{"id":33587,"date":"2023-02-10T12:29:58","date_gmt":"2023-02-10T06:59:58","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-pyramidal-histogram-of-oriented-gradients-trilinear-interpolation\/"},"modified":"2023-02-10T12:29:58","modified_gmt":"2023-02-10T06:59:58","slug":"solved-pyramidal-histogram-of-oriented-gradients-trilinear-interpolation","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-pyramidal-histogram-of-oriented-gradients-trilinear-interpolation\/","title":{"rendered":"[Solved] Pyramidal Histogram Of Oriented Gradients &#8211; Trilinear interpolation"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-35957742\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"35957742\" data-parentid=\"35761354\" data-score=\"2\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>Short answer is: you can&#8217;t apply Trilinear Inerpolation.<\/p>\n<p>Let&#8217;s start with 2x2x2 blocks. Each block, is represented by it&#8217;s centre pixel ( 1,2,3,4 in ugly yellow on my sketch). Each pixel is located at the corner of a cell.<\/p>\n<p>A pixel (the red dot), will be shared by up to 4 blocks that overlap. <\/p>\n<p><a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/jassweb.com\/solved\/wp-content\/uploads\/2023\/02\/Solved-Pyramidal-Histogram-Of-Oriented-Gradients-Trilinear-interpolation.png\"><img decoding=\"async\" src=\"https:\/\/jassweb.com\/solved\/wp-content\/uploads\/2023\/02\/Solved-Pyramidal-Histogram-Of-Oriented-Gradients-Trilinear-interpolation.png\" alt=\"enter image description here\"><\/a><\/p>\n<p>With 3x3x2 block each block centre pixel will be also a cell centre pixel. And each cell pixel will be shared with up to 9 blocks.<\/p>\n<p><a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/jassweb.com\/solved\/wp-content\/uploads\/2023\/02\/1676012398_149_Solved-Pyramidal-Histogram-Of-Oriented-Gradients-Trilinear-interpolation.png\"><img decoding=\"async\" src=\"https:\/\/jassweb.com\/solved\/wp-content\/uploads\/2023\/02\/1676012398_149_Solved-Pyramidal-Histogram-Of-Oriented-Gradients-Trilinear-interpolation.png\" alt=\"enter image description here\"><\/a><\/p>\n<p>You can&#8217;t use Trilinear interpolation. multilinear interpolations require 2^D samples. So you&#8217;ll need to choose a different way to assign the weights.<\/p>\n<p>Remember that we&#8217;re not interested in interpolating values, but using the interpolation coefficients as weights. <\/p>\n<p>Some options that you may use (haven&#8217;t tested them).<\/p>\n<ul>\n<li>\n<p><a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Inverse_distance_weighting\">Inverse distance weighting:<\/a> (trivial and easy, but I remember Euclidean norms didn&#8217;t work work well with images, still give it a chance)<\/p>\n<\/li>\n<li>\n<p>Go 4x4x2 and use bicubic interpolation + linear for the 3rd dimension. <\/p>\n<\/li>\n<li>\n<p>Check if it&#8217;s possible to obtain weight out of Lagrange or cubic spline polynomials.<\/p>\n<\/li>\n<li>\n<p>Use QR decomposition to find a linear solution for the overfitted problem.<\/p>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\">2<\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved Pyramidal Histogram Of Oriented Gradients &#8211; Trilinear interpolation <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] Short answer is: you can&#8217;t apply Trilinear Inerpolation. Let&#8217;s start with 2x2x2 blocks. Each block, is represented by it&#8217;s centre pixel ( 1,2,3,4 in ugly yellow on my sketch). Each pixel is located at the corner of a cell. A pixel (the red dot), will be shared by up to 4 blocks that overlap. &#8230; <a title=\"[Solved] Pyramidal Histogram Of Oriented Gradients &#8211; Trilinear interpolation\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-pyramidal-histogram-of-oriented-gradients-trilinear-interpolation\/\" aria-label=\"More on [Solved] Pyramidal Histogram Of Oriented Gradients &#8211; Trilinear interpolation\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[2253,1823,881,516,349],"class_list":["post-33587","post","type-post","status-publish","format-standard","hentry","category-solved","tag-computer-vision","tag-histogram","tag-image-processing","tag-matlab","tag-python"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] Pyramidal Histogram Of Oriented Gradients - Trilinear interpolation - JassWeb<\/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:\/\/jassweb.com\/solved\/solved-pyramidal-histogram-of-oriented-gradients-trilinear-interpolation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] Pyramidal Histogram Of Oriented Gradients - Trilinear interpolation - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] Short answer is: you can&#8217;t apply Trilinear Inerpolation. Let&#8217;s start with 2x2x2 blocks. Each block, is represented by it&#8217;s centre pixel ( 1,2,3,4 in ugly yellow on my sketch). Each pixel is located at the corner of a cell. A pixel (the red dot), will be shared by up to 4 blocks that overlap. ... 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Let&#8217;s start with 2x2x2 blocks. Each block, is represented by it&#8217;s centre pixel ( 1,2,3,4 in ugly yellow on my sketch). Each pixel is located at the corner of a cell. A pixel (the red dot), will be shared by up to 4 blocks that overlap. ... 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