{"id":157,"date":"2012-10-02T23:28:38","date_gmt":"2012-10-03T03:28:38","guid":{"rendered":"https:\/\/peterabeles.com\/blog\/?p=157"},"modified":"2012-12-22T08:15:34","modified_gmt":"2012-12-22T13:15:34","slug":"incorrect-equations-in-review-and-analysis-of-solutions-of-the-three-point-perspective-pose-estimation-problem","status":"publish","type":"post","link":"https:\/\/peterabeles.com\/blog\/?p=157","title":{"rendered":"Incorrect Equations in &#8220;Review and Analysis of Solutions of the Three Point Perspective Pose Estimation Problem&#8221;"},"content":{"rendered":"<p>In the 1994 paper &#8220;Review and Analysis of Solutions of the Three Point Perspective Pose Estimation Problem&#8221; by R. M. Haralick, C-N Lee, K. Ottenberg, and M. Nolle, I found a couple of important typos in the equations for the Finsterwalder solution.\u00a0 This paper describes several solutions to the Perspective Three Point (P3P) problem, two of those solutions I ended up implementing.\u00a0 The Grunert solution is correct and easy to implement, while the Finsterwalder solution is a little bit more involved.\u00a0 However since the equations are incorrect for Finsterwalder you could be in for a bit of frustration.<\/p>\n<p>I could not find an e-mail address on the first author&#8217;s website.\u00a0 The paper is also a bit old (but still relevant) and the problem was most likely already reported.\u00a0 If I&#8217;m the first person to notice or try to report the problem after 18 years then it&#8217;s a non issue.\u00a0 However, to help others out there (the one or two which have found this website) here are the corrections:<\/p>\n<p>After it has been corrected, the first line in equation (16) should be:<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%28b%5E2+-+m%5E2c%5E2%29u%5E2+%2B+2%28c%5E2%28cos%5Cbeta+-n%29m+-+b%5E2cos%5Cgamma%29u&#038;bg=f7f3ee&#038;fg=333333&#038;s=0' alt='(b^2 - m^2c^2)u^2 + 2(c^2(cos\\beta -n)m - b^2cos\\gamma)u' title='(b^2 - m^2c^2)u^2 + 2(c^2(cos\\beta -n)m - b^2cos\\gamma)u' class='latex' \/><\/p>\n<p>Note that a power of 2 has been added to <strong><em>&#8216;m&#8217;<\/em><\/strong>. The equations on the top of the right column of page 337 also needs to be correct and should be:<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=A+%3D+b%5E2+-+m%5E2c%5E2&#038;bg=f7f3ee&#038;fg=333333&#038;s=0' alt='A = b^2 - m^2c^2' title='A = b^2 - m^2c^2' class='latex' \/><br \/>\n<img src='https:\/\/s0.wp.com\/latex.php?latex=B+%3D+c%5E2%28cos%5Cbeta+-n%29m+-b%5E2cos%5Cgamma&#038;bg=f7f3ee&#038;fg=333333&#038;s=0' alt='B = c^2(cos\\beta -n)m -b^2cos\\gamma' title='B = c^2(cos\\beta -n)m -b^2cos\\gamma' class='latex' \/><br \/>\n<img src='https:\/\/s0.wp.com\/latex.php?latex=C+%3D+-c%5E2+n%5E2+%2B+2c%5E2+n+cos%5Cbeta+%2B+b%5E2+-+c%5E2&#038;bg=f7f3ee&#038;fg=333333&#038;s=0' alt='C = -c^2 n^2 + 2c^2 n cos\\beta + b^2 - c^2' title='C = -c^2 n^2 + 2c^2 n cos\\beta + b^2 - c^2' class='latex' \/><\/p>\n<p>Here a power of two was added to <strong><em>&#8216;m&#8217;<\/em><\/strong> in the first line and <strong><em>&#8216;c&#8217;<\/em><\/strong> in the third line.\u00a0 Hopefully this post will save someone a few hours of aggravation and deriving equations.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the 1994 paper &#8220;Review and Analysis of Solutions of the Three Point Perspective Pose Estimation Problem&#8221; by R. M. Haralick, C-N Lee, K. Ottenberg, and M. Nolle, I found a couple of important typos in the equations for the Finsterwalder solution.\u00a0 This paper describes several solutions to the Perspective Three Point (P3P) problem, two [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-157","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/peterabeles.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/157","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/peterabeles.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/peterabeles.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/peterabeles.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/peterabeles.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=157"}],"version-history":[{"count":10,"href":"https:\/\/peterabeles.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/157\/revisions"}],"predecessor-version":[{"id":167,"href":"https:\/\/peterabeles.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/157\/revisions\/167"}],"wp:attachment":[{"href":"https:\/\/peterabeles.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=157"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/peterabeles.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=157"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/peterabeles.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}