{"id":427,"date":"2024-09-12T11:57:21","date_gmt":"2024-09-12T11:57:21","guid":{"rendered":"https:\/\/cv.inf.elte.hu\/?page_id=427"},"modified":"2026-02-10T14:29:27","modified_gmt":"2026-02-10T14:29:27","slug":"3d-sensing-and-sensor-fusion","status":"publish","type":"page","link":"https:\/\/cv.inf.elte.hu\/index.php\/education\/3d-sensing-and-sensor-fusion\/","title":{"rendered":"3D Sensing and Sensor Fusion"},"content":{"rendered":"\n<p><strong>Lectures, 2026 spring:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>Wednesdays 10:15-11:45 , <\/em>2-219 Graphics Lab (South Building)<\/li>\n\n\n\n<li><em>Wednesdays 14:15-15:45 <\/em>, 0-222 (South Building)<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>Teachers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Peter Kozma<\/li>\n\n\n\n<li><a href=\"mailto:hajder_at_inf.elte.hu\">Levente Hajder<\/a><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Peter Kozma&#8217;s lecture slides:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/Lecture-1-Self-driving-future-Peter-D-Kozma.pdf\">Lecture #1: Self-driving Future<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/Lecture-2-Camera-Sensors-Peter-D-Kozma.pdf\">Lecture #2: Camera Sensors<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/Lecture-3-Lidar-Sensors-Peter-D-Kozma.pdf\">Lecture #3: LiDAR Sensors <\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/Lecture-4-Radar-Sensors-Peter-D-Kozma.pdf\">Lecture #4: Radar Sensors<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/Lecture-5-GNSS-INS-Sensors-Peter-D-Kozma.pdf\">Lecture #5: GNSS-INS Sensors<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Agenda<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Week<\/strong><\/td><td><strong>Tuesday<\/strong><\/td><\/tr><tr><td>1st: Registration week<\/td><td><\/td><\/tr><tr><td>2nd<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2026\/02\/3DSSF_lecture_00-2026spring.pdf\">Introduction<\/a><\/td><\/tr><tr><td>3rd<\/td><td><\/td><\/tr><tr><td>4th<\/td><td><\/td><\/tr><tr><td>5th<\/td><td><\/td><\/tr><tr><td>6th<\/td><td><\/td><\/tr><tr><td>7th<\/td><td><\/td><\/tr><tr><td>8th <\/td><td><\/td><\/tr><tr><td>9th<\/td><td><\/td><\/tr><tr><td>10th<\/td><td><\/td><\/tr><tr><td>11th<\/td><td><\/td><\/tr><tr><td>12th<\/td><td><\/td><\/tr><tr><td>13th<\/td><td><\/td><\/tr><tr><td>14th<\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Exams<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>TDL<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Agenda, 2025 fall &#8211; obsolete<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Week<\/strong><\/td><td><strong>Tuesday<\/strong><\/td><\/tr><tr><td>1st: Registration week<\/td><td><\/td><\/tr><tr><td>2nd<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2025\/09\/3DSSF__lecture_00-2.pdf\">Introduction<\/a><\/td><\/tr><tr><td>3rd<\/td><td>Estimation theory:<a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/matrix.pdf\"> inhomogeneous linear systems<\/a>, <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/Lagrange.pdf\">homogeneous sytems<\/a>, <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/CircleEllipseFitting.pdf\">circle estimation<\/a><\/td><\/tr><tr><td>4th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/LiDARCameraCalib_bySpheres.pdf\">LiDAR-Camera calibration using a spherical target<\/a><\/td><\/tr><tr><td>5th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/LiDARCameraCalib_bySpheres.pdf\">LiDAR-Camera calibration using a spherical target<\/a> (cont)<\/td><\/tr><tr><td>6th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/Lagrange-1.pdf\">Lagrange multilpliers.<\/a> <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/CircleEllipseFitting.pdf\">Ellipse estimation<\/a><\/td><\/tr><tr><td>7th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/pointreg.pdf\">Point set registration<\/a><\/td><\/tr><tr><td>8th &#8211; fall break<\/td><td><\/td><\/tr><tr><td>9th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/Lagrange-1.pdf\" data-type=\"link\" data-id=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/Lagrange-1.pdf\">Optimal point-line distance.<\/a> <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/PontEllipseDist.pdf\">Point-ellipse distance<\/a>. <\/td><\/tr><tr><td>10th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/RANSAC_Tekla.pdf\">Robust fitting: the RANSAC method.