Used in machine learning, finding fractal structure is not as easy often these datasets are modeled on a euclidean space of dimension greater than three, and some of them are not euclidean at all, leaving this chapter introduces the two basic concepts on which this thesis is built: frac- tals and machine. Acknowledgments this phd was completed as a co-shared thesis (french : “cotutelle”) between the laboratory iusti umr cnrs n°7343, aix-marseille university in marseille, france, and the chair of electronic and photonic metrology wrocław university of technology in wrocław, poland. Xiaohan zhang a thesis submitted to the graduate faculty of auburn university the relationship between the fractal dimension, d, and the fractal scaling constant g, is investigated as well d: schematical illustration of fractal dimension of the other five measured rough surfaces calculated by using. Thesis title: a study on coalescence and spline fractal interpolation functions name of thesis supervisor: professor g p kapoor month & year of thesis submission: december 2004 mandelbrot [ les objects fractals : forme, hasard et dimension, flammarion, 1975] intro- duced fractals, to describe objects that were too. Dimensions of self-similar fractals by melissa glass a thesis submitted to the graduate faculty of wake forest university graduate school of arts and sciences in partial fulfillment of the requirements for the degree of master of arts mathematics may 2011 winston-salem, north.
Fractal dimension and julia sets robert delorto eastern washington university follow this and additional works at: http://dcewuedu/theses this thesis is brought to you for free and open access by the student research and creative works at ewu digital commons it has been accepted for inclusion in ewu masters. Some other possible series expansions of contour functions multiscale shape analysis using continuous wavelet transform shape curvature scale space representation 22 set theory approach 221 simple geometrical shape parameters 222 fractals in shape analysis definition of fractal dimension. Dimensions 51 introduction throughout this thesis, we observe close correlations between values of the topological growth rates and various other fractal indices these observations are based on both analytic derivations and numerical computations of the relevant exponents in this chapter we derive inequalities that. This thesis presents an optical area based surface characterization technique, which applies fractal geometry and basic light scattering principles, to correlate surface roughness and fractal dimension the unique contribution of this work is that the theory of electromagnetic scattering observed in rough surfaces and the.
Abstract of the thesis the overlapping variation method algorithm by steven charles williams master of science in computer science san diego state university, 2013 the overlapping variation method algorithm is a restructuring of the standard variation method for estimating fractal dimensions as proposed by. Estimating the fractal dimension of color images is not in this thesis the theory behind estimating fractal dimension of grayscale images is presented, and then extended to work with color images, using the color spectrum in each pixel a novel method for generating fractal sets with different fractal properties.
It may be concluded that fractal properties such as self-similarity and dimension play a key role in the design of such arrays 12 thesis motivation in modern wireless communication systems and increasing of other wireless applications, wider bandwidth, multiband [7-8] and low profile antennas are in great demand for both. Texture segmentation multifractaldiension fractal dimension box counting 1 introduction texture segmentation and classification, based on an extension of fractal dimension (fd) features the fd kamal h sager, fractal based classification for color textural images, phd thesis, department of astronomy.
Effective fractal dimension: foundations and applications by john m hitchcock a dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of doctor of philosophy major: computer science program of study committee: jack h lutz, major professor pavan aduri. Image segmentation via fractal dimension thesis premented to the faculty of the school of engineering of the air force institute of technology air university in partial fulfillment of the requirements for the degree of master of science in electrical engineering ntis cra&i ' dttc yab alato l jones, us. I certify that i have read estimating the fractal dimension of sets determined by nonergodic parameters by joseph paul squillace, and that in my opinion this work meets the criteria for approving a thesis submitted in partial fufillment of the re- quirements for the degree: master of arts in mathematics at san francisco state.