Reconstruction of Three-Dimensional Blood Vessel Model Using Fractal Interpolation

Fractal method is used in the image processing and studying the irregular and the complex shapes in the image. It is also used in the reconstruction and smoothing of one-, two-, and three-dimensional data. In this chapter, we present an interpolating fractal algorithm to reconstruct 3D blood vessels. Firstly, the proposed method determines the blood vessel centerline from the 2D retina image, and then it uses the Douglas-Peucker algorithm to detect the control points. Secondly, we use the 3D fractal interpolation and iterated function systems for the visualization and reconstruction of these blood vessels. The results showed that the obtained reduction rate is between 71 and 94% depending on the tolerance value. The 3D blood vessels model can be reconstructed efficiently by using the 3D fractal interpolation method

Multiscale fractality with application and statistical modeling and estimation for computer experiment of nano-particle fabrication

The first chapter proposes multifractal analysis to measure inhomogeneity of regularity of 1H-NMR spectrum using wavelet-based multifractal tools. The geometric summaries of multifractal spectrum are informative summaries, and as such employed to discriminate 1H-NMR spectra associated with different treatments. The methodology is applied to evaluate the effect of sulfur amino acids. The second part of this thesis provides essential materials for understanding engineering background of a nano-particle fabrication process. The third chapter introduces a constrained random effect model. Since there are certain combinations of process variables resulting to unproductive process outcomes, a logistic model is used to characterize such a process behavior. For the cases with productive outcomes a normal regression serves the second part of the model. Additionally, random-effects are included in both logistics and normal regression models to describe the potential spatial correlation among data. This chapter researches a way to approximate the likelihood function and to find estimates for maximizing the approximated likelihood. The last chapter presents a method to decide the sample size under multi-layer system. The multi-layer is a series of layers, which become smaller and smaller. Our focus is to decide the sample size in each layer. The sample size decision has several objectives, and the most important purpose is the sample size should be enough to give a right direction to the next layer. Specifically, the bottom layer, which is the smallest neighborhood around the optimum, should meet the tolerance requirement. Performing the hypothesis test of whether the next layer includes the optimum gives the required sample size.PhDCommittee Chair: Brani Vidakovic ; Committee Chair: Jye-Chyi (JC) Lu; Committee Co-Chair: Martha Grover; Committee Member: Jianjun Shi; Committee Member: Kamran Paynaba

Quantification of Fracture Roughness by Change Probabilities and Hurst Exponents

The objective of the current study is to utilize an innovative method called “change probabilities” for describing fracture roughness. In order to detect and visualize anisotropy of rock joint surfaces, the roughness of one-dimensional profiles taken in different directions is quantified. The central quantifiers, change probabilities, are based on counting monotonic changes in discretizations of a profile. These probabilities, which usually vary with the scale, can be reinterpreted as scale-dependent Hurst exponents. For a large class of Gaussian stochastic processes, change probabilities are shown to be directly related to the classical Hurst exponent, which generalizes a relationship known for fractional Brownian motion. While related to this classical roughness measure, the proposed method is more generally applicable, therefore increasing the flexibility of modeling and investigating surface profiles. In particular, it allows a quick and efficient visualization and detection of roughness anisotropy and scale dependence of roughness

Mathematical Modeling and Simulation in Mechanics and Dynamic Systems

The present book contains the 16 papers accepted and published in the Special Issue “Mathematical Modeling and Simulation in Mechanics and Dynamic Systems” of the MDPI “Mathematics” journal, which cover a wide range of topics connected to the theory and applications of Modeling and Simulation of Dynamic Systems in different field. These topics include, among others, methods to model and simulate mechanical system in real engineering. It is hopped that the book will find interest and be useful for those working in the area of Modeling and Simulation of the Dynamic Systems, as well as for those with the proper mathematical background and willing to become familiar with recent advances in Dynamic Systems, which has nowadays entered almost all sectors of human life and activity

