Authors:Jasper van de Gronde; Jos B.T.M. Roerdink Pages: 111 - 145 Abstract: Publication date: 2017 Source:Advances in Imaging and Electron Physics, Volume 204 Author(s): Jasper van de Gronde, Jos B.T.M. Roerdink Mathematical morphology is not always straightforward to generalize to situations where values in an image do not admit a natural total order. This mostly due to the limitations of the underlying formalism. Three state-of-the-art solutions for bypassing those limitations are discussed, with example applications ranging from color images interpreted as vector spaces to periodic and hyperbolic value spaces, and categorical data stemming from per-pixel classification of remote sensing images.

Authors:Jesús Angulo; Santiago Velasco-Forero Pages: 1 - 37 Abstract: Publication date: 2017 Source:Advances in Imaging and Electron Physics, Volume 202 Author(s): Jesús Angulo, Santiago Velasco-Forero Sparse modeling involves constructing a succinct representation of initial data as a linear combination of a few typical atoms of a dictionary. This paper deals with the use of sparse representations to introduce new nonlinear image filters which efficiently approximate morphological operators. Reasons why non-negative matrix factorization (NMF) is a dimensional reduction (i.e., dictionary learning) paradigm particularly adapted to the nature of morphological processing are given. In particular, Sparse-NMF representations are studied and used to introduce first approximations to binary dilations/erosions and then to openings/closings. The idea behind consists of processing exclusively the image dictionary and then, the result of processing each image is approximated by multiplying the processed dictionary by the coefficient weights of the current image. These operators are then extended to gray-scale images and their interest for feature detection is illustrated. The practical relevance of our approach is considered for two applications on multivariate image processing. The first case deals with multispectral texture modeling using Boolean random set theory; the second case with multi-scale decomposition of hyperspectral images and its interest in spectral–spatial pixel classification.

Authors:Clifford M. Krowne Pages: 39 - 74 Abstract: Publication date: 2017 Source:Advances in Imaging and Electron Physics, Volume 202 Author(s): Clifford M. Krowne Superconductivity can be modified by various effects related to randomness, disorder, structural defects, and other similar physical effects. Their affects on superconductivity are important because such effects are intrinsic to certain material system's preparation, or may be intentionally produced. In this chapter, we show in the context of a Cooper instability relationship, that introduction of disorder through impurities could possibly lead to an increase in T c . This is an old subject, having been addressed decades ago in the view of simpler substances, including metal alloy materials. Today, with the advances in material science, nanoscience, and atomic level preparation of materials and devices, this subject should be reexamined. That is our purpose here, especially in light of some recent discoveries made in the area of the metal–insulator transition, to be covered herein. One may obtain a formula for T c which is recognizable, and relatable to BCS theory, by using many-body quantum field theory for condensed matter expeditiously, using quantum Green's functions, polarization functions (correlation functions), and vertex functions, to extract out an analytical formula for T c . The reader will find use made of perturbational Feynman diagrammatic techniques, finite temperature quantum Matsubara Green's functions, and quantum perturbational derivations without the diagrams.

Authors:Taryl L. Kirk Abstract: Publication date: Available online 10 October 2017 Source:Advances in Imaging and Electron Physics Author(s): Taryl L. Kirk The use of low energy electrons in the analysis of materials at the nanoscale will play a significant role over many research areas including biological, medical, data storage, computing and renewable energy. This recent trend in these fields is to employ low energy primary electrons for better resolution and specificity of the resulting analysis. Here, we will discuss the method we have implemented that combines the essential functionalities of two types of microscopies; thereby, creating a quite compact instrument that can readily be integrated into ultrahigh vacuum scanning probe microscopy systems. The close proximity between the source and the specimen provides a means of overcoming the limitations of conventional scanning electron microscopes and opens the possibility to use lower primary beam energies (< 50 eV). We have named this technique, “near field emission scanning electron microscopy,” and this chapter will summarize the developmental phases of the device.

Authors:A.B. Bok; J.B. le Poole; J. Roos; H. de Lang Abstract: Publication date: Available online 12 September 2017 Source:Advances in Imaging and Electron Physics Author(s): A.B. Bok, J.B. le Poole, J. Roos, H. de Lang The optical properties of several models of mirror electron microscope are described. Contrast formation is explained in detail and many results in different areas are presented. A design that employs quadrupoles is mentioned.

