Projection Matrix | LearnOpenCV

Geometry of Image Formation

February 20, 2020 8 Comments 10 min read

Camera Calibration Structure From Motion

February 20, 2020 By 8 Comments

In this post, we will explain the image formation from a geometrical point of view. Specifically, we will cover the math behind how a point in 3D gets projected on the image plane. This post ...

img:is([sizes="auto" i],[sizes^="auto," i]){contain-intrinsic-size:3000px 1500px;}.lazyload,.lazyloading{max-width:100%;}img.wp-smiley,img.emoji{display:inline !important;border:none !important;box-shadow:none !important;height:1em !important;width:1em !important;margin:0 .07em !important;vertical-align:-.1em !important;background:none !important;padding:0 !important;}.wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em;}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none;}.wp-block-boldblocks-youtube-block .visually-hidden{clip:rect(0 0 0 0);-webkit-clip-path:inset(50%);clip-path:inset(50%);height:1px;overflow:hidden;position:absolute;white-space:nowrap;width:1px;}.wp-block-boldblocks-youtube-block .yb-player{background-color:#000;background-position:50%;background-size:cover;contain:content;cursor:pointer;display:block;position:relative;}.wp-block-boldblocks-youtube-block .yb-player:after{content:"";display:block;padding-bottom:var(--byeb--aspect-ratio,56.25%);}.wp-block-boldblocks-youtube-block .yb-player>iframe{border:0;height:100%;left:0;position:absolute;top:0;width:100%;z-index:1;}.wp-block-boldblocks-youtube-block .yb-player.is-activated{cursor:unset;}.wp-block-boldblocks-youtube-block .yb-player.is-activated>.yb-btn-play{display:none;opacity:0;pointer-events:none;}.wp-block-boldblocks-youtube-block .yb-btn-play{all:unset;background-color:transparent;background-image:url("data:image/svg+xml;utf8,<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 68 48\"><path d=\"M66.52 7.74c-.78-2.93-2.49-5.41-5.42-6.19C55.79.13 34 0 34 0S12.21.13 6.9 1.55c-2.93.78-4.63 3.26-5.42 6.19C.06 13.05 0 24 0 24s.06 10.95 1.48 16.26c.78 2.93 2.49 5.41 5.42 6.19C12.21 47.87 34 48 34 48s21.79-.13 27.1-1.55c2.93-.78 4.64-3.26 5.42-6.19C67.94 34.95 68 24 68 24s-.06-10.95-1.48-16.26z\" fill=\"red\"/><path d=\"M45 24 27 14v20\" fill=\"white\"/></svg>");border:none;cursor:pointer;display:block;filter:grayscale(100%);height:48px;left:50%;margin:0;position:absolute;top:50%;transform:translate3d(-50%,-50%,0);transition:filter .1s cubic-bezier(0,0,.2,1);width:68px;z-index:1;}.wp-block-boldblocks-youtube-block .yb-btn-play.nitro-lazy{background-image:none !important;}.wp-block-boldblocks-youtube-block .yb-btn-play:focus,.wp-block-boldblocks-youtube-block .yb-player:hover>.yb-btn-play{filter:none;}.wp-block-boldblocks-youtube-block figcaption{margin-bottom:1em;margin-top:.5em;}.wp-block-co-authors-plus-coauthors.is-layout-flow [class*=wp-block-co-authors-plus]{display:inline;}.wp-block-co-authors-plus-avatar :where(img){height:auto;max-width:100%;vertical-align:bottom;}.wp-block-co-authors-plus-coauthors.is-layout-flow .wp-block-co-authors-plus-avatar :where(img){vertical-align:middle;}.wp-block-co-authors-plus-avatar:is(.alignleft,.alignright){display:table;}.wp-block-co-authors-plus-avatar.aligncenter{display:table;margin-inline:auto;}.wp-block-co-authors-plus-image{margin-bottom:0;}.wp-block-co-authors-plus-image :where(img){height:auto;max-width:100%;vertical-align:bottom;}.wp-block-co-authors-plus-coauthors.is-layout-flow .wp-block-co-authors-plus-image :where(img){vertical-align:middle;}.wp-block-co-authors-plus-image:is(.alignfull,.alignwide) :where(img){width:100%;}.wp-block-co-authors-plus-image:is(.alignleft,.alignright){display:table;}.wp-block-co-authors-plus-image.aligncenter{display:table;margin-inline:auto;}.dashicons{font-family:dashicons !important;}.wp-block-vpb-video *{box-sizing:border-box;}.wp-block-vpb-video .vpbVideoPlayer{margin:0 auto;max-width:100%;overflow:hidden;}.wp-block-vpb-video .vpbVideoPlayer .videoWrapper button{color:#fff !important;}.wp-block-vpb-video .vpbVideoPlayer .plyr input[type=range]::-webkit-slider-runnable-track{box-shadow:none;}.wp-block-vpb-video .vpbVideoPlayer .plyr input[type=range]::-moz-range-track{box-shadow:none;}.wp-block-vpb-video .vpbVideoPlayer .plyr input[type=range]::-ms-track{box-shadow:none;}:root{--wp--preset--aspect-ratio--square:1;--wp--preset--aspect-ratio--4-3:4/3;--wp--preset--aspect-ratio--3-4:3/4;--wp--preset--aspect-ratio--3-2:3/2;--wp--preset--aspect-ratio--2-3:2/3;--wp--preset--aspect-ratio--16-9:16/9;--wp--preset--aspect-ratio--9-16:9/16;--wp--preset--color--black:#000;--wp--preset--color--cyan-bluish-gray:#abb8c3;--wp--preset--color--white:#fff;--wp--preset--color--pale-pink:#f78da7;--wp--preset--color--vivid-red:#cf2e2e;--wp--preset--color--luminous-vivid-orange:#ff6900;--wp--preset--color--luminous-vivid-amber:#fcb900;--wp--preset--color--light-green-cyan:#7bdcb5;--wp--preset--color--vivid-green-cyan:#00d084;--wp--preset--color--pale-cyan-blue:#8ed1fc;--wp--preset--color--vivid-cyan-blue:#0693e3;--wp--preset--color--vivid-purple:#9b51e0;--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple:linear-gradient(135deg,rgba(6,147,227,1) 0%,#9b51e0 100%);--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan:linear-gradient(135deg,#7adcb4 