Two globally significant cases are reported: 1) research in this thesis created prototype segments for the worldâs largest telescope; 2) research in this thesis made surfaces underpinning the redefinition of one of the seven SI base units â the kelvin - and also what will be the newly (and permanently) defined value for the Boltzmann constant.
Theresearchdemonstratestwounderlyingphilosophiesofprecisionengineering, the critical roles of determinism and of precision measurement in precise manufacturing.
The thesis presents methods, and reports their implementation, for the manufacture of freeform surfaces through a comprehensive strategy for tool path generation using minimum axis-count ultra-precision machine tools. In the context of freeform surface machining, the advantages of deterministic motion performance of three-axis machines are brought to bear through a novel treatment of the mathematics of variable contact point geometry. This is applied to ultra-precision diamond turning and ultra-precision large optics grinding with the Cranfield Box machine. New techniques in freeform surface representation, tool path generation, freeform tool shape representation and error compensation are presented.
A comprehensive technique for very high spatial resolution CMM areal scanning of freeform surfaces is presented, with a new treatment of contact error removal, achieving interferometer-equivalent surface representation, with 1,000,000+ points and sub-200 nm rms noise without the use of any low-pass filtering
Determination of an Ultimate Pit Limit Utilising Fractal Modelling to Optimise NPV
The speed and complexity of globalisation and reduction of natural resources on the one hand, and interests of large multinational corporations on the other, necessitates proper management of mineral resources and consumption. The need for scientific research and application of new methodologies and approaches to maximise Net Present Value (NPV) within mining operations is essential.
In some cases, drill core logging in the field may result in an inadequate level of information and subsequent poor diagnosis of geological phenomenon which may undermine the delineation or separation of mineralised zones. This is because the interpretation of individual loggers is subjective. However, modelling based on logging data is absolutely essential to determine the architecture of an orebody including ore distribution and geomechanical features. For instance, ore grades, density and RQD values are not included in conventional geological models whilst variations in a mineral deposit are an obvious and salient feature. Given the problems mentioned above, a series of new mathematical methods have been developed, based on fractal modelling, which provide a more objective approach. These have been established and tested in a case study of the Kahang Cu-Mo porphyry deposit, central Iran.
Recognition of different types of mineralised zone in an ore deposit is important for mine planning. As a result, it is felt that the most important outcome of this thesis is the development of an innovative approach to the delineation of major mineralised (supergene and hypogene) zones from âbarrenâ host rock. This is based on subsurface data and the utilisation of the Concentration-Volume (C-V) fractal model, proposed by Afzal et al. (2011), to optimise a Cu-Mo block model for better determination of an ultimate pit limit. Drawing on this, new approaches, referred to DensityâVolume (DâV) and RQD-Volume (RQD-V) fractal modelling, have been developed and used to delineate rock characteristics in terms of density and RQD within the Kahang deposit (Yasrebi et al., 2013b; Yasrebi et al., 2014). From the results of this modelling, the density and RQD populations of rock types from the studied deposit showed a relationship between density and rock quality based on RQD values, which can be used to predict final pit slope. Finally, the study introduces a Present Value-Volume (PV-V) fractal model in order to identify an accurate excavation orientation with respect to economic principals and ore grades of all determined voxels within the obtained ultimate pit limit in order to achieve an earlier pay-back period.Institute of Materials, Minerals and Mining, the global network IOM3Cornish Institute of EngineersWhittle Consulting (Business Optimisation for the Mining Industry