Estimating the probability of an invalid match for matching using the rank transform

A fundamental problem faced by stereo matching algorithms is the matching or correspondence problem. A wide range of algorithms have been proposed for the correspondence problem. For all matching algorithms, it would be useful to be able to compute a measure of the probability of correctness, or reliability of a match. This paper focuses in particular on one class for matching algorithms, which are based on the rank transform. The interest in these algorithms for stereo matching stems from their invariance to radiometric distortion, and their amenability to fast hardware implementation. This work differs from previous work in that it derives, from first principles, an expression for the probability of a correct match. This method was based on an enumeration of all possible symbols for matching. The theoretical results for disparity error prediction, obtained using this method, were found to agree well with experimental results. However, disadvantages of the technique developed in this chapter are that it is not easily applicable to real images, and also that it is too computationally expensive for practical window sizes. Nevertheless, the exercise provides an interesting and novel analysis of match reliability.

Kaolinite particle sizes in the <2 µM range using laser scattering

The Clay Minerals Society Source Clay kaolinites, Georgia KGa-1 and KGa-2, have been subjected to particle size determinations by 1) conventional sedimentation methods, 2) electron microscopy and image analysis, and 3) laser scattering using improved algorithms for the interaction of light with small particles. Particle shape, size distribution, and crystallinity vary considerably for each kaolinite. Replicate analyses of separated size fractions showed that in the <2 µm range, the sedimentation/centrifugation method of Tanner and Jackson (1947) is reproducible for different kaolinite types and that the calculated size ranges are in reasonable agreement with the size bins estimated from laser scattering. Particle sizes determined by laser scattering must be calculated using Mie theory when the dominant particle size is less than ∼5 µm. Based on this study of two well-known and structurally different kaolinites, laser scattering, with improved data reduction algorithms that include Mie theory, should be considered an internally consistent and rapid technique for clay particle sizing.

Fourier Lucas-Kanade Algorithm

In this paper we propose a framework for both gradient descent image and object alignment in the Fourier domain. Our method centers upon the classical Lucas & Kanade (LK) algorithm where we represent the source and template/model in the complex 2D Fourier domain rather than in the spatial 2D domain. We refer to our approach as the Fourier LK (FLK) algorithm. The FLK formulation is advantageous when one pre-processes the source image and template/model with a bank of filters (e.g. oriented edges, Gabor, etc.) as: (i) it can handle substantial illumination variations, (ii) the inefficient pre-processing filter bank step can be subsumed within the FLK algorithm as a sparse diagonal weighting matrix, (iii) unlike traditional LK the computational cost is invariant to the number of filters and as a result far more efficient, and (iv) this approach can be extended to the inverse compositional form of the LK algorithm where nearly all steps (including Fourier transform and filter bank pre-processing) can be pre-computed leading to an extremely efficient and robust approach to gradient descent image matching. Further, these computational savings translate to non-rigid object alignment tasks that are considered extensions of the LK algorithm such as those found in Active Appearance Models (AAMs).

Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

An efficient numerical method to compute nonlinear solutions for two-dimensional steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck's (1996, J. Fluid Mech., 330, 339-347). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free-surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free-surface a priori while solving for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify eleven basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free-surface, given the free-surface shape itself.

Sensitivity of peak positions to flight-path parameters in a deep-inelastic scattering neutron TOF spectrometer

The effects of small changes in flight-path parameters (primary and secondary flight paths, detector angles), and of displacement of the sample along the beam axis away from its ideal position, are examined for an inelastic time-of-flight (TOF) neutron spectrometer, emphasising the deep-inelastic regime. The aim was to develop a rational basis for deciding what measured shifts in the positions of spectral peaks could be regarded as reliable in the light of the uncertainties in the calibrated flight-path parameters. Uncertainty in the length of the primary or secondary flight path has the least effect on the positions of the peaks of H, D and He, which are dominated by the accuracy of the calibration of the detector angles. This aspect of the calibration of a TOF spectrometer therefore demands close attention to achieve reliable outcomes where the position of the peaks is of significant scientific interest and is discussed in detail. The corresponding sensitivities of the position of peak of the Compton profile, J(y), to flight-path parameters and sample position are also examined, focusing on the comparability across experiments of results for H, D and He. We show that positioning the sample to within a few mm of the ideal position is required to ensure good comparability between experiments if data from detectors at high forward angles are to be reliably interpreted.