0%,#00d082 100%);--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange:linear-gradient(135deg,rgba(252,185,0,1) 0%,rgba(255,105,0,1) 100%);--wp--preset--gradient--luminous-vivid-orange-to-vivid-red:linear-gradient(135deg,rgba(255,105,0,1) 0%,#cf2e2e 100%);--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray:linear-gradient(135deg,#eee 0%,#a9b8c3 100%);--wp--preset--gradient--cool-to-warm-spectrum:linear-gradient(135deg,#4aeadc 0%,#9778d1 20%,#cf2aba 40%,#ee2c82 60%,#fb6962 80%,#fef84c 100%);--wp--preset--gradient--blush-light-purple:linear-gradient(135deg,#ffceec 0%,#9896f0 100%);--wp--preset--gradient--blush-bordeaux:linear-gradient(135deg,#fecda5 0%,#fe2d2d 50%,#6b003e 100%);--wp--preset--gradient--luminous-dusk:linear-gradient(135deg,#ffcb70 0%,#c751c0 50%,#4158d0 100%);--wp--preset--gradient--pale-ocean:linear-gradient(135deg,#fff5cb 0%,#b6e3d4 50%,#33a7b5 100%);--wp--preset--gradient--electric-grass:linear-gradient(135deg,#caf880 0%,#71ce7e 100%);--wp--preset--gradient--midnight:linear-gradient(135deg,#020381 0%,#2874fc 100%);--wp--preset--font-size--small:13px;--wp--preset--font-size--medium:20px;--wp--preset--font-size--large:36px;--wp--preset--font-size--x-large:42px;--wp--preset--spacing--20:.44rem;--wp--preset--spacing--30:.67rem;--wp--preset--spacing--40:1rem;--wp--preset--spacing--50:1.5rem;--wp--preset--spacing--60:2.25rem;--wp--preset--spacing--70:3.38rem;--wp--preset--spacing--80:5.06rem;--wp--preset--shadow--natural:6px 6px 9px rgba(0,0,0,.2);--wp--preset--shadow--deep:12px 12px 50px rgba(0,0,0,.4);--wp--preset--shadow--sharp:6px 6px 0px rgba(0,0,0,.2);--wp--preset--shadow--outlined:6px 6px 0px -3px rgba(255,255,255,1),6px 6px rgba(0,0,0,1);--wp--preset--shadow--crisp:6px 6px 0px rgba(0,0,0,1);}:where(.is-layout-flex){gap:.5em;}:where(.is-layout-grid){gap:.5em;}body .is-layout-flex{display:flex;}.is-layout-flex{flex-wrap:wrap;align-items:center;}.is-layout-flex > :is(*,div){margin:0;}body .is-layout-grid{display:grid;}.is-layout-grid > :is(*,div){margin:0;}:where(.wp-block-columns.is-layout-flex){gap:2em;}:where(.wp-block-columns.is-layout-grid){gap:2em;}:where(.wp-block-post-template.is-layout-flex){gap:1.25em;}:where(.wp-block-post-template.is-layout-grid){gap:1.25em;}.has-black-color{color:var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-color{color:var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-color{color:var(--wp--preset--color--white) !important;}.has-pale-pink-color{color:var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-color{color:var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-color{color:var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-color{color:var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-color{color:var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-color{color:var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-color{color:var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-color{color:var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-color{color:var(--wp--preset--color--vivid-purple) !important;}.has-black-background-color{background-color:var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-background-color{background-color:var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-background-color{background-color:var(--wp--preset--color--white) !important;}.has-pale-pink-background-color{background-color:var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-background-color{background-color:var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-background-color{background-color:var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-background-color{background-color:var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-background-color{background-color:var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-background-color{background-color:var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-background-color{background-color:var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-background-color{background-color:var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-background-color{background-color:var(--wp--preset--color--vivid-purple) !important;}.has-black-border-color{border-color:var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-border-color{border-color:var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-border-color{border-color:var(--wp--preset--color--white) !important;}.has-pale-pink-border-color{border-color:var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-border-color{border-color:var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-border-color{border-color:var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-border-color{border-color:var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-border-color{border-color:var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-border-color{border-color:var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-border-color{border-color:var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-border-color{border-color:var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-border-color{border-color:var(--wp--preset--color--vivid-purple) !important;}.has-vivid-cyan-blue-to-vivid-purple-gradient-background{background:var(--