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Science Forum Index » Image Processing Forum » cylindrical panoramas and homographies
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| damo suzuki |
 Posted: Sat Mar 15, 2008 11:01 am |
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Guest
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Hi,
Hi, not sure if this is the right place where to post, but I need to
create an application for creation of (possibly) cylindrical
panoramas but I'm very confused about some of the maths behind it.
Well, I know that if I know focal distance and capture my images with
a perfectly aligned tripod, I can simply estimate the horizontal
traslation between my images and then "easily" stitch my panorama.
However I want to build it from handheld (with not excessive
movement)
and here is where my confusion begins.
I want to estimate motion as follows:
1) find matching features on overlap region
2)estimate an homography between pairwise images
a b c
H= d e f
g h 1
Do i need to estimate this on already cylindrical warped images or on
input rectilinear images?
If I need to do this on rectilinear images,as I think, how do I
reproject them on the cylindrical surface taking into account the
estimated homography?
Thanks to anyone willing to provide some useful hints.
alf. |
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| J |
| Posted: Sat Mar 15, 2008 10:44 pm |
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Guest
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Hi
You can approach this in a number of ways. You could warp the images
using a cylindrical warp then align using just pure translations,
which is probably the easiest method but wont work very well with a
hand-held. A better alternative is to compute the homography as you
say. There is a really good paper on this by Szeliski at microsoft
research, he uses a nice 3-parameter system to compute the
homographies and it works really well, which I would higly recommend
to you.
Regards
Jason |
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| damo suzuki |
| Posted: Tue Apr 29, 2008 7:04 am |
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Guest
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On Mar 16, 10:44 am, J <ja...@visionexperts.co.uk> 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.
Basically I'm estimating an homography Hij (8 DOF) for each image pair
(i,j) and the combine the homographies using a simple chaining rule
Hik=Hi,i+1 * Hi+1,i+2 * * Hn,k. All images are acnhored to the first
frame.
An other strange mathematical problem that I'm facing is the
following:
- I take the corners of each image, and apply homography to them
obtaining the warped corners (so that I can build a kind of bounding
box to be used for inverse warping).
-Supposing that all images have been captured from left to right, the
warped box corners should obey the following order:
if x1,y1 is a warped corner for one image the corresponding warped
conrer u1,v1 of the following image should be such that x1<=u1,
because all images are being projected on the same plane of the first
one (which I use as reference). This holds up to a certain point, and
I don't know why, since when I have more than four frames (this will
have been acquired, say with a panning angle > 90 degrees when
compared with the first image) something curios happens and warped
corners become kind of swapped (i.e. u1<=x1).
I guess I have explained very badly what I mean, sorry, but if someone
could help, also thru private e-mail I would be grateful. e-mail would
be liquidtreeNOSPAMPLEASE@gmail.com. Just remove the NOSPAMPLEASE
sentence.
Quote: Hi
You can approach this in a number of ways. You could warp the images
using a cylindrical warp then align using just pure translations,
which is probably the easiest method but wont work very well with a
hand-held. A better alternative is to compute the homography as you
say. There is a really good paper on this by Szeliski at microsoft
research, he uses a nice 3-parameter system to compute the
homographies and it works really well, which I would higly recommend
to you.
Regards
Jason |
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| serg271 |
| Posted: Tue Apr 29, 2008 11:40 am |
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On Apr 29, 8:04 pm, damo suzuki <liquidt...@gmail.com> wrote:
Quote: On Mar 16, 10:44 am, J <ja...@visionexperts.co.uk> 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.
Quote: 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. |
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| damo suzuki |
| Posted: Tue Apr 29, 2008 8:21 pm |
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Guest
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On Apr 29, 11:40 pm, serg271 <serg...@gmail.com> wrote:
Quote: On Apr 29, 8:04 pm, damo suzuki <liquidt...@gmail.com> wrote:
On Mar 16, 10:44 am, J <ja...@visionexperts.co.uk> 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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