Authors:Angulo Abstract: Publication date: Available online 1 September 2017 Source:Advances in Imaging and Electron Physics Author(s): Jesús Angulo The purpose of this theoretical paper is to study the convolution of two functions in the ( max , min ) -algebra. More precisely, a formal definition of morphological operators in ( max , min ) -algebra is introduced and their relevant properties from an algebraic viewpoint are stated and proved. Some previous works in mathematical morphology have already encountered this type of operators but a systematic study of them has not yet been undertaken in the morphological literature. It is shown in particular that their fundamental property is the equivalence with level set processing using Minkowski addition and subtraction. Some powerful results from nonlinear analysis can be straightforward related to the present ( max , min ) -operators. On the one hand, the theory of viscosity solutions of the Hamilton–Jacobi equation with Hamiltonians containing u and Du is summarized, in particular, the corresponding Hopf–Lax–Oleinik formulas are given. On the other hand, results on quasi-concavity preservation, Lipschitz approximation and conjugate/transform related to ( max , min ) -convolutions are discussed. Links between ( max , min ) -convolutions and some previous approaches of unconventional morphology, in particular fuzzy morphology and viscous morphology, are fully reviewed. In addition, the interest of ( max , min ) -convolutions in Boolean random function characterization is considered. Links of ( max , min ) -morphology framework to geodesic dilation and erosion are also provided. We discuss two important conclusions. First, it is proved in the paper that ( max , min ) -openings are compatible with Matheron's axiomatic of Euclidean granulometries for functions with quasiconcave structuring functions. Second, it is also shown that the adjoint supmin convolution is the operator underlying the extension of Matheron's characterization of Boolean random closed sets to the case of Boolean random upper semicontinuous function. For all these reasons, we state that ( max , min ) -convolution provides the natural framework to generalize some key notions from Matheron's theory from sets to functions.

Authors:Clifford M. Krowne Abstract: Publication date: Available online 31 August 2017 Source:Advances in Imaging and Electron Physics Author(s): Clifford M. Krowne Superconductivity can be modified by various effects related to randomness, disorder, structural defects, and other similar physical effects. Their affects on superconductivity are important because such effects are intrinsic to certain material system's preparation, or may be intentionally produced. Here we show that the introduction of disorder through impurities could possibly lead to an increase in the superconducting gap Δ ( T ) , where this disorder is of an unconventional non-alloy type. Furthermore, by use of this Δ ( T ) in a microscopic approach, critical magnetic field H c , its slope d H c / d T , and heat capacity C e l are found. This is an old subject, having been addressed decades ago in the view of simpler substances, including metal alloy materials. Today, with the advances in material science, nanoscience, and atomic level preparation of materials and devices, this subject should be reexamined. That is our purpose here, especially in light of some recent discoveries made in the area of the metal–insulator transition, to be covered herein. Use is made of many-body quantum field theory for condensed matter, employing quantum Green's functions, to extract out analytical formulas. The reader will find use made of perturbational Feynman propagator techniques, and finite temperature quantum Matsubara Green's functions. Relationship to BCS theory is indicated throughout the presentation.

Authors:Albert Septier Abstract: Publication date: Available online 31 July 2017 Source:Advances in Imaging and Electron Physics Author(s): Albert Septier

Authors:Ashkan Ashrafi Abstract: Publication date: Available online 16 June 2017 Source:Advances in Imaging and Electron Physics Author(s): Ashkan Ashrafi The Walsh–Hadamard Transforms refer to a series of transforms related to Walsh functions and Hadamard matrix. These transforms have numerous applications in different areas of engineering and science. There are many versions of the Walsh–Hadamard Transform. In this article, the most important versions of the Walsh–Hadamard Transforms are reviewed. We start with the definition of the Walsh functions and finish the article with the Conjugate Symmetric Sequency-Ordered Hadamard Transform.

Authors:Sameen Ahmed Khan Abstract: Publication date: Available online 26 June 2017 Source:Advances in Imaging and Electron Physics Author(s): Sameen Ahmed Khan A unified formalism of light beam optics and light polarization is presented. The starting point of our formalism is an exact matrix-representation of Maxwell's equations in an inhomogeneous medium, which is presented in detail. The beam-optical Hamiltonians are derived without any specifications on the form of the varying refractive index. The new formalism generalizes the traditional and non-traditional prescriptions of Helmholtz optics. As for the light polarization, the elegant Mukunda–Simon–Sudarshan rule for transition from scalar to vector wave optics is obtained as the paraxial limit of the general formalism presented here. The new formalism is a suitable candidate to extend traditional theory of polarization beyond the paraxial approximation. The unified formalism of light beam-optics and light polarization further strengthens the Hamilton's optical-mechanical analogy, particularly in the wavelength-dependent regime.

Authors:Gaston Dupouy Abstract: Publication date: Available online 20 June 2017 Source:Advances in Imaging and Electron Physics Author(s): Gaston Dupouy In 1968, when this article first appeared, electron microscopy in the megavolt range was still very new. The advantages and problems of operation at such high voltages are set out very readably and many examples of micrographs, mostly obtained with the Toulouse high-voltage electron microscope, are included. Beam–specimen interactions at high voltage are explored. Detailed descriptions of the construction of such microscopes are provided.