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple) !important;}.has-light-green-cyan-to-vivid-green-cyan-gradient-background{background:var(--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan) !important;}.has-luminous-vivid-amber-to-luminous-vivid-orange-gradient-background{background:var(--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange) !important;}.has-luminous-vivid-orange-to-vivid-red-gradient-background{background:var(--wp--preset--gradient--luminous-vivid-orange-to-vivid-red) !important;}.has-very-light-gray-to-cyan-bluish-gray-gradient-background{background:var(--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray) !important;}.has-cool-to-warm-spectrum-gradient-background{background:var(--wp--preset--gradient--cool-to-warm-spectrum) !important;}.has-blush-light-purple-gradient-background{background:var(--wp--preset--gradient--blush-light-purple) !important;}.has-blush-bordeaux-gradient-background{background:var(--wp--preset--gradient--blush-bordeaux) !important;}.has-luminous-dusk-gradient-background{background:var(--wp--preset--gradient--luminous-dusk) !important;}.has-pale-ocean-gradient-background{background:var(--wp--preset--gradient--pale-ocean) !important;}.has-electric-grass-gradient-background{background:var(--wp--preset--gradient--electric-grass) !important;}.has-midnight-gradient-background{background:var(--wp--preset--gradient--midnight) !important;}.has-small-font-size{font-size:var(--wp--preset--font-size--small) !important;}.has-medium-font-size{font-size:var(--wp--preset--font-size--medium) !important;}.has-large-font-size{font-size:var(--wp--preset--font-size--large) !important;}.has-x-large-font-size{font-size:var(--wp--preset--font-size--x-large) !important;}:where(.wp-block-post-template.is-layout-flex){gap:1.25em;}:where(.wp-block-post-template.is-layout-grid){gap:1.25em;}:where(.wp-block-columns.is-layout-flex){gap:2em;}:where(.wp-block-columns.is-layout-grid){gap:2em;}:root :where(.wp-block-pullquote){font-size:1.5em;line-height:1.6;}.no-js img.lazyload{display:none;}figure.wp-block-image img.lazyloading{min-width:150px;}.lazyload,.lazyloading{--smush-placeholder-width:100px;--smush-placeholder-aspect-ratio:1/1;width:var(--smush-image-width,var(--smush-placeholder-width)) !important;aspect-ratio:var(--smush-image-aspect-ratio,var(--smush-placeholder-aspect-ratio)) !important;}.lazyload,.lazyloading{opacity:0;}.lazyloaded{opacity:1;transition:opacity 400ms;transition-delay:0ms;}.homepage_comments_data .read-time{color:#303236;font-size:12px;}.homepage_comments_data .read-time::before{content:"—";margin:0 6px 0 2px;}.homepage_comments_data{display:flex;justify-content:space-between;align-items:center;font-size:12px;color:#303236;padding-bottom:8px;width:100%;flex-wrap:nowrap;}.homepage_comments_data .left-meta{display:flex;flex-wrap:wrap;align-items:center;gap:10px;flex:1 1 auto;min-width:0;}.homepage_comments_data .left-meta .read-time::before,.homepage_comments_data .left-meta .comments::before{content:"—";margin:0 6px;}.homepage_comments_data .right-meta{position:relative;display:none;align-items:center;flex-shrink:0;margin-left:10px;}.homepage_comments_data .right-meta .share-toggle{display:none;background:none;border:none;font-size:18px;color:#303236;cursor:pointer;}.homepage_comments_data .right-meta .share-icons-wrapper{display:none;align-items:center;gap:10px;}.post figure{margin:1em 0px !important;}.single-post .homepage_comments_data .right-meta{display:flex;}.single-post .homepage_comments_data .right-meta .share-icons-wrapper{display:flex;}.single-post .elementor-share-btn__icon i{margin:0px !important;}@media screen and (max-width: 600px){.single-post .homepage_comments_data .right-meta .share-icons-wrapper{display:none;}.homepage_comments_data .left-meta{max-width:90%;}.homepage_comments_data .right-meta{max-width:10%;}.homepage_comments_data .left-meta{font-size:10px;}.homepage_comments_data .read-time{font-size:10px;}.homepage_comments_data{flex-wrap:nowrap;}.homepage_comments_data .right-meta{flex-direction:column;align-items:flex-end;}.homepage_comments_data .right-meta .share-toggle{display:inline-block;}.homepage_comments_data .right-meta .share-icons-wrapper{display:none;position:absolute;top:100%;right:0;background:#fff;padding:10px;border:1px solid #ccc;box-shadow:0 4px 8px rgba(0,0,0,.1);z-index:99;flex-direction:row;flex-wrap:wrap;}.homepage_comments_data .right-meta.active .share-icons-wrapper{display:flex;}}@media only screen and (max-width: 800px){#menu-top-bar{display:none;}}.e-con.e-parent:nth-of-type(n+4):not(.e-lazyloaded):not(.e-no-lazyload),.e-con.e-parent:nth-of-type(n+4):not(.e-lazyloaded):not(.e-no-lazyload) *{background-image:none !important;}@media screen and (max-height: 1024px){.e-con.e-parent:nth-of-type(n+3):not(.e-lazyloaded):not(.e-no-lazyload),.e-con.e-parent:nth-of-type(n+3):not(.e-lazyloaded):not(.e-no-lazyload) *{background-image:none !important;}.e-con.e-parent:nth-of-type(n+3):not(.e-lazyloaded):not(.e-no-lazyload).nitro-lazy,.e-con.e-parent:nth-of-type(n+3):not(.e-lazyloaded):not(.e-no-lazyload) *.nitro-lazy{background-image:none !important;}}@media screen and (max-height: 640px){.e-con.e-parent:nth-of-type(n+2):not(.e-lazyloaded):not(.e-no-lazyload),.e-con.e-parent:nth-of-type(n+2):not(.e-lazyloaded):not(.e-no-lazyload) *{background-image:none !important;}.e-con.e-parent:nth-of-type(n+2):not(.e-lazyloaded):not(.e-no-lazyload).nitro-lazy,.e-con.e-parent:nth-of-type(n+2):not(.e-lazyloaded):not(.e-no-lazyload) *.nitro-lazy{background-image:none !important;}}.e-con.e-parent:nth-of-type(n+4):not(.e-lazyloaded):not(.e-no-lazyload).nitro-lazy,.e-con.e-parent:nth-of-type(n+4):not(.e-lazyloaded):not(.e-no-lazyload) *.nitro-lazy{background-image:none !important;}.single.single-post.postid-75054 figure{margin-left:0;margin-right:0;text-align:center !important;}.wp-block-image .aligncenter{margin-left:auto !important;margin-right:auto !important;}@media only screen and (min-width: 1024px){body .elementor-28323 .elementor-element.elementor-element-73d97576 .elementskit-menu-container{background-color:inherit !important;}}#ez-toc-sticky-container a{color:#000;font-size:14px;}.subscribe-box{display:inline-block;background-color:#f5f5f5;padding:5rem;box-shadow:0px 1px 3px rgba(0,0,0,.15);border:none;border:none !important;font-size:1.8rem;font-family:Poppins;background-image:none !important;border-radius:15px;font-weight:400;}.subscribe-box.nitro-lazy{background-image:none !important;}.home #toppromobar{display:none !important;}.ez-toc-sticky-fixed .ez-toc-sidebar,.ez-toc-sticky-fixed .ez-toc-sidebar .ez-toc-sticky-title-container{background:rgba(255,255,255,0);box-shadow:none;}.ez-toc-sticky-fixed{margin-top:100px;}.ez-toc-sticky-grey.show + a{display:none;}#ez-toc-sticky-container a:visited{color:#3389ff !important;}#ez-toc-container.ez-toc-transparent{background:none;display:none;}.ez-toc-sticky-fixed.show{background:#fff;}html{scroll-behavior:smooth;}body.single.single-post .site-container{margin-top:0 !important;}.elementor-field-type-recaptcha_v3.elementor-field-group-field_8b488fd{display:none !important;}.single.single-post .site-inner{margin-top:100px !important;}header.site-header{display:none;}.audio-podcast{background:#f4f6fa;padding:15px 30px;border-radius:15px;text-align:center;box-shadow:0px 1px 3px rgba(0,0,0,.15);}.audio-podcast:before{font-size:1.7rem;font-family:Poppins;content:"🎤︎ Prefer listening? Check out the “PODCAST” version of this article.";color:#006cff;text-align:center;width:100%;margin-bottom:15px;display:inline-block;font-weight:500;}.audio-podcast audio{border-radius:5px;}audio::-webkit-media-controls-panel{background-color:#138dff;}.elementskit-submenu-panel > li > a sup{font-weight:600;}.dialog-close-button{top:15px !important;right:15px !important;}.wp-block-list{word-wrap:wrap;}.search.search-results{}#genesis-sidebar-primary img{border-radius:5px;box-shadow:0px 1px 3px rgba(0,0,0,.15);}.download-code a{margin-top:15px;border-radius:10px;padding:14px 35px;}.download-code{border-color:none;background-color:#f5f5f5;padding:41px 50px 41px 100px !important;box-shadow:0px 1px 3px rgba(0,0,0,.15);border:none;font-size:2rem;font-family:Poppins;background-image:none !important;border-radius:15px;}.download-code.nitro-lazy{background-image:none !important;}.download-code:before{content:"";display:block;background-image:url("https://cdn-ilclanb.nitrocdn.com/IekjQeaQhaYynZsBcscOhxvktwdZlYmf/assets/images/optimized/rev-84d680d/learnopencv.com/wp-content/uploads/2024/12/programing-language1.png");width:8rem;height:10rem;background-size:100%;background-repeat:no-repeat;position:absolute;left:15px;}.t-consentPrompt{display:none !important;}.sale-section h2{}.elementor-divider__text a{background:#d48b35;background:linear-gradient(90deg,rgba(212,139,53,1) 0%,rgba(243,217,127,1) 34%,rgba(219,158,71,1) 66%,rgba(243,216,126,1) 100%) !important;background-clip:text !important;color:transparent !important;}.elementor-divider__text{border:1px solid #f3d97f;padding:.8rem 1.5rem;border-radius:5px;}.elementor-widget-divider .elementor-divider__element{margin:0 3rem;}body .elementor-37961 .elementor-element.elementor-element-2565d6f > .elementor-widget-container{margin:0 !important;}#custom_html-17 .swiper-pagination{text-align:left;}#CybotCookiebotDialog{display:none !important;}.is-type-video .wp-block-embed__wrapper{padding-top:56.25%;}h1.entry-title{display:initial;}body article.format-standard .rll-youtube-player{padding:0 !important;position:absolute !important;top:0;left:0;width:100%;height:100%;}#genesis-sidebar-primary .swiper-slide-contents > div{position:absolute;bottom:-45px;left:0;right:0;}#client .swiper-slide-inner{background:rgba(0,0,0,0) !important;padding:0px !important;}#menu-item-16744>a,#menu-item-16744>a i{color:#006cff !important;}#genesis-sidebar-primary .swiper-slide{margin-bottom:50px !important;overflow:visible !important;}#genesis-sidebar-primary .swiper-slide .elementor-button{border-radius:0 !important;}#genesis-sidebar-primary .swiper-container{overflow-y:visible !important;}.wp-block-embed-embed-handler.wp-embed-aspect-16-9.wp-has-aspect-ratio .wp-block-embed__wrapper{-webkit-padding-before:0 !important;}.post-tags a{line-height:2.2;}.toc-gutenberg ul{margin-left:0 !important;}.postid-4102 .is-type-video .wp-block-embed__wrapper{padding-top:0;}.wpc-posts-found p{text-align:center;margin-bottom:5px;}.wpc-filter-title{border-bottom:1px