Fractal Analysis

Fractal analysis is becoming more and more common in all walks of life. This includes biomedical engineering, steganography and art. Writing one book on all these topics is a very difficult task. For this reason, this book covers only selected topics. Interested readers will find in this book the topics of image compression, groundwater quality, establishing the downscaling and spatio-temporal scale conversion models of NDVI, modelling and optimization of 3T fractional nonlinear generalized magneto-thermoelastic multi-material, algebraic fractals in steganography, strain induced microstructures in metals and much more. The book will definitely be of interest to scientists dealing with fractal analysis, as well as biomedical engineers or IT engineers. I encourage you to view individual chapters

Advanced of Mathematics-Statistics Methods to Radar Calibration for Rainfall Estimation; A Review

Ground-based radar is known as one of the most important systems for precipitation measurement at high spatial and temporal resolutions. Radar data are recorded in digital manner and readily ingested to any statistical analyses. These measurements are subjected to specific calibration to eliminate systematic errors as well as minimizing the random errors, respectively. Since statistical methods are based on mathematics, they offer more precise results and easy interpretation with lower data detail. Although they have challenge to interpret due to their mathematical structure, but the accuracy of the conclusions and the interpretation of the output are appropriate. This article reviews the advanced methods in using the calibration of ground-based radar for forecasting meteorological events include two aspects: statistical techniques and data mining. Statistical techniques refer to empirical analyses such as regression, while data mining includes the Artificial Neural Network (ANN), data Kriging, Nearest Neighbour (NN), Decision Tree (DT) and fuzzy logic. The results show that Kriging is more applicable for interpolation. Regression methods are simple to use and data mining based on Artificial Intelligence is very precise. Thus, this review explores the characteristics of the statistical parameters in the field of radar applications and shows which parameters give the best results for undefined cases. DOI: 10.17762/ijritcc2321-8169.15012

The climatic significance of tropical forest edges and their representation in global climate models

An emerging theme in global climate modelling is whether land covers created in the clearance of tropical humid forests influence water exchange between remnant forest patches and the atmosphere, and, if so, how this affects regional and global water exchange. Fieldwork presented in this thesis ascertains whether the amount of water transferred to the atmosphere from a humid tropical forest situated in Sabah, Northern Borneo, Malaysia, differs between its edge and interior due to the influence of surrounding clearings through horizontal heat transfer. Using satellite imagery to measure the shape and size of tropical forests, field measurements of water transfer were extrapolated to continental and global levels to infer how differences in water exchange with the atmosphere between forest edges and interiors may influence regional and global forest-atmosphere water exchange. Mean sap flow in trees within 50 meters of a forest-clearing boundary was found to be 73% greater than that in trees further into the forest; an observation supported by the decreased canopy temperature also recorded there. Evaporation from the forest canopy constituted a high fraction of annual rainfall (33%), but showed no edge effect similar to that of sap flow. Edge plots, however, expressed evapotranspiration rates 22% lower than forest interiors (657-890 mm yr-1), owing to the lower number and size of trees there. One edge plot, however, exhibited evapotranspiration 49.5% greater than that of forest interiors. Gradients of air temperature, vapour pressure deficit and wind speed from the adjacent clearing to the forest interior indicated that warm, dry air moving from the clearing to the forest was the most credible cause of increased sap flow of trees near the forest edge. This hypothesis was supported by a strong correlation between the amount of vapour in the air moving from the clearing and tree water use. It was estimated that the influence of differences in water transfer to the atmosphere between the edges and interiors of tropical forest would not alter global water transfer to the atmosphere by more than 0.25-4%, or by 4-7% in the most fragmented tropical continent, Africa. However, it remains unclear whether the inclusion of tropical forest edge effects within climate models is necessary, as the pioneering nature of this thesis, and of existing studies reviewed within it, means that solid conclusions will be dependent upon future work. This thesis concludes with suggestions for future research that will most effectively consolidate the provisional conclusions and recommendations herein