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@PhDThesis{Souza:2017:AnCoPa,
               author = "Souza, Vanessa Cristina Oliveira de",
                title = "An{\'a}lise computacional de padr{\~o}es estruturais 
                         n{\~a}o-lineares a partir de imagens digitais com estudos de caso 
                         em ci{\^e}ncias ambientais e espaciais",
               school = "Instituto Nacional de Pesquisas Espaciais (INPE)",
                 year = "2017",
              address = "S{\~a}o Jos{\'e} dos Campos",
                month = "2017-06-09",
             keywords = "an{\'a}lise de flutua{\c{c}}{\~a}o destendenciada 
                         bi-dimensional, textura, classifica{\c{c}}{\~a}o, 
                         paraleliza{\c{c}}{\~a}o, GPGPU/CUDA, Bi-dimensional detrended 
                         fluctuation analysis, texture, classification, parallelization, 
                         GPGPU/CUDA.",
             abstract = "A An{\'a}lise de Flutua{\c{c}}{\~a}o Destendenciada (DFA) tem 
                         sido amplamente utilizada na verifica{\c{c}}{\~a}o de 
                         propriedades de escala de s{\'e}ries temporais unidimensionais. 
                         Al{\'e}m de revelar a presen{\c{c}}a ou n{\~a}o de mem{\'o}ria 
                         na s{\'e}rie (persist{\^e}ncia), o m{\'e}todo DFA possibilita 
                         compreender melhor o processo que originou o sinal analisado e a 
                         for{\c{c}}a da correla{\c{c}}{\~a}o. Nesse ponto, o operador do 
                         DFA (\$\alpha\$) infere tamb{\'e}m sobre a rugosidade do 
                         sinal, isto porque quanto maior a persist{\^e}ncia, menor a 
                         rugosidade. Quando tal caracter{\'{\i}}stica {\'e} expandida 
                         para sinais bi-dimensionais, em especial imagens digitais, a 
                         no{\c{c}}{\~a}o de persist{\^e}ncia infere tamb{\'e}m sobre a 
                         textura desses sinais. O DFA foi generalizado para operar em 
                         sinais bi-dimensionais em 2006 (DFA-2D) e, desde ent{\~a}o, 
                         diversos estudos v{\^e}m sendo feitos, especialmente utilizando o 
                         \$\alpha\$ como um operador textural. Diferente dos operadores 
                         texturais comuns que atuam sobre a varia{\c{c}}{\~a}o de brilho 
                         na imagem, o DFA-2D utiliza o arcabou{\c{c}}o te{\'o}rico da 
                         teoria dos fractais e infere a textura a partir da 
                         caracter{\'{\i}}stica de autossimilaridade do sinal. Neste 
                         contexto, os objetivos desse trabalho foram ; i) explorar 
                         quest{\~o}es controversas ou n{\~a}o tratadas ainda para o 
                         DFA-2D na literatura e ii) avan{\c{c}}ar no estado da arte da 
                         t{\'e}cnica bi-dimensional em suas vers{\~o}es mono e 
                         multifractal, avaliando a resposta em um conjunto diverso de dados 
                         e tamb{\'e}m melhorando sua performance por meio da 
                         paraleliza{\c{c}}{\~a}o, utilizando GPGPU/CUDA. Sendo assim, 
                         essa tese pretendeu contribuir com dois aspectos do DFA-2D 
                         criticados na literatura : a dificuldade de 
                         interpreta{\c{c}}{\~a}o do operador \$\alpha\$ e o alto custo 
                         computacional. Foram estudados conjuntos de dados simulados cuja 
                         resposta {\'e} conhecida (fBm e fGn), conjuntos cl{\'a}ssicos de 
                         dados simulados n{\~a}o tratados na literatura com o DFA-2D (como 
                         ru{\'{\i}}dos do tipo 1/f e redes de mapas acoplados). A 
                         an{\'a}lise tamb{\'e}m incluiu conjuntos de dados reais, cujas 
                         aplica{\c{c}}{\~o}es utilizando o DFA-2D s{\~a}o in{\'e}ditas, 
                         como a classifica{\c{c}}{\~a}o morfol{\'o}gica de gal{\'a}xias 
                         e a infer{\^e}ncia de rugosidade efetiva para estudos de energia 
                         e{\'o}lica, por meio da classifica{\c{c}}{\~a}o de Modelos 
                         Digitais de Eleva{\c{c}}{\~a}o topogr{\'a}fica (MDE). Para os 
                         sinais simulados, o DFA-2D (mono e multifractal) caracterizou de 
                         forma satisfat{\'o}ria os sinais. Para os sinais reais, os 
                         resultados mostraram que, mesmo quando o operador \$\alpha\$ 
                         n{\~a}o atinge uma boa taxa de classifica{\c{c}}{\~a}o, seu uso 
                         {\'e} muito informativo, caracterizando o sinal, e n{\~a}o 
                         apenas classificando-o. Al{\'e}m disso, o DFA-2D aplicado a dados 