Measurement of anisotropies of the kinetic energy and anharmonicity in pyrolytic graphite by neutron Compton scattering

Neutron Compton scattering (NCS) measurements of the anisotropy of the momentum distribution and the mean Laplacian of the interatomic potential ∇2V have been performed using electron volt neutrons, with wave vector transfers between 24 Å−1 and 98 Å−1. The measured momentum distribution of the atoms displays significantly more anisotropy than a calculation using a model density of states. We have observed anisotropies in ∇2V for the first time. The results suggest that the atomic potential is harmonic within the graphite planes, but anharmonic for vibrations perpendicular to the planes.

Neutron Compton scattering from selectively deuterated acetanilide

With the aim of developing the application of neutron Compton scattering (NCS) to molecular systems of biophysical interest, we are using the Compton spectrometer EVS at ISIS to characterize the momentum distribution of protons in peptide groups. In this contribution we present NCS measurements of the recoil peak (Compton profile) due to the amide proton in otherwise fully deuterated acetanilide (ACN), a widely studied model system for H-bonding and energy transfer in biomolecules. We obtain values for the average width of the potential well of the amide proton and its mean kinetic energy. Deviations from the Gaussian form of the Compton profile, analyzed on the basis of an expansion due to Sears, provide data relating to the Laplacian of the proton potential. (C) 1998 Elsevier Science B.V. All rights reserved.

A case for optimising fracture healing through inverse dynamization

The mechanical conditions in the repair tissues are known to influence the outcome of fracture healing. These mechanical conditions are determined by the stiffness of fixation and limb loading. Experimental studies have shown that there is a range of beneficial fixation stiffness for timely healing and that fixation stiffness that is either too flexible or too stiff impairs callus healing. However, much less is known about how mechanical conditions influence the biological processes that make up the sequence of bone repair and if indeed mechanical stimulation is required at all stages of repair. Secondary bone healing occurs through a sequence of events broadly characterised by inflammation, proliferation, consolidation and remodelling. It is our hypothesis that a change in fixation stiffness from very flexible to stiff can shorten the time to healing relative to constant fixation stiffness. Flexible fixation has the benefit of promoting greater callus formation and needs to be applied during the proliferative stage of repair. The greater callus size helps to stabilize the fragments earlier allowing mineralization to occur faster. Together with stable/rigid fixation applied during the latter stage of repair to ensure mineralization of the callus. The predicted benefits of inverse dynamization are shortened healing in comparison to very flexible fixation and healing time comparable or faster than stable fixation with greater callus stiffness.

Rapid quantification of methamphetamine: using Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy (ATR-FTIR) and Chemometrics

In Australia and increasingly worldwide, methamphetamine is one of the most commonly seized drugs analysed by forensic chemists. The current well-established GC/MS methods used to identify and quantify methamphetamine are lengthy, expensive processes, but often rapid analysis is requested by undercover police leading to an interest in developing this new analytical technique. Ninety six illicit drug seizures containing methamphetamine (0.1% - 78.6%) were analysed using Fourier Transform Infrared Spectroscopy with an Attenuated Total Reflectance attachment and Chemometrics. Two Partial Least Squares models were developed, one using the principal Infrared Spectroscopy peaks of methamphetamine and the other a Hierarchical Partial Least Squares model. Both of these models were refined to choose the variables that were most closely associated with the methamphetamine % vector. Both of the models were excellent, with the principal peaks in the Partial Least Squares model having Root Mean Square Error of Prediction 3.8, R2 0.9779 and lower limit of quantification 7% methamphetamine. The Hierarchical Partial Least Squares model had lower limit of quantification 0.3% methamphetamine, Root Mean Square Error of Prediction 5.2 and R2 0.9637. Such models offer rapid and effective methods for screening illicit drug samples to determine the percentage of methamphetamine they contain.

