Any good way to determine coplanarity among 4 points?

[MRT]

Hi,

Can someone suggest a method? I need to implement it on computer.

Thanks in advance!

 

[robphy]

Choose one point as an origin. Form three displacement vectors from that point. Calculate the scalar triple product (the determinant in 3d). Coplanar if zero.

 

[MRT]

Hi robphy,
thanks for ur help. But the problem is that I'm working with 2-d images. So there is no 3D information.

is there any other way of determining coplanarity?
I read something about using invariants but i have great difficulty understanding the paper. The link is here below:
http://www-users.cs.york.ac.uk/~nep/research/iros01.pdf
under section 2.2.

If someone can explain to me how to determine the point k, j, i,l in that section, i will really appreciate your help.

Thanks in advance!

 

[HallsofIvy]

Hi robphy,
thanks for ur help. But the problem is that I'm working with 2-d images. So there is no 3D information.

Perhaps it would help if you would tell us what in the world you mean by "coplanarity" in 2d?? If you have no 3D information then there is no way to determine 3D properties.

 

[MRT]

Sorry for not giving a clear idea of my problem.


The problem is as follows:

I have a 2D image of a scene. I classify the scene as ground plane and non-ground plane. I have 4 points lying on these ground plane. For each point, there will be a value (x, y), with x and y representing its pixel location.

Is there a way to determine if these 4 points lie on the same plane with just this 2-D information?

Thanks in advance again!

 

[jim mcnamara]

You can't do that. 2d representations of 3d are missing information - specifically the "z" coordinate, if you chose {x,y,z} for your system.

You're obviously writing graphics code. Rather than stating it the way you did, what are you really trying to do? ie., what is your goal?

 

[MRT]

I'm actually trying to find the homography matrix H for the ground plane. I need this matrix H to classify non-ground and ground pixels. The eventual goal is to build a navigation map based on camera capture of the surrounding environment.

 

[Tide]

I suggest using two cameras at two locations to provide two images of the same scene.

 

[MRT]

sorry. i forgot one more constraint. I'm working with only one camera. :)

 

[rachmaninoff]

Then you don't have any depth perception.

 

[Tide]

sorry. i forgot one more constraint. I'm working with only one camera. :)

Can you take two pictures with the same camera from two different points? Otherwise, unless you have objects of known size, position and orientation in your single picture, you are out of luck! :)

 

[robphy]

Why one camera view may not be enough:
http://www.yorku.ca/eye/necker.htm
http://dogfeathers.com/java/necker.html

Googling "homography matrix" yielded:
http://gandalf-library.sourceforge.net/tutorial/report/node112.html
http://cs.gmu.edu/~kosecka/lect4.ppt