Digital Image Processing

This book presents several recent advances that are related or fall under the umbrella of 'digital image processing', with the purpose of providing an insight into the possibilities offered by digital image processing algorithms in various fields. The presented mathematical algorithms are accompanied by graphical representations and illustrative examples for an enhanced readability. The chapters are written in a manner that allows even a reader with basic experience and knowledge in the digital image processing field to properly understand the presented algorithms. Concurrently, the structure of the information in this book is such that fellow scientists will be able to use it to push the development of the presented subjects even further

A design methodology for rock slopes susceptible to wedge failure using fracture system modelling

This paper demonstrates how the use of fracture system modelling can be linked to limit equilibrium analysis of rock slopes susceptible to wedge failure. The use of fracture systems highlights some of the limitations inherent in traditional structural data analysis and representation. Consequently it allows for more comprehensive input data that can be used for stability analysis of rock slopes. In particular the developed methodology addresses important issues such as spatial variability and wedge size distributions. The paper introduces a series of guidelines for interpretation of the results of rock slopes. The proposed techniques arguably result in an improved level of confidence in the design of rock slopes susceptible to wedge failur

Towards the ab initio based theory of the phase transformations in iron and steel

Despite of the appearance of numerous new materials, the iron based alloys and steels continue to play an essential role in modern technology. The properties of a steel are determined by its structural state (ferrite, cementite, pearlite, bainite, martensite, and their combination) that is formed under thermal treatment as a result of the shear lattice reconstruction "gamma" (fcc) -> "alpha" (bcc) and carbon diffusion redistribution. We present a review on a recent progress in the development of a quantitative theory of the phase transformations and microstructure formation in steel that is based on an ab initio parameterization of the Ginzburg-Landau free energy functional. The results of computer modeling describe the regular change of transformation scenario under cooling from ferritic (nucleation and diffusion-controlled growth of the "alpha" phase to martensitic (the shear lattice instability "gamma" -> "alpha"). It has been shown that the increase in short-range magnetic order with decreasing the temperature plays a key role in the change of transformation scenarios. Phase-field modeling in the framework of a discussed approach demonstrates the typical transformation patterns

Computing global shape measures

Global shape measures are a convenient way to describe regions. They are generally simple and efficient to extract, and provide an easy means for high level tasks such as classification as well as helping direct low-level computer vision processes such as segmentation. In this chapter a large selection of global shape measures (some from the standard literature as well as other newer methods) are described and demonstrated

Quantum Gravity and Matter: Counting Graphs on Causal Dynamical Triangulations

An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate technical tools, one is interested in measuring and classifying how the quantum fluctuations of geometry alter the behaviour of matter, compared with that on a fixed background geometry. In the simplified context of two dimensions, we show how a method invented to analyze the critical behaviour of spin systems on flat lattices can be adapted to the fluctuating ensemble of curved spacetimes underlying the Causal Dynamical Triangulations (CDT) approach to quantum gravity. We develop a systematic counting of embedded graphs to evaluate the thermodynamic functions of the gravity-matter models in a high- and low-temperature expansion. For the case of the Ising model, we compute the series expansions for the magnetic susceptibility on CDT lattices and their duals up to orders 6 and 12, and analyze them by ratio method, Dlog Pad\'e and differential approximants. Apart from providing evidence for a simplification of the model's analytic structure due to the dynamical nature of the geometry, the technique introduced can shed further light on criteria \`a la Harris and Luck for the influence of random geometry on the critical properties of matter systems.Comment: 40 pages, 15 figures, 13 table