I guess the equations in 9:01 are incorrect.. Even the professor Cyrill indicated that the equation (f-g)⋅r should be (g-f)⋅r, the following equations are weird. I guess the following equations would be (q + μs - p - λr)⋅s = 0 and (q + μs - p - λr)⋅r = 0.
You're right. Although the left vector should still be (f-g), to be consistent with the two equations in slide 11 with the real parameters are substituted in. Those two equations are correct. The left vectors in the equations in slide 9 should've been (f - g) = (p+λr - (q+μs))
Shouldn't the right hand side of the matrix form of the equation in 12:02 be one column vector? The ] [ brackets between the transposed vectors and r, s shouldn't be there.
Well spotted. This is a mistake on the slides. In the right hand side of the lower equations the "] [" must be removed, otherwise we would not get the desired 2D vector. Thanks for pointing out this mistake.
@CyrillStachniss Thanks for the great video professor. I have a question on quality of triangulation? Is there a way I can estimate the uncertainty or the covariance matrix of the triangulated point? The lines may not perfectly intersect (due to noise in relative poses) and the pixel sizes could define a larger unprojected area. Is there any source where I can learn about how I can encode this uncertainty as a covariance matrix? You do show this for the 2 view case, is there a way to estimate this for the multiview case?
Another question I had is about hand eye calibration. I've tried to capture images from a pattern and the same time record the position of the robot , however I was expected to get one fix result but it's not the case! obviously the transformation between the robot and camera coordinate system is fixed but can slightly be different I think in x element of translation bc it depends on focal length! I've tried to capture images in a range(movements 1-4cm from the pattern) but the estimated transformation seems to have the best result for the middle of the range! would you please shed some light on this? I cannot end up with an estimated transformation can have good results in different distances!
I have a question on "Absolute orientation". If we can estimate 3D points from stereo camera (=we know the baseline) and control points w.r.t. global frame, then we don't need to estimate "scale" parameter right? In this case, 6 DoF?
D. Cyrill, Does this algorithm is used to generate the DSM ( dense surface model ) as a point cloud ? if not, which one does the photogrammetric software such as PhotoModeler use ?
Thank you for the great lecture. I think that Matlab implementation for triangulation use SVD which is a linear solution for that, do you know any other implementation that offers non-linear solution for triangulation and you've used it in your lab maybe?!
Here you mention that you get the 3D points in the local frame ruclips.net/video/UZlRhEUWSas/видео.html. But however we don't have the scale information from the essential estimation until we get the control points. Am I missing something ?
For the photogrammetric model, we do not have the scale. If we use a stereo setup with known baseline, we have a good estimate. Thus, it depends on the precise camera setup
I guess the equations in 9:01 are incorrect..
Even the professor Cyrill indicated that the equation (f-g)⋅r should be (g-f)⋅r, the following equations are weird.
I guess the following equations would be (q + μs - p - λr)⋅s = 0 and (q + μs - p - λr)⋅r = 0.
You're right. Although the left vector should still be (f-g), to be consistent with the two equations in slide 11 with the real parameters are substituted in. Those two equations are correct. The left vectors in the equations in slide 9 should've been (f - g) = (p+λr - (q+μs))
thanks for making this nice explanation public and freely accessible
Shouldn't the right hand side of the matrix form of the equation in 12:02 be one column vector? The ] [ brackets between the transposed vectors and r, s shouldn't be there.
Well spotted. This is a mistake on the slides. In the right hand side of the lower equations the "] [" must be removed, otherwise we would not get the desired 2D vector. Thanks for pointing out this mistake.
Corrections:
11:56 Mistake in the brackets in the last row, right hand side. Remove inner ][
I almost watch all the videos from Prof. Stachniss. Thank you for your lecture.
Finally it’s here. Was waiting for this!
@CyrillStachniss Thanks for the great video professor. I have a question on quality of triangulation? Is there a way I can estimate the uncertainty or the covariance matrix of the triangulated point? The lines may not perfectly intersect (due to noise in relative poses) and the pixel sizes could define a larger unprojected area. Is there any source where I can learn about how I can encode this uncertainty as a covariance matrix? You do show this for the 2 view case, is there a way to estimate this for the multiview case?
Thank you Cyrill for this streamlined explanation, but can I ask you about the name of the reference or paper you took that from?
Created based on notes by Wolfgang Förstner
How can one find the camera constant c for a real camera during the calibration process. It would be a great help if anyone could answer that
See video on camera calibration (Zhangs method) in my list of videos
Hey is there any article, journal paper, or book where I can find those explanations, especially the Geometric Solution?
very well explained. waiting for a video on sensor fusion of camera images and 3D point cloud
Again, this comes exactly when i need it 👌
Another question I had is about hand eye calibration. I've tried to capture images from a pattern and the same time record the position of the robot , however I was expected to get one fix result but it's not the case! obviously the transformation between the robot and camera coordinate system is fixed but can slightly be different I think in x element of translation bc it depends on focal length! I've tried to capture images in a range(movements 1-4cm from the pattern) but the estimated transformation seems to have the best result for the middle of the range! would you please shed some light on this? I cannot end up with an estimated transformation can have good results in different distances!
I have a question on "Absolute orientation". If we can estimate 3D points from stereo camera (=we know the baseline) and control points w.r.t. global frame, then we don't need to estimate "scale" parameter right? In this case, 6 DoF?
If the baseline is perfect, no. Otherwise a scale correction can be useful
D. Cyrill, Does this algorithm is used to generate the DSM ( dense surface model ) as a point cloud ? if not, which one does the photogrammetric software such as PhotoModeler use ?
Thank you for the great lecture. I think that Matlab implementation for triangulation use SVD which is a linear solution for that, do you know any other implementation that offers non-linear solution for triangulation and you've used it in your lab maybe?!
Here you mention that you get the 3D points in the local frame ruclips.net/video/UZlRhEUWSas/видео.html. But however we don't have the scale information from the essential estimation until we get the control points. Am I missing something ?
For the photogrammetric model, we do not have the scale. If we use a stereo setup with known baseline, we have a good estimate. Thus, it depends on the precise camera setup
I really like these courses but someone can tell me why there are advertizings every 3 to 4 mn ? It is really annoying and was not the case before...
Sorry for that. I now disabled Midroll Ads
@@CyrillStachniss Thank you very much for your kindness
Thank you so much Professor.
Amazing!!!
this lecture I didnt like. many points in it was not clear enough as they were in other lectures
Don't