solid;padding-bottom:10px;margin-bottom:10px;font-weight:500;}.wpc-filter-chip-name{font-family:Poppins;font-size:12px;font-weight:500;}.wpc-filters-main-wrap li.wpc-term-item label{margin-top:5px;}.wpc-posts-found p,.wpc-filters-main-wrap li.wpc-term-item a{font-size:14px;font-family:Poppins;font-weight:500;}.wpc-term-count{color:#006cff;opacity:1;font-size:12px;font-weight:500;line-height:19px;margin-left:0;}.wpc-search-field{border-radius:10px;background:rgba(230,230,230,.07);padding:10px;padding-left:30px;font-size:16px;font-family:Poppins;font-weight:500;}.wpc-filters-section{background:#f4f6fa;padding:20px 15px;border-radius:15px;}.wpc-search-icon{}.post-categories,.post-tags{font-size:14px;}#text-14{display:none;}.elementskit-menu-hamburger{border:none !important;}#genesis-sidebar-primary .sidebar-tag .ekit-wid-con .elementskit-section-title-wraper.text_left{line-height:18px !important;}.single.single-post #text-14{display:inherit !important;}.elementor-pagination{text-align:center;font-family:Poppins;font-weight:500;}.sidebar-tag .entry{margin-bottom:0;}#genesis-sidebar-primary .sidebar-tag li a:hover{color:#fff !important;}.sidebar-tag .elementkit-nav-item{border:none !important;}.elementskit-submenu-panel > li > a sup{color:red;}.ekit-menu-dropdown-toggle > sup{color:red;padding:0;bottom:0;top:10px;position:absolute;}.elementskit-navbar-nav .elementskit-submenu-panel{min-width:300px !important;font-weight:500;font-family:Poppins !important;}.widget.widget_wpt .widget-wrap{border-radius:15px;background:#f4f6fa;padding:20px 15px;}.wpt_widget_content ul{margin-bottom:3px;}.wpt-loading:before{background-color:rgba(255,255,255,.3) !important;border-radius:15px !important;}body .wpt_widget_content .tab_title a{color:#fff;background:#0a0a0a !important;}.wpt_widget_content{border:none !important;}.wpt_widget_content ul{text-align:center;}.wpt_widget_content .tab-content li{list-style-type:none;float:left;width:100%;width:100%;-moz-box-sizing:border-box;box-sizing:border-box;margin:0 0 11px 0;margin:10px 0 0 0;padding:0px 15px 5px 15px;padding:10px !important;border-bottom:none;text-align:left;color:#444;background:#fff !important;background:#fff;position:relative;border-radius:10px;box-shadow:0 0px 8px rgba(0,0,0,.1);}.wpt_widget_content .inside{background:rgba(0,0,0,0) !important;padding-top:0;}.wpt_widget_content ul.wpt-tabs li{list-style:none;display:inline-block !important;width:auto !important;float:inherit !important;text-align:center;padding:10px 20px !important;padding:0 !important;margin:0 15px !important;min-width:120px !important;border:none !important;}body .wpt_widget_content .tab_title a{margin-left:0;border-left:0;color:#fff;background:#0a0a0a !important;background:none !important;border-bottom:none !important;font-weight:500 !important;font-family:Poppins !important;border-radius:15px !important;font-size:15px;min-width:120px !important;line-height:30px !important;padding-top:0 !important;}.wpt_thumb_small{border-radius:5px;}body .wpt_widget_content .tab_title a{background:#1e1e1e !important;margin:0 !important;padding:0 !important;}.wpt_widget_content .tab_title.selected a,.wpt_widget_content .tab_title a{border:none !important;}.wpt_widget_content .wp-post-image{border-radius:5px !important;}.breadcrumb{background:#f7f7f7;color:#006cff !important;padding:10px 15px;font-size:13px;font-family:Poppins;font-weight:500;position:absolute;top:-65px;left:0;right:0;border-radius:15px;}.wpt_widget_content .wpt-pagination{padding-bottom:5px;}.wpt_widget_content .wpt-pagination{padding-bottom:0px !important;padding-top:10px !important;}#genesis-sidebar-primary .inside li a:hover{color:#1c1c1d !important;text-decoration:underline;}#genesis-sidebar-primary .wpt-tabs li a:hover{color:#fff !important;background:#006cff !important;}.wpt_widget_content .wpt-postmeta,.wpt_comment_content,.wpt_excerpt,.wpt-pagination a{color:#006cff !important;font-size:12px !important;font-family:Poppins;font-weight:500;}.wpt_widget_content .entry-title{font-size:13px;}.breadcrumb a{color:#1c1c1d;opacity:.9;}.breadcrumb a:hover{text-decoration:underline;}.single.single-post .site-container{margin-top:50px !important;}#cookie-revoke-hidden{display:none;}.scrolled-class a{cursor:pointer;}.download-code-bar{display:none;animation:fadeIn 1s;}.download-code-bar.scrolled-class{position:fixed;top:0;left:0;right:0;width:100%;z-index:9999;animation:fadeIn 1s;display:inherit;}@keyframes fadeIn{0%{opacity:0;}100%{opacity:1;}}#full img{width:100%;}html{scroll-behavior:smooth;}@media only screen and (max-width: 1180px){body .elementor-slide-description img{display:none;}}.postid-41729 .author_details:nth-child(2){display:none;}body div .series-bar .fa-chevron-down:before{content:"" !important;}.elementor-button span{color:#fff !important;}.break-code .lines{word-break:break-all !important;}#custom_html-16{text-align:center;}#genesis-sidebar-primary .wpt-tabs .tab_title.selected a:hover{color:#fff !important;}.eicon-close:before{content:"" !important;}.dialog-lightbox-message{z-index:1;position:relative;}.sidebar li{border-bottom:1px solid #ccc;}#genesis-sidebar-primary li a:hover{color:#006cff !important;}.eicon-close{font-family:"Font Awesome 5 Free" !important;font-style:normal !important;}.home{background-color:#fff;}#tpbr_box{font-size:20px !important;}#tpbr_calltoaction{box-shadow:0px 