                         reais apresentou dificuldades e desafios impercept{\'{\i}}veis 
                         nos sinais simulados. Por fim, a paraleliza{\c{c}}{\~a}o 
                         mostrou-se eficaz, diminuido consideravelmente o tempo de 
                         processamento pelo DFA-2D. ABSTRACT: The Detrended Fluctuation 
                         Analysis (DFA) has been widely used to verify the scaling 
                         properties of unidimensional time series. Besides revealing the 
                         presence or absence of memory in the series (persistence), the DFA 
                         method allows understanding the process that originated the 
                         analyzed signal, as well as the strength of the correlation. The 
                         DFA operator () also infers about the signal roughness, because 
                         the larger the persistence, the smaller the roughness. When such 
                         feature is expanded to bi-dimensional signals, especially in 
                         digital images, the notion of persistence also infers on the 
                         texture of these signals. The DFA method was generalized to 
                         operate on bi-dimensional signals in 2006 (DFA-2D) and, since 
                         then, several studies have been performed using the () as a 
                         textural operator. Differently from the common textural operators, 
                         which focus on the brightness variation of an image, the DFA- 2D 
                         exploits the theoretic framework from the fractal theory and 
                         infers the texture using the auto similarity feature of the 
                         signal. In this context, the goals of this work were: i) to 
                         explore controversial or not yet treated issues for the DFA-2D in 
                         the literature and ii) advance the state of the art in the 
                         bi-dimensional technique in its two versions mono e multifractal 
                         evaluating the response in a diverse set of data and also 
                         improving its performance by means of parallelization, using 
                         GPGPU/CUDA. Therefore, this thesis provides contributions in two 
                         aspects of the DFA-2D which are criticized in the literature: the 
                         interpretation difficulty related to the \$\alpha\$ operator 
                         and high computational cost of the method. Simulated sets of data 
                         that present a well-known response (fBm and fGn) has been studied, 
                         as well as classical sets of simulated data not treated in the 
                         literature using the DFA-2D (such as noise data of type 1/f and 
                         coupled map networks). The analysis also included sets of real 
                         data, providing umprecedent applications using the DFA-2D, such as 
                         the morphological classification of galaxies and the inference of 
                         effective roughness for eolic energy studies, by using the 
                         classification of Models of Digital Elevation (MDE). The DFA-2D 
                         (mono and multifractal) was able to categorize simulated signals 
                         in a satisfactory manner. For real signals, the results show that, 
                         even when the \$\alpha\$ operator does not reach a good 
                         classification rate, its usage is very informative, characterizing 
                         the signal and not only classifying it. Besides, the DFA-2D 
                         applied to real data presented difficulties and challenges 
                         imperceptible in simulated signals. Lastly, the parallelization 
                         has proven to be effective in order to lower the processing time 
                         required by the DFA-2D.",
            committee = "Stephany, Stephan (presidente) and Rosa, Reinaldo Roberto 
                         (orientador) and Assireu, Arcilan Trevenzoli (orientador) and 
                         Guimar{\~a}es, Lamartine Nogueira Frutuoso and Zamith, Marcelo 
                         Panaro de Moraes and Bolzan, Maur{\'{\i}}cio Jos{\'e} Alves",
         englishtitle = "Computational analysis of non-linear structural patterns from 
                         digital images with case studies in environmental and space 
                         sciences",
             language = "pt",
                pages = "189",
                  ibi = "8JMKD3MGP3W34P/3P7RU3B",
                  url = "http://urlib.net/rep/8JMKD3MGP3W34P/3P7RU3B",
           targetfile = "publicacao.pdf",
        urlaccessdate = "28 nov. 2020"
}


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