<\/a> <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/IRLSQ.pdf\">Iterative &amp; Weighted Least-Squares Estimation<\/a><\/td><\/tr><tr><td>11th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/10\/lec01_camera.pdf\">Camera calibration. <\/a> <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2025\/11\/LiDARCameraChessboard.pdf\">LiDAR-camera calibration via chessboard patterns.<\/a>  <\/td><\/tr><tr><td>12th<\/td><td>Demo on MATLAB LiDAR-Camera calibration. <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2025\/11\/matlab_calib_data.zip\">Data for Matlab<\/a><\/td><\/tr><tr><td>13th<\/td><td><a href=\"https:\/\/cg.inf.elte.hu\/wp-content\/uploads\/2025\/10\/BSc_EA_02_ENG_handout.pdf\">Barycentric corrdinates (slides 32-41).<\/a> <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2025\/12\/EPnP_lecture-1.pdf\">EPnP algorithm<\/a><\/td><\/tr><tr><td>14th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2025\/12\/rogrigues.pdf\">Rodrigues formula<\/a>. <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2025\/12\/Cayley2.pdf\">Application of Cayley parameters.<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Exams<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>TDL<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>2024 fall<\/strong><\/p>\n\n\n\n<p><strong>Agenda<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Week<\/strong><\/td><td><strong>Tuesday<\/strong><\/td><\/tr><tr><td>1st: Registration week<\/td><td><\/td><\/tr><tr><td>2nd<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/3DSSF__lecture_00.pdf\">Introduction<\/a><\/td><\/tr><tr><td>3rd<\/td><td>Estimation theory:<a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/matrix.pdf\"> inhomogeneous linear systems<\/a>, <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/Lagrange.pdf\">homogeneous sytems<\/a>, <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/CircleEllipseFitting.pdf\">circle estimation<\/a><\/td><\/tr><tr><td>4th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/LiDARCameraCalib_bySpheres.pdf\">LiDAR-Camera calibration using a spherical target<\/a><\/td><\/tr><tr><td>5th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/09\/pointreg.pdf\">Point set registration<\/a><\/td><\/tr><tr><td>6th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/11\/AhadliTarlan_materials.zip\">ByAhadliTartlan<\/a><\/td><\/tr><tr><td>7th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/11\/AhadliTarlan_materials.zip\">ByAhadliTartlan<\/a><\/td><\/tr><tr><td>8th<\/td><td>LiDAR-Camera MATLAB toolbox using chessboards<\/td><\/tr><tr><td>9th &#8211; fall break<\/td><td><\/td><\/tr><tr><td>10th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/11\/AhadliTarlan_materials.zip\">ByAhadliTartlan<\/a><\/td><\/tr><tr><td>11th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/11\/AhadliTarlan_materials.zip\">ByAhadliTartlan<\/a><\/td><\/tr><tr><td>12th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2025\/03\/3DSSF__lecture_05_LieTheory.pdf\" data-type=\"link\" data-id=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2025\/03\/3DSSF__lecture_05_LieTheory.pdf\">Lie theory<\/a><\/td><\/tr><tr><td>13th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2025\/03\/3DSSF__lecture_05_LieTheory.pdf\" data-type=\"link\" data-id=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2025\/03\/3DSSF__lecture_05_LieTheory.pdf\">Lie theory<\/a> (cont.)<\/td><\/tr><tr><td>14th<\/td><td><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/PontEllipseDist.pdf\">Point-ellipse distance<\/a>. <a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/IRLSQ.pdf\">Iterative &amp; Weighted Least-Squares Estimation<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Peter Kozma&#8217;s lecture slides:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/Lecture-1-Self-driving-future-Peter-D-Kozma.pdf\">Lecture #1: Self-driving Future<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/Lecture-2-Camera-Sensors-Peter-D-Kozma.pdf\">Lecture #2: Camera Sensors<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/Lecture-3-Lidar-Sensors-Peter-D-Kozma.pdf\">Lecture #3: LiDAR Sensors <\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/Lecture-4-Radar-Sensors-Peter-D-Kozma.pdf\">Lecture #4: Radar Sensors<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/cv.inf.elte.hu\/wp-content\/uploads\/2024\/12\/Lecture-5-GNSS-INS-Sensors-Peter-D-Kozma.pdf\">Lecture #5: GNSS-INS Sensors<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Exams<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>18th December 11:00<\/li>\n\n\n\n<li>3rd January 16:00 (room 0-409, South Building)<\/li>\n\n\n\n<li>17th January 16:00 (room 2-502, South Building)<\/li>\n\n\n\n<li>31st January 16:00 (room 0-412, South Building)<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>Topics for oral exam (preliminary)<\/strong><\/p>\n\n\n\n<p>At the oral exam, two topics will be randomly selected.