2px 0px 0px rgba(0,0,0,.34);background:#f0482c !important;font-size:18px;padding:0 20px !important;}.sidebar .widget{margin-bottom:30px;}.code-blk .line td{font-size:16px !important;}@media only screen and (max-width: 800px){.site-title{text-align:left;}h1.entry-title{font-size:21px !important;}h2{font-size:19px !important;}h3{font-size:21px !important;}#genesis-nav-primary{float:right !important;margin-top:20px;}.site-header .title-area{text-align:left;float:left;width:50%;}.entry-title{font-size:36px;font-size:23px;}.wp-block-image,.aligncenter{margin:0;width:100%;}.common_authors .author_details{display:inline-block !important;width:auto;flex:inherit;}body > div{font-size:16px;}body .entry{margin-bottom:30px !important;}}@media only screen and (max-width: 500px){.download-code{padding:30px 15px !important;font-size:16px;}.download-code:before{position:inherit !important;margin-bottom:-10px;width:6rem;height:8rem;}body article{margin-bottom:15px;}.site-title a{font-size:23px !important;}#genesis-nav-primary{float:right !important;margin-top:20px;}.site-header .title-area{text-align:left;float:left;width:70%;}.entry-title{font-size:18px;}.wp-block-image,.aligncenter{margin:0;width:100%;}.common_authors .author_details{display:inline-block !important;width:auto;flex:inherit;}body > div{font-size:15px;}body .entry{margin-bottom:15px !important;}}.custom_read_more{background:#006cff;padding:10px 20px;color:#fff;margin-top:15px;display:block;float:left;font-size:16px;font-weight:500;}.archive-pagination .active a{background-color:#006cff;}.archive-pagination li{display:inline;margin-right:5px;}.is-menu-wrapper{right:80px;top:35px;}.home .post-categories a:nth-child(n+6),.home .post-tags a:nth-child(n+6){display:none;}p:empty:before{content:inherit;}body p,.elementor-widget-text-editor{color:#1e1e1e;font-size:18px;font-weight:400;line-height:29px;}h2{color:#333;font-size:31px;font-weight:500;}h3{color:#333;font-size:26px;font-weight:500;letter-spacing:0px;}h4{color:#333;font-size:23px;font-weight:500;letter-spacing:0px;}h2 strong,h3 strong{font-weight:500;}h1,h2,h3,h4,h5,h6,.entry-title a{font-family:"Poppins",Sans-serif !important;font-weight:500;}figcaption,p,em,strong,b,body{font-family:"Roboto",Sans-serif !important;}body{font-weight:400;}ol li{color:#3c3c3c;font-family:"Roboto",Sans-serif;font-size:16px;font-weight:400;line-height:29px;}.sidebar .widget-title,.sidebar h4{font-weight:600;font-size:18px;text-transform:capitalize;}figcaption{color:#3c3c3c;font-size:16px;font-weight:400;line-height:29px;}.sidebar li{font-weight:400;}@media only screen and (max-width: 768px){.elementor-slide-heading h1{font-size:2rem !important;}.wpc_show_bottom_widget .wpc-filters-scroll-container{background:#fff;min-height:inherit !important;overflow:scroll;}.wpc_show_bottom_widget .wpc-filters-main-wrap .wpc-filters-open-button-container{display:block !important;}.wpc-overlay-visible body,html.wpc-overlay-visible{overflow:inherit !important;}.wpc-overlay-visible .wpc_show_bottom_widget .wpc-filters-overlay{display:none !important;}.elementkit-tab-nav{display:inherit !important;}.elementkit-tab-nav a{margin-bottom:5px !important;font-size:13px !important;padding-left:15px !important;padding-right:15px !important;}body p,.elementor-widget-text-editor,ol li{font-size:14px !important;line-height:24px;}p{margin:0 0 15px;}.breadcrumb{top:-100px;font-size:12px;border-radius:0;}.single.single-post .site-container{margin-top:70px !important;}.toc-gutenberg{padding:15px !important;}.toc-gutenberg li{font-size:14px;padding:0;margin:0 !important;}.download-code-bar.scrolled-class .elementor-widget-container{border:0 !important;}.download-code-bar.scrolled-class{bottom:0 !important;top:inherit;}.subscribe-box{font-size:14px;}.subscribe-box h3{font-size:24px;}body p{font-size:16px;}}a.elementor-widget-text-editor{color:#3c3c3c !important;}.site-footer p{color:#fff !important;}.site-footer a:hover,#genesis-footer-widgets a:hover{color:#006cff !important;}#user-profile-6 p{font-size:16px !important;}#cookie-notice{background-color:#1a1a1a !important;}#cookie-notice .cn-button{background:#006cff !important;color:#fff !important;}#cookie-notice a{color:#006cff !important;}.subscribe-btn{background:#006cff;color:#fff;font-weight:500;font-size:16px;line-height:20px;padding:15px;display:inline-block;max-width:300px;box-shadow:none;text-decoration:none !important;}a.button.loblue{background-color:#006cff !important;border:1px solid #006cff !important;color:#fff !important;}.cv4faces,.download-code{border-color:#006cff;}h1.entry-title{font-size:33px;font-weight:500;color:#1c1c1d;}.custom_read_more:hover{background:#303236;color:#fff;}.subscribe-box{font-size:16px;border-style:dashed;border-color:#006cff;transition:background .3s,border .3s,border-radius .3s,box-shadow .3s;margin-top:30px;margin-bottom:30px;padding:5% 3%;text-align:center;background:#f9f9f9;}.subscribe-btn:hover{background:#303236;color:#fff;}.eicon-close:before{content:"";font-family:"Font Awesome 5 Free";}.eicon-close{font-style:normal !important;}.subscribe-box{display:inline-block;}.ql-img-displayed-equation{cursor:pointer;}.elementor-widget-theme-post-content{color:inherit;}.toc-gutenberg:before{content:"Table of