{"id":1110,"date":"2019-03-08T14:56:01","date_gmt":"2019-03-08T17:56:01","guid":{"rendered":"https:\/\/sbia.org.br\/lnlm\/?page_id=1110"},"modified":"2019-03-08T14:56:01","modified_gmt":"2019-03-08T17:56:01","slug":"vol16-no1-art3","status":"publish","type":"page","link":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/","title":{"rendered":"\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL"},"content":{"rendered":"<p><strong>T\u00edtulo:\u00a0<\/strong>\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL<\/p>\n<p><strong>Autores:<\/strong>\u00a0Emanuel D.R. Sena e Andr\u00e9 L.F. Almeida<\/p>\n<p align=\"justify\"><strong>Resumo:<\/strong> Nesse artigo de revis\u00e3o o problema de reconhecimento facial \u00e9 investigado do ponto de vista da \u00e1lgebra multilinear, mais especificamente por meio de decomposi\u00e7\u00f5es tensoriais fazendo uso das <em>wavelets<\/em> de Gabor. A extra\u00e7\u00e3o de caracter\u00edsticas ocorre em dois est\u00e1gios: primeiramente as <em>wavelets<\/em> de Gabor s\u00e3o aplicadas de maneira hol\u00edstica na sele\u00e7\u00e3o de caracter\u00edsticas; em segundo as imagens faciais s\u00e3o modeladas como um tensor de ordem superior de acordo com o fatores multimodais presentes. Com isso aplicamos a decomposi\u00e7\u00e3o tensorial <em>Higher Order Singular Value Decomposition<\/em> (HOSVD) para separar os fatores\u00a0que influenciam na forma\u00e7\u00e3o das imagens. O m\u00e9todo de reconhecimento facial proposto possui uma alta taxa de acerto e estabilidade\u00a0quando h\u00e1 varia\u00e7\u00e3o nos diversos fatores multimodais, tais como, posi\u00e7\u00e3o facial, condi\u00e7\u00e3o de ilumina\u00e7\u00e3o e express\u00e3o facial. Propomos ainda uma maneira sistem\u00e1tica para realiza\u00e7\u00e3o da valida\u00e7\u00e3o cruzada em modelos tensoriais para estima\u00e7\u00e3o da taxa de erro em sistemas de reconhecimento facial que exploram a natureza multilinear do conjunto de imagens. Atrav\u00e9s do particionamento aleat\u00f3rio dos dados organizado como um tensor, a valida\u00e7\u00e3o cruzada modo-n proporciona a cria\u00e7\u00e3o de <em>folds<\/em> extraindo subtensores no modo desejado, caracterizando um m\u00e9todo estratificado e suscept\u00edvel a repeti\u00e7\u00f5es da valida\u00e7\u00e3o cruzada\u00a0com diferentes particionamentos.<\/p>\n<p><strong>Palavras-chave:<\/strong> Reconhecimento Facial, <em>Wavelets<\/em> de Gabor, \u00c1lgebra Multilinear, Decomposi\u00e7\u00f5es Tensoriais, Valida\u00e7\u00e3o<br \/>\nCruzada.<\/p>\n<p><strong>P\u00e1ginas:<\/strong> 15<\/p>\n<p><strong>C\u00f3digo DOI:<\/strong> <a href=\"http:\/\/dx.doi.org\/10.21528\/LNLM-vol16-no1-art3\">10.21528\/LNLM-vol16-no1-art3<\/a><\/p>\n<p><strong>Artigo em PDF:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2019\/03\/vol16-no1-art3.pdf\">vol16-no1-art3.pdf<\/a><\/p>\n<p><strong>Arquivo BibTex:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2019\/03\/vol16-no1-art3.bib\">vol16-no1-art3.bib<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>T\u00edtulo:\u00a0\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL Autores:\u00a0Emanuel D.R. Sena e Andr\u00e9 L.F. Almeida Resumo: Nesse artigo de revis\u00e3o o problema de reconhecimento facial \u00e9 investigado do ponto de vista da \u00e1lgebra multilinear, mais especificamente por meio de decomposi\u00e7\u00f5es tensoriais fazendo <a href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1059,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1110","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL - Learning and NonLinear Models<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL - Learning and NonLinear Models\" \/>\n<meta property=\"og:description\" content=\"T\u00edtulo:\u00a0\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL Autores:\u00a0Emanuel D.R. Sena e Andr\u00e9 L.F. Almeida Resumo: Nesse artigo de revis\u00e3o o problema de reconhecimento facial \u00e9 investigado do ponto de vista da \u00e1lgebra multilinear, mais especificamente por meio de decomposi\u00e7\u00f5es tensoriais fazendo Read More ...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/\" \/>\n<meta property=\"og:site_name\" content=\"Learning and NonLinear Models\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/\",\"name\":\"\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL - Learning and NonLinear Models\",\"isPartOf\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#website\"},\"datePublished\":\"2019-03-08T17:56:01+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Browse issues\",\"item\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Learning &#038; Nonlinear Models &#8211; L&#038;NLM &#8211; Volume 16 &#8211; N\u00famero 1\",\"item\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#website\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/\",\"name\":\"Learning and NonLinear Models\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/sbia.org.br\/lnlm\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#organization\",\"name\":\"Learning and NonLinear Models\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png\",\"contentUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png\",\"width\":398,\"height\":94,\"caption\":\"Learning and NonLinear Models\"},\"image\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL - Learning and NonLinear Models","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/","og_locale":"pt_BR","og_type":"article","og_title":"\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL - Learning and NonLinear Models","og_description":"T\u00edtulo:\u00a0\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL Autores:\u00a0Emanuel D.R. Sena e Andr\u00e9 L.F. Almeida Resumo: Nesse artigo de revis\u00e3o o problema de reconhecimento facial \u00e9 investigado do ponto de vista da \u00e1lgebra multilinear, mais especificamente por meio de decomposi\u00e7\u00f5es tensoriais fazendo Read More ...","og_url":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/","og_site_name":"Learning and NonLinear Models","twitter_card":"summary_large_image","twitter_misc":{"Est. tempo de leitura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/","url":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/","name":"\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL - Learning and NonLinear Models","isPartOf":{"@id":"https:\/\/sbia.org.br\/lnlm\/#website"},"datePublished":"2019-03-08T17:56:01+00:00","breadcrumb":{"@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/vol16-no1-art3\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Browse issues","item":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/"},{"@type":"ListItem","position":2,"name":"Learning &#038; Nonlinear Models &#8211; L&#038;NLM &#8211; Volume 16 &#8211; N\u00famero 1","item":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol16-no1\/"},{"@type":"ListItem","position":3,"name":"\u00c1LGEBRA MULTILINEAR APLICADA AO RECONHECIMENTO FACIAL"}]},{"@type":"WebSite","@id":"https:\/\/sbia.org.br\/lnlm\/#website","url":"https:\/\/sbia.org.br\/lnlm\/","name":"Learning and NonLinear Models","description":"","publisher":{"@id":"https:\/\/sbia.org.br\/lnlm\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sbia.org.br\/lnlm\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"pt-BR"},{"@type":"Organization","@id":"https:\/\/sbia.org.br\/lnlm\/#organization","name":"Learning and NonLinear Models","url":"https:\/\/sbia.org.br\/lnlm\/","logo":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/","url":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png","contentUrl":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png","width":398,"height":94,"caption":"Learning and NonLinear Models"},"image":{"@id":"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/pages\/1110","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/comments?post=1110"}],"version-history":[{"count":0,"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/pages\/1110\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/pages\/1059"}],"wp:attachment":[{"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/media?parent=1110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}