The temperature dependence of the momentum distribution of beryllium measured by neutron Compton scattering

In this paper we report a new neutron Compton scattering (NCS) measurement of the ground state single atom kinetic energy of polycrystalline beryllium at momentum transfers in the range 27}104 As ~1 and temperatures in the range 110}1150 K. The measurements have been made with the electron Volt spectrometer (eVS) at the ISIS facility and the measured kinetic energies are shown to be &10% higher than calculations made in the harmonic approximation.

Evidence for the adsorption of molecules at special sites located at copper/zinc oxide interfaces. Part 2. -- A fourier-transform infrared spectroscopy study of methanol adsorption on reduced and oxidised Cu/ZnO/SiO2 catalysts

FTIR spectra are reported of methanol adsorbed at 295 K on ZnO/SiO 2, on reduced Cu/ZnO/SiO2 and on Cu/ZnO/SiO2 which had been preoxidised by exposure to nitrous oxide. Methanol on ZnO/SiO2 gave methoxy species on ZnO and SiO, in addition to both strongly and weakly physisorbed methanol on SiO2. The corresponding adsorption of methanol on reduced Cu/ZnO/SiO2 also gave methoxy species on Cu and a small amount of bridging formate. Reaction of methanol with a reoxidised Cu/ZnO/SiO2 catalyst resulted in an enhanced quantity of methoxy species on Cu. Heating adsorbed species on Cu/ZnO/SiO2 at 393 K led to the loss of methoxy groups on Cu and the concomitant formation of formate species on both ZnO and Cu. The comparable reaction on a reoxidised Cu/ZnO/SiO2 catalyst gave an increased amount of formate species on ZnO and this correlated with an increased quantity of methoxy groups lost from Cu. An explanation is given in terms of adsorption of formate and formaldehyde species at special sites located at the copper/zinc oxide interface.

Evidence for the adsorption of molecules at special sites located at copper/zinc oxide interfaces: Part 1. -- A Fourier-transform infrared study of formic acid and formaldehyde adsorption on reduced and oxidised Cu/ZnO/SiO2 catalysts

Fourier-transform infrared (FTIR) spectra are reported of formic acid and formaldehyde on ZnO/SiO2, reduced Cu/ZnO/SiO2 and reoxidised Cu/ZnO/SiO2 catalyst. Formic acid adsorption on ZnO/SiO2 produced mainly bidentate zinc formate species with a lesser quantity of unidentate zinc formate. Formic acid on reduced Cu/ZnO/SiO2 catalyst resulted not only in the formation of bridging copper formate structures but also in an enhanced amount of formate relative to that for ZnO/SiO2 catalyst. Formic acid on reoxidised Cu/ZnO/SiO2 gave unidentate formate species on copper in addition to zinc formate moieties. The interaction of formaldehyde with ZnO/SiO2 catalyst resulted in the formation of zinc formate species. The same reaction on reduced Cu/ZnO/SiO2 catalyst gave bridging formate on copper and a remarkable increase in the quantity of formate species associated with the zinc oxide. Adsorption of formaldehyde on a reoxidised Cu/ZnO/SiO2 catalyst produced bridging copper formate and again an apparent increase in the concentration of zinc formate species. An explanation in terms of the adsorption of molecules at special sites located at the interface between copper and zinc oxide is given.

