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Trabalho De Conclusão De Curso UNIVERSIDADE FEDERAL DE JUIZ DE FORA CURSO DE GRADUAÇÃO EM ENGENHARIA DE PRODUÇÃO LEONARDO ROCHA VIDAL A PROEMINÊNCIA GEOGRÁFICA COMO MÉTRICA PARA CARACTERIZAÇÃO DE GRUPOS EM HISTOGRAMAS BIDIMENSIONAIS JUIZ DE FORA 2019 LEONARDO ROCHA VIDAL A PROEMINÊNCIA GEOGRÁFICA COMO MÉTRICA PARA CARACTERIZAÇÃO DE GRUPOS EM HISTOGRAMAS BIDIMENSIONAIS Trabalho de Conclusão de Curso apresentado a Faculdade de Engenharia da Universidade Federal de Juiz de Fora, como requisito parcial para a obtenção do título de Engenheiro de Produção. Orientador: D. Sc. Fernando Marques de Almeida Nogueira JUIZ DE FORA 2019 AGRADECIMENTOS Agradeço a Deus, por sempre iluminar e guiar meu caminho, me dando forças para buscar meus maiores sonhos e objetivos. Agradeço aos meus pais, Luis Alberto e Fátima, minha família e todos amigos e amigas, por sempre serem companheiros, por sempre me motivarem a ser uma pessoa melhor e por me mostrarem novas perspectivas do mundo. Agradeço à Universidade por proporcionar um ambiente com foco no aprendizado e por facilitar o acesso ao conhecimento. Aos mestres, por passarem seus ensinamentos e compartilharem sua sabedoria, contribuindo para a formação de melhores profissionais. Aos colegas, por compartilharem essa jornada e seus desafios. Agradeço ao professor Fernando Nogueira, por me guiar e orientar neste trabalho, me auxiliando nos momentos de dificuldade e dedicando sua atenção e tempo na elaboração deste projeto. RESUMO A utilização e tratamento de dados tem se tornado um aspecto cada vez mais importante para a tomada de decisão em diversos ambientes profissionais. Nesse sentido, este trabalho apresenta uma métrica para caracterização de grupos (clusters) em histogramas bidimensionais baseada em uma grandeza topográfica conhecida como Proeminência Geográfica. Para demonstrar a viabilidade do conceito, o problema de cálculo da proeminência geográfica foi contextualizado e modelado matematicamente, e sua solução foi desenvolvida através de um algoritmo. Após a implementação da solução, modelos de dados foram testados e comparados e os resultados obtidos demonstraram a viabilidade no emprego dessa métrica para caracterização de grupos distintos em histogramas bidimensionais. PALAVRAS-CHAVE: Proeminência geográfica, grupos, classificação. ABSTRACT The use and processing of data has become an increasingly important factor in decision making in several professional environments. In this sense, the present work introduces a measure to define groups (clusters) in bidimensional histograms based on a topographic concept known as topographic prominence. In order to show the viability of the measure, the problem to calculate the topographic prominence was contextualized and mathematically modeled, and its solution was developed through an algorithm. After the development of the solution, data models were tested and compared and the results showed that the use of the measure was in fact viable to distinguish groups in bidimensional histograms. KEYWORDS: Topographic prominence, groups, clustering LISTA DE FIGURAS Figura 1 - Critérios de classificação da pesquisa científica em Engenharia de Produção ................................................................................................................................... 17 Figura 2 - Cálculo da proeminência. .......................................................................... 20 Figura 3 - Exemplo do problema de proeminência modelado em rede...................... 23 Figura 4 - Identificação de picos na matriz ................................................................ 27 Figura 5 - Matriz inicial de crescimento .................................................................... 29 Figura 6 - Matriz com a região em expansão ............................................................. 30 Figura 7 - Matriz com a região expandida ................................................................. 30 Figura 8 - Segmento de reta formado por 휌 e 휃 ......................................................... 41 Figura 9 - Espaço Imagem e Espaço de Hough.......................................................... 42 Figura 10 - Imagem utilizada na transformada de Hough - Exemplo 1 ..................... 44 Figura 11 - Transformada de Hough (método MATLAB) – Exemplo 1 ................... 46 Figura 12 - Transformada de Hough (método da proeminência) – Exemplo 1 ......... 47 Figura 13 -Imagem utilizada na transformada de Hough - Exemplo 2 ...................... 48 Figura 14 - Transformada de Hough (método MATLAB) – Exemplo 1 ................... 49 Figura 15 - Transformada de Hough (método da proeminência) – Exemplo 2 ......... 50 LISTA DE GRÁFICOS Gráfico 1 - Histograma de uma variável .................................................................... 