Direct Solution for Estimating the Fundamental and Essential Matrix (Cyrill Stachniss)

[@vivekbagaria3759]

Each lecture is worth millions of $! Thanks for the lecture professor!

[@davidfriesen9625]

This is great! Finally something worth watching on KZbin. I'm trying to teach myself SLAM and structure from motion. I have a pet peeve though: worse than fingernails on a chalkboard, is a lecturer who says "equals to", which is easily confused for "equals two". English grammar dictates "is equal to zero" or "equals zero" but never "equals to zero", unless you want a note taker to write " = 2 0 "

[@MatyyRdk]

I like your style of teaching. One can get to know all the details, but don't get lost in between because you explain all the steps and keep repeating the important points. Thanks for making these!

[@medhyvinceslas4151]

Thank you Cyrill. Always a pleasure to learn from your Channel.

[@ioannapanagiotidou7394]

amazing work. thanks for sharing

[@RaigyoEcU]

always very helpful, reading Multiple View Geometry and then watching your lectures help so much understanding all the concepts of epipolar geometry

[@aminfadaei4056]

great lecture thank you so much, your lectures are helping me a lot this semester

[@sheno4064]

Thank you for this series of lectures; it's conducive!

[@jeffabc1997]

incredible lecture. thank you so much!

[@molosist]

Great lecture! A small note: in the slide that appears on 14:18 "regular" means invertible/nonsingular (it might cause some confusion)

[@Henqi]

Thank you for an informative lecture! Helped me a lot when doing my exercise!

[@johnl4885]

Excellent video. If S is the unknown skew and R is the rotation matrix, would another path to an answer be given by, EE' = S^2 then set S = sqrt(-EE')? Of course the sqrt would have +/- on the first two eigenvalues going with the SVD route, also requiring a test for acceptable lines of sight.

[@abdelrahmanwaelhelaly1871]

in what coordinates is R and T given in? so if T is [1,1,1] is it 1 pixel or 1m or 1 cm or one focal length unit

[@alanjohnstone8766]

A great series of lectures. Could you tell me how to detect zero or very small translation and then how to estimate the rotation separately. Thanks

[@a1k0n]

38:38 As far as preconditioning for estimating the essential matrix -- would it suffice to instead just divide your x' and x'' coordinates through by their z coordinates (labeled as c' and c'' in your slide at 34:30), so that they are [x y 1] vectors? x and y would be limited by the tangent of the field of view in that case.

[@CyrillStachniss]

You are working in the camera coordinate frame here and the distance between the projection center and the image plane are the camera constants c' and c''.

[@medhyvinceslas4151]

Is it correct to say that the epipole can be found simply by taking the point resulting of the intersection of 2 random epipolar lines ?

[@aliberatcetin6765]

great.....

[@hetshah7490]

amazing video for Fundamental and Essential Matrix. I was trying to clear this topics from 2 consecutive days and finally your video provided the clarity. I also have one question; that after finding the epipolar line for the point; how can we search on that epipolar line and find the exact point ? If you have any materials or implementations; please share how to connect to them. Again, Thank You.

[@CyrillStachniss]

Search along the line for pixel similarity, eg via normalized cross correlation. You may check my photogrammetry 1 lecture on cross correlation to get some insights.

[@ThomasDeegancool]

Why do we use SVD instead of least squares to solve Af = 0?

[@shadowlegion3115]

That's also what Im thinking about. Any clues?

[@inbb510]

It is because the least squares solution is very sensitive to noise, something which is present in all photos. It is a very ill-conditioned solution. If you still want to use least squares, doing a Tikhonov regularisation will get around this problem.

[@이상하-u6g]

I think SVD can be kind of least square solution! It is because the last row vector of Vt makes it the minimum value.

[@sansonisebastian233]

Is the same solution but i guess that is because you need apply a restriction of rank(F)=2. In the book called: "Multiple view geometry in computer vision" by Hartley and Zisserman, 2nd edition, there are another explanations of this problem. In particular take a look in page 280 before of "11.1.1 The singularity constraint".

[@AndreiChegurovRobotics]

As always great lecture! Could not figure out why Fundamental Matrix shall be rank=2? (kzbin.info/www/bejne/sImYf5iPYqyHhZI)

[@CyrillStachniss]

F must have a rank deficiency in order to formulate the coplanarity constraint, which is x^t F x = 0

[@CyrillStachniss]

A more formal reason: the definition of F contains a matrix product involving a skew symmetric matrix (which is of rank 2) and thus the overall product is of rank 2

[@AndreiChegurovRobotics]

@@CyrillStachniss Thank you Professor