Authors:Ernst Ruska Abstract: Publication date: Available online 16 May 2017 Source:Advances in Imaging and Electron Physics Author(s): Ernst Ruska The builder of the first electron microscope with magnetic lenses assesses the difficulties of improving the resolution of the electron microscope, as they appeared in 1966. Each of the obstacles is examined in turn and its importance gauged. The condenser objective is described and clearly illustrated as is a cooling system designed to limit radiation damage.

Authors:John C.H. Spence Abstract: Publication date: Available online 24 April 2017 Source:Advances in Imaging and Electron Physics Author(s): John C.H. Spence The recent invention of the X-ray laser (XFEL), with its high spatial coherence and ability to outrun radiation damage, has provided unprecedented new opportunities for structural biology. Here, we review the challenges and advances which have occurred over the past 7 years since the first beamtimes, provide their historical context, and describe the underlying principles of the new techniques used and the XFEL. The main focus is on the achievements and prospects for imaging protein dynamics at near-atomic spatial resolution under physiological and controlled chemical conditions, in the correct thermal bath, and a summary of the many approaches to this aim. Radiation damage, comparisons of XFEL and synchrotron work, single-particle diffraction, fast solution scattering, pump-probe studies on photosensitive proteins, mixing jets, caged molecules, pH jump, and other reaction initiation methods, and the thermodynamics of molecular machines are all discussed, in addition to data analysis methods for all the instrumental modes. The ability of the XFEL to separate chemical reaction effects in dynamical imaging from radiation-induced effects (by minimizing these), while imaging at the physiological temperatures required for molecular machines, is highlighted.

Authors:Christopher J. Edgcombe Abstract: Publication date: Available online 20 April 2017 Source:Advances in Imaging and Electron Physics Author(s): Christopher J. Edgcombe A brief survey is given of prespecimen plates used to generate vortex beams, followed by some details of postspecimen plates as now used to provide image intensity modulation from phase objects. Spectral transfer theory applied to some simple model systems shows that the maximum size of object that can be imaged accurately with the Zernike plate depends not only on the object diameter but also on the system parameters. Further analysis suggests that when a Hilbert plate is located exactly on the cylindrical axis, the usual choice of an added phase of π minimizes the linear response of intensity to the phase of a weak-phase object. A linear response may be available if the added phase is reduced to π/2.

Authors:Inder Jeet Taneja Abstract: Publication date: Available online 20 March 2017 Source:Advances in Imaging and Electron Physics Author(s): Inder Jeet Taneja In the literature on information theory, there exist many divergence measures. These are known by Jensen difference divergence measure, J-Divergence, and arithmetic and geometric mean divergence. These are symmetric in pair of probability distributions. There is an interesting inequality relating these measures. These are with logarithmic expressions. Still there are measures without logarithmic expressions, known as, Hellinger's distance, triangular discrimination, etc. All these measures can be unified in three different parametric generalizations having much more particular cases. On the other sides, arithmetic, geometric, harmonic, square-root means, etc. are also well famous mathematics. In parametric situation, generalized Gini-mean is also known in literature. We can create new measures by using the idea of difference of means arising due to inequalities among these means. The same can also be done with difference of divergence measures. The aim of this work is to relate these differences arising due to inequalities among the divergence measures and means, and to find relations among them. Refinement inequalities are also studied.

Authors:Román Castañeda; Giorgio Matteucci Pages: 1 - 37 Abstract: Publication date: Available online 12 October 2017 Source:Advances in Imaging and Electron Physics Author(s): Román Castañeda, Giorgio Matteucci To describe wave interference, a wave function with a direct physical meaning is used. On the contrary the distribution of material particles in an interference pattern is calculated with a probability wave function whose interpretation presents controversial features. Here, a general law is reported which provides a unified explanation of wave and material particle interference. We will show that the wave superposition principle as well as the counterintuitive features such as wave–particle duality, self-interference and wave collapse are not needed to explain observed interference patterns. With the present model, the contestable features regarding the physical meaning of the probability wave are removed. Simulations of experimental results show clearly that the predictive accuracy of our model overcomes that one of the standard optical method. Finally, an original interpretation of the uncertainty principle in connection with the diffraction modulation of interference patterns is also reported.

Authors:Allen J.F. Metherell Pages: 147 - 230 Abstract: Publication date: Available online 12 October 2017 Source:Advances in Imaging and Electron Physics Author(s): Allen J.F. Metherell This article describes the electron optics used in the energy analyzing and energy selecting transmission electron microscopes constructed in the 1960s. The former instrument used a cylindrical electrostatic lens as the energy analyzer and the electron optics of this lens is described in detail. The latter instrument used a magnetic prism and an electrostatic mirror as the energy-selecting device and the electron optics of this device is also described in detail.