14 Gráfico 2 - Histograma bidimensional ....................................................................... 15 Gráfico 3 - Histograma Peso x Altura ........................................................................ 33 Gráfico 4 - Histograma Peso x Altura das proeminências ......................................... 34 Gráfico 5 - Imagem do Histograma Peso x Altura ..................................................... 35 Gráfico 6 - Porcentagem de cada sexo na região partindo de A ................................ 36 Gráfico 7 - Porcentagem de cada Sexo na região partindo de C ................................ 36 Gráfico 8 - Histograma Notas Português x Inglês ...................................................... 38 Gráfico 9 - Histograma das Proeminências das Notas Português x Inglês ................ 38 Gráfico 10 - Imagem do Histograma das Notas Português x Inglês .......................... 39 Gráfico 11 - Espaço de Hough para uma imagem ...................................................... 42 Gráfico 12 - Superfície de um espaço acumulador .................................................... 43 Gráfico 13 - Espaço de Hough para a imagem do Exemplo 1 ................................... 44 Gráfico 14 - Superfície formada pelo espaço de Hough da imagem do Exemplo 1 .. 45 Gráfico 15 - Espaço de Hough para a imagem do Exemplo 2 ................................... 48 Gráfico 16 - Superfície formada pelo espaço de Hough da imagem do Exemplo 2 .. 49 LISTA DE TABELAS Tabela 1– Relação dos 15 picos mais proeminentes no mundo ................................. 21 Tabela 2 - Relação Peso x Altura ............................................................................... 32 Tabela 3 - Conjunto de dados hipotéticos que relaciona notas de alunos nas disciplinas de Português e Inglês. ............................................................................................. 37 LISTA DE FLUXOGRAMAS Fluxograma 1 - Funcionamento do algoritmo ............................................................ 26 SUMÁRIO 1. INTRODUÇÃO....................................................................................................................... 14 1.1 CONSIDERAÇÕES INICIAIS ........................................................................................ 14 1.2 JUSTIFICATIVA ............................................................................................................. 16 1.3 ESCOPO DO TRABALHO ............................................................................................. 16 1.4 ELABORAÇÃO DOS OBJETIVOS ................................................................................ 16 1.5 DEFINIÇÃO DA METODOLOGIA ............................................................................... 17 1.6 ESTRUTURA DO TRABALHO ..................................................................................... 18 2. PROEMINÊNCIA GEOGRÁFICA............................................................................................... 19 2.1 PROEMINÊNCIA GEOGRÁFICA.................................................................................. 19 2.1.1 ALTURA ABSOLUTA, ALTITUDE E PROEMINÊNCIA GEOGRÁFICA ................................................................ 19 2.1.2 CUME-PAI E SUBCUMES .................................................................................................................. 21 3. MODELAGEM E SOLUÇÃO DO PROBLEMA ............................................................................. 22 3.1 DEFINIÇÃO DO PROBLEMA DE PROEMINÊNCIA ................................................................... 22 3.2 FUNCIONAMENTO GERAL DO ALGORITMO ........................................................................ 25 3.2.1 FLUXOGRAMA DO FUNCIONAMENTO DO ALGORITMO ........................................................................... 25 3.2.2 DESCRIÇÃO DETALHADA DE CADA ETAPA ............................................................................................ 26 4. APLICAÇÃO DA ABORDAGEM EM MODELOS PROPOSTOS...................................................... 31 4.1 HISTOGRAMAS .................................................................................................................. 31 4.1.1 HISTOGRAMA DA RELAÇÃO ENTRE PESO E ALTURA DE UM GRUPO DE PESSOAS .......................................... 31 4.1.2 HISTOGRAMA DA RELAÇÃO DE NOTAS EM AVALIAÇÕES DE DUAS DISCIPLINAS ........................................... 37 4.1.3 OUTRAS VARIÁVEIS ........................................................................................................................ 40 4.2 TRANSFORMADA DE HOUGH .............................................................................................. 40 4.2.1 TRANSFORMADA DE HOUGH PARA IDENTIFICAÇÃO DE RETAS ................................................................
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