Contents";font-size:21px;font-weight:400;margin-bottom:30px;display:block;}.toc-gutenberg{padding:30px 40px;max-height:var(--toc-body-max-height);overflow-y:auto;background:#fafafa;margin:30px 0 !important;border:1px solid #dfdfdf;}.toc-gutenberg li a{text-decoration:none;color:#006cff;}.toc-gutenberg li{margin-bottom:.5em;margin-left:15px;display:block;}.toc-gutenberg li ol{margin-top:.5em;margin-left:15px !important;}.toc-gutenberg li a:hover{color:#343434;}.toc-gutenberg,.toc-gutenberg ol{counter-reset:item;}.toc-gutenberg li:before{content:counters(item,".") ". ";counter-increment:item;}.is-search-input{border-radius:5px 0 0 5px !important;}.is-form-style button span{border-radius:0 5px 5px 0 !important;}.is-form-style input.is-search-input,.is-search-icon,.is-search-submit{height:45px !important;}.is-search-icon{width:36px;padding-top:11px !important;}.elementor-28323 .elementor-widget:not(:last-child),.elementor-element-6171d7cd .elementor-widget:not(:last-child){margin-bottom:0 !important;}.e--pointer-underline .elementor-item::after{height:2px;}li.elementorSubscribePopup{display:none;}@media only screen and (max-width:1024px){li.elementorSubscribePopup{display:inherit !important;}.elementor-28323 .elementor-element.elementor-element-65831edc{order:2;}.elementor-28323 .elementor-element.elementor-element-22c7dd84{order:1;}}@media only screen and (max-width:768px){.scrolled-class a{font-size:12px !important;}.elementor-28323 .elementor-element.elementor-element-37c43e1e{order:3 !important;text-align:center;}.elementor-28323 .elementor-element.elementor-element-22c7dd84{order:3 !important;}.elementor-28323 .elementor-element.elementor-element-73d97576 .elementskit-menu-hamburger{float:left !important;}}#custom_html-13 h4{color:#e51075;font-weight:700;}.eicon-close::before{font-weight:900;}[class^="eicon"]{font-weight:900;}[class^="eicon"]::before,[class*=" eicon-"]::before{content:"" !important;}@media only screen and (max-width: 800px){#ekit-megamenu-top-bar #menu-top-bar{display:initial !important;}}.elementor-28323 .elementor-element.elementor-element-73d97576 .elementskit-menu-container{background-color:#131417 !important;}.elementor-33489{margin-bottom:30px;}article.has-post-thumbnail .entry-image-link img{width:100% !important;}.slider{background-color:#fff !important;}.slider .flexible-widgets{padding:30px 0 0px;background:none;}.elementskit-single-testimonial-slider{margin-bottom:0 !important;}.flexible-widgets .widget{margin:0 0 0px;}#wpt_widget-2 .entry-title{font-size:14px !important;}#wpt_widget-2 .entry-title a{}.wpt_widget_content .tab_title.selected a{background:#006cff !important;border-bottom:1px solid #006cff !important;color:#fff;}body .wpt_widget_content .tab_title a{display:block;background:#f6f6f6;border-left:1px solid #f6f6f6;border-bottom:1px solid #f6f6f6;padding:2px 0 4px;line-height:2.4;text-decoration:none;position:relative;font-weight:600;font-family:Rubik;}.flexible-widgets{padding:0px 0 0px;}.swiper-container-horizontal > .swiper-pagination-bullets{text-align:left;}.flexible-widgets{padding:0px !important;}.journal-title,#journal hr{display:none;}.front-page .site-container .site-inner{padding-top:40px;}#text-15 .swiper-container:before{content:"OpenCV Course Testimonials";color:#333;font-weight:400;font-size:20px;padding:20px;display:block;font-family:Rubik;margin-bottom:-20px;}.sidebar .widget{margin-bottom:20px !important;}.wpt_widget_content ul.wpt-tabs li{border-bottom:1px solid #e4e4e4;}body .wpt_widget_content .tab_title a{background:none;border-bottom:0px solid #f6f6f6;font-weight:400;font-family:Rubik;border-radius:5px 5px 0 0;font-size:15px;}.elementor-28323 .elementor-element.elementor-element-2a57c272 .elementor-heading-title{font-family:"Raleway",Sans-serif !important;}#client img{height:50px !important;width:auto !important;}.elementor-widget-theme-post-featured-image img{width:100%;max-width:880px;}#page-id-38110 #custom_html-16{display:none !important;}.wp-block-embed.aligncenter{text-align:center !important;}.ekit-nav-menu--overlay{display:none !important;}#custom_html-9{margin-bottom:0 !important;}.entry-content a{color:#006cff;}.subscribe-btn{color:#fff !important;}#menu-item-40872 img{max-height:25px;}.eicon-close:before{content:"";font-family:"Font Awesome 5 Free";font-weight:900;}i{font-style:normal !important;}.elementor-slide-description a{background:#006cff;color:#fff;font-weight:500;font-size:18px;line-height:20px;padding:15px;display:inline-block;max-width:300px;border-radius:5px;}.elementor-slide-description a:first-child{margin-right:15px !important;}.elementor-slide-description a:last-child{background:#131417;}@media only screen and (max-width: 786px){.elementor-slide-description div{display:none !important;}.elementor-slide-description a{font-size:14px !important;padding:10px 15px !important;}.swiper-slide-contents{text-align:center;}.elementor-slide-description br{display:none;}.swiper-pagination{display:none;}.elementor-37961 .elementor-element.elementor-element-236ef7fc .swiper-slide-contents{width:100% !important;}.elementor-slide-heading{margin-bottom:10px !important;}.elementor-pagination-position-outside .swiper-container{padding-bottom:0;}.elementor-37961 .elementor-element.elementor-element-6eb020fe > .elementor-container > .elementor-row > .elementor-column > .elementor-column-wrap > .elementor-widget-wrap{align-content:flex-end !important;align-items:flex-end !important;}#banner .swiper-slide-inner{background:rgba(0,0,0,.62);padding:15px 15px;}.elementor-37961 .elementor-element.elementor-element-236ef7fc .swiper-slide{height:175px !important;}.elementor-37961 .elementor-element.elementor-element-3dd738f7 img{max-width:300px;}#banner a:hover{background:#fff !important;color:#006cff;}#banner .elementor-main-swiper{padding-bottom:0 !important;}.elementor-element-77914c9b{position:absolute;bottom:0;z-index:9;}#banner .elementor-widget:not(:last-child){margin-bottom:0px;}}.content .entry{width:100%;}.more-link{display:none;}#menu-item-41897 img{max-height:25px;}.elementor-slide-description a{max-width:390px !important;}.wp-block-embed__wrapper{position:relative;width:100%;overflow:hidden;}.wp-block-embed__wrapper #journal{width:100%;}article.format-standard .rll-youtube-player{position:relative !important;}#journal{position:inherit !important;}.wp-block-syntaxhighlighter-code{word-wrap:anywhere;}.elementor-28323 .elementor-element.elementor-element-73d97576 .elementskit-navbar-nav > li > a{cursor:pointer;}.wp-block-embed-embed-handler.wp-embed-aspect-16-9.wp-has-aspect-ratio .wp-block-embed__wrapper{position:relative;overflow:hidden;width:100%;padding-top:56.25%;}.wp-block-embed-embed-handler.wp-embed-aspect-16-9.wp-has-aspect-ratio .wp-block-embed__wrapper iframe,.is-type-video .wp-block-embed__wrapper iframe{position:absolute;top:0;left:0;bottom:0;right:0;width:100%;height:100%;}figcaption{text-align:center;}.syntaxhighlighter.code-blk{font-size:90% !important;}#smart_push_smio_allow{background:#006cff !important;color:#fff !important;}#smart_push_smio_window{border-radius:5px !important;}#smart_push_smio_msg{font-family:Poppins !important;font-size:16px !important;font-weight:600 !important;line-height:24px !important;color:#000 !important;}#smart_push_smio_note{font-family:Poppins !important;font-size:14px !important;font-weight:400 !important;line-height:21px !important;color:#000 !important;}.elementor-slide-heading h1{font-family:"Rubik",Sans-serif !important;font-weight:inherit;}body #cookie-notice{max-width:350px;left:30px;bottom:30px;color:#fff !important;min-width:inherit !important;background-color:rgba(26,26,26,0) !important;}.cookie-notice-container{color:#001e00 !important;font-family:Poppins;text-align:left !important;background:#fff !important;padding:20px 15px;border-radius:18px;box-shadow:0 0 18px rgba(0,0,0,.2);}body #cn-accept-cookie{margin-top:5px !important;margin-left:0 !important;}body .cn-close-icon{right:15px;top:20px;}body #cookie-notice .cn-button{border-radius:25px !important;padding:12px 29px !important;font-family:Poppins !important;background:#001e00 !important;}body #cookie-notice .cn-button:hover{background:#006cff !important;}#menu-item-51149 > a > .highlight{animation:blinker 1s alternate-reverse linear infinite;}@-webkit-keyframes blinker{0%{opacity:0;}50%{opacity:1;}100%{opacity:1;}}.wp-block-syntaxhighlighter-code .syntaxhighlighter{background-color:#30302f !important;}.wp-block-syntaxhighlighter-code .syntaxhighlighter .line.alt1{background-color:#30302f !important;}.wp-block-syntaxhighlighter-code .syntaxhighlighter .line.alt2{background-color:#30302f !important;}.wp-block-syntaxhighlighter-code .syntaxhighlighter .line.highlighted.alt1,.syntaxhighlighter .line.highlighted.alt2{background-color:#30302f !important;}.elementor-50569 .elementor-element.elementor-element-911a724 > .elementor-container > .elementor-column > .elementor-widget-wrap{align-content:center;align-items:center;}.elementor-50569 .elementor-element.elementor-element-911a724{border-style:solid;border-width:0px 0px 1px 0px;border-color:#dcdcdc;margin-top:5px;margin-bottom:5px;}.elementor-50569 .elementor-element.elementor-element-911a724,.elementor-50569 .elementor-element.elementor-element-911a724 > .elementor-background-overlay{border-radius:0px 0px 0px 0px;}.elementor-50569 .elementor-element.elementor-element-1349af6 .elementskit-section-title-wraper .elementskit-section-title{color:#1c1c1c;margin:0px 0px 0px 0px;font-family:"DM Sans",Sans-serif;font-size:16px;font-weight:600;line-height:26px;}.elementor-50569 .elementor-element.elementor-element-1349af6 .elementskit-section-title-wraper .elementskit-section-title > span{color:#000;}.elementor-50569 .elementor-element.elementor-element-1349af6 .elementskit-section-title-wraper .elementskit-section-title:hover > span{color:#000;}.elementor-50569 .elementor-element.elementor-element-1349af6 .elementskit-section-title-wraper .elementskit-section-subtitle{color:var(--e-global-color-primary);font-family:"Poppins",Sans-serif;font-size:12px;font-weight:600;line-height:2.6em;margin:0px 0px 0px 0px;}@media (max-width:767px){.elementor-50569 .elementor-element.elementor-element-dacd427{width:70%;}}@media (max-width:1024px) and (min-width:768px){.elementor-50569 .elementor-element.elementor-element-dacd427{width:70%;}}

Geometry of Image Formation

Get Started with OpenCV

Subscribe to receive the download link, receive updates, and be notified of bug fixes

Which email should I send you the download link?