A combined temperature-programmed reaction spectroscopy and Fourier-transform infrared spectroscopy study of CO2/H2 and CO/CO2/H2 interactions with model ZnO/SiO2, Cu/SiO2 and Cu/ZnO/SiO2 methanol-synthesis catalysts

The reaction of CO2 and H2 with ZnO/SiO2 catalyst at 295 K gave predominantly hydrogencarbonate on zinc oxide and a small quantity of formate was evolved after heating at 393 K. Elevation of the reaction temperature to 503 K enhanced the rate of formation of zinc formate species. Significantly these formate species decomposed at 573 K almost entirely to CO2 and H2. Even after exposure of CO2-H2 or CO-CO2-H2 mixtures to highly defected ZnO/SiO2 catalyst, the formate species produced still decomposed to give CO2 and H2. It was concluded that carboxylate species which were formed at oxygen anion vacancies on polar Zn planes were not significantly hydrogenated to formate. Consequently it was proposed that the non-polar planes on zinc oxide contained sites which were specific for the synthesis of methanol. The interaction of CO2 and H2 with reduced Cu/ZnO/SiO2 catalyst at 393 K gave copper formate species in addition to substantial quantities of formate created at interfacial sites between copper and zinc oxide. It was deduced that interfacial formate species were produced from the hydrogenation of interfacial bidentate carbonate structures. The relevance of interfacial formate species in the methanol synthesis reaction is discussed. Experiments concerning the reaction of CO2-H2 with physical mixtures of Cu/SiO2 and ZnO/SiO2 gave results which were simply characteristic of the individual components. By careful consideration of previous data a detailed proposal regarding the role of spillover hydrogen is outlined. Admission of CO to a gaseous CO2-H2 feedstock resulted in a considerably diminished amount of formate species on copper. This was ascribed to a combination of over-reduction of the surface and site-blockage.

Evidence for the adsorption of molecules at special sites located at copper/zinc oxide interfaces. Part 3. -- Fourier-transform infrared study of methyl formate adsorption on reduced and oxidised Cu/ZnO/SiO2 catalysts

FTIR spectra are reported of methyl formate adsorbed at 295 K on ZnO/SiO2, reduced Cu/ZnO/SiO2 and on Cu/ZnO/SiO2 which had been preoxidised by exposure to nitrous oxide. Methyl formate on ZnO/SiO2 gave adsorbed zinc formate species and strongly physisorbed molecular methanol on silica. The comparable reaction of methyl formate with reduced Cu/ZnO/SiO2 catalyst produced bridging formate species on copper and a diminished quantity of zinc formate relative to that formed on ZnO/SiO2 catalyst. This effect is explained in terms of site blockage on the ZnO surface by small copper clusters. Addition of methyl formate to a reoxidised Cu/ZnO/SiO2 catalyst produced a considerably greater amount of formate species on zinc oxide and methoxy groups on copper were detected. The increase in concentration of zinc formate species was rationalised in terms of rearrangement of unidentate copper formate species to become bonded to copper and zinc oxide sites located at the interface between these two components.

A fourier-transform infrared study of CO2 and CO2/H2 interactions with caesium-doped copper catalysts

FTIR spectra are reported of CO2 and COi/Hi on a silica-supported caesium-doped copper catalyst. Adsorption of COj on a "caesium"/silica surface resulted in the formation of COj and complexed CO species. Exposure of CO2 to' a caesium-doped reduced copper catalyst produced not only these species but also two forms of adsorbed carboxylate giving bands at 1550, 1510, 1365 and 1345 cm"1. Reaction of carboxylate species with hydrogen at 388 K gave formate species on copper and caesium oxide in addition to methoxy groups associated with caesium oxide. Methoxy species were not detected on undoped copper catalyst suggesting that caesium may be a promoter for the methanol synthesis reaction. Methanol decomposition on a caesium-doped copper catalyst produced a small number of formate species on copper and caesium oxide. Methoxy groups on caesium oxide decomposed to CO and U.2, and subsequent reaction between CO and adsorbed oxygen resulted in carboxylate formation. Methoxy species located at interfacial sites appeared to exhibit unusual adsorption properties.