Re: cylindrical panoramas and homographies

On Apr 29, 11:40 pm, serg271 <serg...@xxxxxxxxx> wrote:
On Apr 29, 8:04 pm, damo suzuki <liquidt...@xxxxxxxxx> wrote:

On Mar 16, 10:44 am, J <ja...@xxxxxxxxxxxxxxxxxxx> wrote:
Ehm..I forgot to check this post. Ok, well, I've seen the mentioned
paper, but what I want is to use the homographic estimation algorithm
I already have implemented and then project the output on a cylinder
or sphere. Maybe it sounds stupid, and I'm kind of dummy, but I'm not
able to do this. I can't understand what's the relationship between
the homography, estimated on rectilinear images, and the cylindrical
projection.

You can not build cylindrical projection from homography. You can
instead approximate it bi stitching you frames pairwise,
and stitching last to first. You will have you cylinder, but that will
not be cylindrical projection.
If you want more exact cylindrical projection you should make 3d
reconstruction of feature point from epipolar geometry
and after you get 3d coordinates of them just project them on cylinder
and interpolate between them.

because all images are being projected on the same plane of the first
one (which I use as reference).

If I understand what you are doing you correctly that is the reason.
You are trying to unwrap circular panorama to flat plane with
homography, and that is not right. You should try instead project
second on first, third on second etc. last on first. That way you will
get your cylindrical wrap.



On the web I found a .PPT by Jack Tumblin, which is well known name,
called "Wrapping the world around your Camera:
Warps, Morphs, Panoramas, and Mirror Spheres" (you can find it here
www.cs.northwestern.edu/~jet/Teach/2004_3spr_IBMR/Projective2D_PanoSphereWarp.ppt)
Here he outlines the following steps, somehow the same I'm trying


"Choose a ‘reference’ image plane, extend it
Add images: for each one,
find H from overlap correspondences (in P2)
transform new image to reference plane"


Here H is an homography, and I guess that in order to "transform new
image to reference plane" pairwise homographies should be chained by
matrix multiplication.

Then he writes

"Can’t use planar method beyond 180° FOV;
Make spherical image: ‘wrap around’ origin
How? Spherical coords
write 3D sphere eqn in P2 coords:
x1 = cos(theta)cos(phi)
x3 = -sin(theta)cos(phi)
x2 = cos(phi)
‘Inverse Map’ warp:
Find x’ = H-1·[x1, x2, x3] for each image
Blend color(s) found at x’ for each image"

So it seems that he is using the homographies to get a spherical
panorama. Am I missing something??????


.

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