{"id":166,"date":"2020-12-04T00:11:34","date_gmt":"2020-12-04T00:11:34","guid":{"rendered":"http:\/\/med-space.org\/youssef-zaz-master\/?page_id=166"},"modified":"2020-12-12T20:31:01","modified_gmt":"2020-12-12T20:31:01","slug":"produit-de-convolution-en-image","status":"publish","type":"page","link":"https:\/\/yzaz.net\/master\/produit-de-convolution-en-image\/","title":{"rendered":"Produit de convolution en image"},"content":{"rendered":"<p>La convolution est le processus consistant \u00e0 ajouter chaque \u00e9l\u00e9ment de l&#8217;image \u00e0 ses voisins imm\u00e9diats, pond\u00e9r\u00e9 par les \u00e9l\u00e9ments du noyau.<br \/>\nUn filtre de convolution (ou masque ou noyau) est g\u00e9n\u00e9ralement une matrice 2n + 1 2n + 1.<br \/>\nCalcul : somme de produits, on parle de filtre lin\u00e9aire<\/p>\n<div style=\"text-align: center; border: 2px solid #1c75c8; padding: 3px; background-color: #c5ddf6;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\nR( x,y) =\\sum ^{u=n}_{u=-n}\\sum ^{v=n}_{v=-n} I( x+u,y+v) .K( u+n,v+n)\n\n<\/span><\/div>\n<p>Pour \u00e9viter de modifier la luminance de l\u2019image, la somme des coefficients du filtre doit \u00eatre \u00e9gale \u00e0 1.<\/p>\n<p>Etapes:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-434 size-full\" src=\"http:\/\/med-space.org\/youssef-zaz-master\/wp-content\/uploads\/2020\/12\/conv1.jpg\" alt=\"\" width=\"623\" height=\"349\" srcset=\"https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv1.jpg 623w, https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv1-300x168.jpg 300w\" sizes=\"(max-width: 623px) 100vw, 623px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-435 size-full\" src=\"http:\/\/med-space.org\/youssef-zaz-master\/wp-content\/uploads\/2020\/12\/conv2.jpg\" alt=\"\" width=\"755\" height=\"415\" srcset=\"https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv2.jpg 755w, https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv2-300x165.jpg 300w\" sizes=\"(max-width: 755px) 100vw, 755px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-436 size-full\" src=\"http:\/\/med-space.org\/youssef-zaz-master\/wp-content\/uploads\/2020\/12\/conv3.jpg\" alt=\"\" width=\"755\" height=\"416\" srcset=\"https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv3.jpg 755w, https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv3-300x165.jpg 300w\" sizes=\"(max-width: 755px) 100vw, 755px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-437 size-full\" src=\"http:\/\/med-space.org\/youssef-zaz-master\/wp-content\/uploads\/2020\/12\/conv4.jpg\" alt=\"\" width=\"755\" height=\"416\" srcset=\"https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv4.jpg 755w, https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv4-300x165.jpg 300w\" sizes=\"(max-width: 755px) 100vw, 755px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-438 size-full\" src=\"http:\/\/med-space.org\/youssef-zaz-master\/wp-content\/uploads\/2020\/12\/conv5.jpg\" alt=\"\" width=\"755\" height=\"416\" srcset=\"https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv5.jpg 755w, https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv5-300x165.jpg 300w\" sizes=\"(max-width: 755px) 100vw, 755px\" \/><\/p>\n<p><strong>Calcul sur les bords de l\u2019image<\/strong><br \/>\nPlusieurs possibilit\u00e9s sont envisageables :<br \/>\n\u2022 Mettre \u00e0 z\u00e9ro<br \/>\n\u2022 Convolution partielle utilisant une portion du filtre<br \/>\n\u2022 Compl\u00e9ter les valeurs manquantes en construisant le miroir de l\u2019image<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-439 size-full\" src=\"http:\/\/med-space.org\/youssef-zaz-master\/wp-content\/uploads\/2020\/12\/conv6.jpg\" alt=\"\" width=\"330\" height=\"299\" srcset=\"https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv6.jpg 330w, https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv6-300x272.jpg 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><\/p>\n<p>Exercice :<br \/>\nCalculer le produit de convolution de l\u2019image ci-dessous avec le noyau.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-440 size-full\" src=\"http:\/\/med-space.org\/youssef-zaz-master\/wp-content\/uploads\/2020\/12\/conv7.jpg\" alt=\"\" width=\"564\" height=\"301\" srcset=\"https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv7.jpg 564w, https:\/\/yzaz.net\/master\/wp-content\/uploads\/2020\/12\/conv7-300x160.jpg 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>La convolution dans le traitement d\u2019images :<\/strong><\/p>\n<ul>\n<li>Filtrage lin\u00e9aire des bruits<\/li>\n<li>D\u00e9tection de contours<\/li>\n<li>Rehaussement de contraste<\/li>\n<\/ul>\n<p>On distingue deux familles de filtres:<\/p>\n<ul>\n<li>Filtre passe\u2010bas : att\u00e9nue le bruit et les d\u00e9tails<\/li>\n<li>Filtre passe\u2010haut : accentue les d\u00e9tails et les contours<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<div class=\"mh-excerpt\"><p>La convolution est le processus consistant \u00e0 ajouter chaque \u00e9l\u00e9ment de l&#8217;image \u00e0 ses voisins imm\u00e9diats, pond\u00e9r\u00e9 par les \u00e9l\u00e9ments du noyau. Un filtre de <a class=\"mh-excerpt-more\" href=\"https:\/\/yzaz.net\/master\/produit-de-convolution-en-image\/\" title=\"Produit de convolution en image\">[&#8230;]<\/a><\/p>\n<\/div>","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":45,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"_links":{"self":[{"href":"https:\/\/yzaz.net\/master\/wp-json\/wp\/v2\/pages\/166"}],"collection":[{"href":"https:\/\/yzaz.net\/master\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/yzaz.net\/master\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/yzaz.net\/master\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/yzaz.net\/master\/wp-json\/wp\/v2\/comments?post=166"}],"version-history":[{"count":7,"href":"https:\/\/yzaz.net\/master\/wp-json\/wp\/v2\/pages\/166\/revisions"}],"predecessor-version":[{"id":443,"href":"https:\/\/yzaz.net\/master\/wp-json\/wp\/v2\/pages\/166\/revisions\/443"}],"wp:attachment":[{"href":"https:\/\/yzaz.net\/master\/wp-json\/wp\/v2\/media?parent=166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}