Fundamental and Essential Matrix - 5 Minutes with Cyrill

[@labean112]

Fucking amazing, wish I found this sooner.

[@squirrelbrains2197]

Thank you for your good work. You explain the concepts so well, that you actually make me motivated to study during this "corona crisis semester". (I'm not even a student of your university)

[@old_dobiko]

this? one of the xd

[@nithinga4386]

Hello Sir, I have been following your lectures....this 5 minute series is really helpful...Crisp and clear to deep dive on your own later

[@SpatialAIKR]

The F/E matrices are needed to easily find the correspondences between the pair of images by reducing the search space from 2d to 1d. How to compute the F/E matrix is that by using the correspondence between the pair of images.. Both are correct but contradictory.

[@asan9130]

Professor Stachniss, thank you very much for the amazing content about 3D-CV. I would ask, having these two images and after running 5 / 7 point algorithms, we found corresponds as you mentioned. How can we estimate a 3D pose of detected correspondence points relative to one of the two cameras?

[@yuchengluo3747]

thx for sharing you knowledge with us, its a great help for my work

[@zainmehdi8886]

@ Cyrill Stachniss. Thank you so much for these useful videos. I just have one suggestion that if you could also point to the most appropriate literature if someone wants to dig these topics in detail. That would really prevent novices like me from wandering about for finding the best literature.

[@Michalszczepanski91]

Hello, you can take a look into this position: Multiple view geometry in computer vision Book by Richard Hartley and Andrew Zisserman, best regards

[@zainmehdi8886]

@@Michalszczepanski91 Thanks Alot

[@Dyxuki]

May I ask in pratice what's the use the fundamental matrix? As the Rotation and Translation can only be recovered from the essential matrix E. So we must always pre-calibrate the intrinsics for stereo to work?

[@milesladders5465]

Great Playlist of 5 minute videos.. Thank you so much. It was mentioned that Fundamental Matrix is used or uncalibrated camera but towards the end the (4:21) it was mentioned that F has 7 DOF extra parameters for calibration. Did you mean to say that uncalibrated camera's fundamental matrix has calibration data or I am interpreting it incorrectly.

[@CyrillStachniss]

F has 7 deg of freedom, but not seven extras. In contrast, E has 5 dof. The 2 dof extra come into the game from the calibration information

[@abdjahdoiahdoai]

Hey, can you talk about how these 5/8 points algorithm linked with Ransac, also, there's a 1 point Ransac if we do automotive constraint

[@CyrillStachniss]

Yes, there are variants requiring less points (eg work by Davide Scaramuzza) but they then require a special setup or other external constraints constraints. 5/8-point are general algorithms. You cannot go below 5 in the general calibrated camera case (as E has 5 DoFs)

[@rolandgavrilescu3099]

How is finding F / E achieved in practice? Do we compute an O(n^2) search in the pair of frames to find the correspondences if we don't have them manually annotated?

[@CyrillStachniss]

For finding E, the gold standard is Nister's 5 Point Algorithm. Correspondences can be found by searching in features descriptor space and several outlier rejection techniques.

[@kameelamareen]

Why is it that the Fundamental Matrix has only 7DOFs ? So 5 for rotation , shouldn't it be extra 5 for each calibration matrix assuming not same camera ? Hence total of 15 ?

[@CyrillStachniss]

Nine values (3 by 3 matrix) minus one because it is homogeneous (scale ambiguity) minus one for the rank deficiency (it is of rank 2) equals seven

[@kameelamareen]

@@CyrillStachniss Thank you for your reply , then all other DOFs are coupled in some way in the matrix. Best regards from TUM !

[@도정찬]

thank you so much for great video cyrill!!

[@Michalszczepanski91]

Hello, isn't it a bit of an abuse to say that the fundamental matrix is use for uncalibrated cameras? Can we say that (stereo) cameras are uncalibrated in situations when we known their intrinsic (K) parameters but we don't know their extrinsic position so: rotation and translation? Regard, thanks for content!

[@CyrillStachniss]

If you know the intrinsics (K), you will only care about the extrinsics and thus you will go for estimating the essential matrix and not the fundamental matrix. So estimate F for uncalibrated cameras (i.e., unknown intrinsics) and E for calibrated ones (i.e., known intrinsics).

[@Michalszczepanski91]

@@CyrillStachniss Cyrill Stachniss That sounds logical! Thanks, I'd like to take this opportunity to make sure I understand it, can we say that cameras are "uncalibrated" if its extrinsic or intrinsic or both types of parameters are not known?

[@thibaultbruyere]

@@Michalszczepanski91 the definition of an uncalibrated camera is that you don't know its intrinsics parameters, and the goal of fundamental and essential matrices is to get some extrinsics parameters (and some intrinsics parameters if you don't have them)

[@JohnCena-hi2ri]

@@thibaultbruyere So basically if we are computing E, when we are calibrating camera we only care about intrinsics parameters, extrinsics parameters are inessential anyway? Also this cofuses me. From matrix E we can get R and t => but that is for camera2 with respect to camera1?If we want to estimate motion do we need to have R and t for camera1 with respect to world coordinates?