<\/p>\n\n\n\n<p><em>Qestions from Peter Kozma:<\/em><\/p>\n\n\n\n<p>1. Self-driving future.<br>2. Camera.<br>3. LiDAR.<br>4. RADAR.<br>5. GNSS-INS.<\/p>\n\n\n\n<p><em>Questions from Levente Hajder<\/em><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Circle and sphere fitting.<\/li>\n\n\n\n<li>Optimal line and plane fitting.<\/li>\n\n\n\n<li>Ellipse fitting on camera images.<\/li>\n\n\n\n<li>Calculation of point-line and point-ellipse distances.<\/li>\n\n\n\n<li>Robust estimation: the RANSAC algorithm<\/li>\n\n\n\n<li>Robust eszimation: application of the L1 norm; the iterative reweighted least squares algorithm.<\/li>\n\n\n\n<li>Optimal point registration algorithm.<\/li>\n\n\n\n<li>Sphere center estimation from camera images via ellipse detection.<\/li>\n\n\n\n<li>Lidar-camera calibration via a spherical target. Pose (rotation+translation) estimation between a camera and a LiDAR device.<\/li>\n\n\n\n<li>Lidar-camera calibration using chessboards.<\/li>\n\n\n\n<li>The Effective Perspective n Point (EPnP) method.<\/li>\n\n\n\n<li>Representations of a rotation: orthogonal matrices, Rodrigues formula, Cayley parameters.<\/li>\n\n\n\n<li><s>Lie theory \u2013 SO(3): Describe the relation of skew symmetric matrices, infinitesimal rotation. How to derive the exponential map. Closed from for the exponential and logarithmic maps. Alternative representations of 3D rotation<\/s>.<\/li>\n\n\n\n<li><s>Lie theory \u2013 SE(3): Describe &amp; define notable linear groups (GL(n) etc.). Representation of rigid motion, Exp, Log. Application(s) of SE(3)<\/s>.<\/li>\n\n\n\n<li><s>Lie theory \u2013 Applications: Describe the relation of a Lie group and its corresponding Lie algebra. Why is the Identity element of the group so important? Exp, Log, boxplus, boxminus. Interpolation. Uncertain 3D rotation, composition<\/s>&#8230;<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Final grade<\/h3>\n\n\n\n<p>The final grade is the sum of oral exam (max. 25+25=50) and assignment scores. At least 20 points should be reached both from oral exam and assignment scores.<\/p>\n\n\n\n<p>Thresholds for marks as follows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Excellent (5): &gt;=85<\/li>\n\n\n\n<li>Good (4): 70-84<\/li>\n\n\n\n<li>Satisfactory (3): 55-69<\/li>\n\n\n\n<li>Pass (2): 40-54<\/li>\n\n\n\n<li>Fail (1): 0-39<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Lectures, 2026 spring: Teachers: Peter Kozma&#8217;s lecture slides: Agenda Week Tuesday 1st: Registration week 2nd Introduction 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th 14th Exams Agenda, 2025 fall &#8211; obsolete Week Tuesday 1st: Registration week 2nd Introduction 3rd Estimation theory: inhomogeneous linear systems, homogeneous sytems, circle estimation 4th LiDAR-Camera calibration using [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"parent":422,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"folder":[],"class_list":["post-427","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/cv.inf.elte.hu\/index.php\/wp-json\/wp\/v2\/pages\/427","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cv.inf.elte.hu\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cv.inf.elte.hu\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cv.inf.elte.hu\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/cv.inf.elte.hu\/index.php\/wp-json\/wp\/v2\/comments?post=427"}],"version-history":[{"count":70,"href":"https:\/\/cv.inf.elte.hu\/index.php\/wp-json\/wp\/v2\/pages\/427\/revisions"}],"predecessor-version":[{"id":1279,"href":"https:\/\/cv.inf.elte.hu\/index.php\/wp-json\/wp\/v2\/pages\/427\/revisions\/1279"}],"up":[{"embeddable":true,"href":"https:\/\/cv.inf.elte.hu\/index.php\/wp-json\/wp\/v2\/pages\/422"}],"wp:attachment":[{"href":"https:\/\/cv.inf.elte.hu\/index.php\/wp-json\/wp\/v2\/media?parent=427"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/cv.inf.elte.hu\/index.php\/wp-json\/wp\/v2\/folder?post=427"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}