Homography transfer from point matches
View Patent ↗An infinity homography for an image pair within an image sequence is transferred to other image pairs within the image sequence utilizing point matches for the subject image pairs. An image set including the image pair for which the infinity homography is known and a third image are selected. Then intermediate parameters for homography transfer for one image pair overlapping the known infinity homography image pair is computed from the known infinity homography and epipoles and fundamental matrices of the overlapping image pairs, to derive the infinity homography for the selected overlapping image pair. The process may then be repeated until infinity homographies for all image pairs of interest within the image sequence have been derived.
1. A system for transferring a known infinity homography, comprising:
an image processor processing an image sequence, the image sequence comprising two images to which the known infinity homography applies and an additional image, wherein the image processor:
selects an image pair from the image sequence, the selected image pair including one of the two images to which the known infinity homography applies and the additional image determines intermediate transfer parameters for a homography for the selected image pair; and
derives an infinity homography for the selected image pair from the known infinity homography.
2. The system according to claim 1 , wherein the image processor determines a scalar multiple for the homography for the selected image pair and a vector multiple of epipoles for the selected image pair.
3. The system according to claim 1 , wherein the additional image is sequential within the image sequence to one of the two images to which the known infinity homography applies.
4. The system according to claim 1 , wherein the two images to which the known infinity homography applies are consecutive images within the image sequence.
5. The system according to claim 1 , wherein the two images to which the known infinity homography applies are consecutive images i,j within the image sequence, the additional image is image k consecutive with images i,j within the image sequence, wherein the image processor solves
c
jk
[
e
ik
]
x
H
jk
+
[
e
ik
]
x
e
jk
z
jk
T
=
c
ik
F
ik
H
ij
∞
-
1
,
where H jk is a homography for images j,k, c jk is a scalar multiple for the homography H jk , e jk are epipoles for images j,k,
z
jk
T
is a transpose of an unknown vector multiple for the epipoles e jk , [e ik ] x is derived from the epipoles e ik for images i,k, c ik is a scalar multiple for a homography H ik for images i,k, F ik is a fundamental matrix for images i,k, and
H
ij
∞
-
1
is an inverse of the known infinity homography.
6. The system according to claim 1 , wherein the known infinity homography relates image points for a second image within the image sequence to image points for a first image within the image sequence.
7. A system for processing an image sequence, comprising:
a video system including an input for receiving the image sequence, the image sequence comprising two images to which a known infinity homography applies and an additional image; and
an image processor within the video system processing the image sequence, wherein the image processor:
selects an image pair from the image sequence, the selected image pair including one of the two images to which the known infinity homography applies and the additional image determines intermediate transfer parameters for a homography for the selected image pair; and
derives an infinity homography for the selected image pair from the known infinity homography.
8. The system according to claim 7 , wherein the image processor determines a scalar multiple for the homography for the selected image pair and a vector multiple for epipoles for the selected image pair.
9. The system according to claim 7 , wherein the additional image is sequential within the image sequence to one of the two images to which the known infinity homography applies.
10. The system according to claim 7 , wherein the two images to which the known infinity homography applies are consecutive images within the image sequence.
11. The system according to claim 7 , wherein the two images to which the known infinity homography applies are consecutive images i,j within the image sequence, the additional image is image k consecutive with images i,j within the image sequence, wherein the image processor solves
c
jk
[
e
ik
]
x
H
jk
+
[
e
ik
]
x
e
jk
z
jk
T
=
c
ik
F
ik
H
ij
∞
-
1
,
where H jk is a homography for images j,k, c jk is a scalar multiple for the homography H jk , e jk are epipoles for images j,k,
z
jk
T
is a transpose of an unknown vector multiple for the epipoles e jk , [e ik ] x is derived from the epipoles e ik for images i,k, c ik is a scalar multiple for a homography H ik for images i,k, F ik is a fundamental matrix for images i,k, and
H
ij
∞
-
1
is an inverse of the known infinity homography.
12. The system according to claim 7 , wherein the known infinity homography relates image points for a second image within the image sequence to image points for a first image within the image sequence.
13. A method for transferring a known infinity homography for two images within an image sequence to other image pairs within the image sequence, comprising the steps of:
selecting an image pair from the image sequence, the selected image pair including one of the two images to which the known infinity homography applies and an additional image within the image sequence determining intermediate transfer parameters for a homography for the selected image pair; and
deriving an infinity homography for the selected image pair from the known infinity homography.
14. The method according to claim 13 , wherein the step of determining intermediate transfer parameters for a homography for the selected image pair further comprises:
determining a scalar multiple for the homography for the selected image pair and a vector multiple for epipoles for the selected image pair.
15. The method according to claim 13 , wherein the step of selecting an image pair from the image sequence further comprises:
selecting the additional image from images sequential within the image sequence to one of the two images to which the known infinity homography applies.
16. The method according to claim 13 , wherein the two images to which the known infinity homography applies are consecutive images within the image sequence.
17. The method according to claim 13 , wherein the two images to which the known infinity homography applies are consecutive images i,j within the image sequence, the additional image is image k consecutive with images i,j within the image sequence, and wherein the step of deriving an infinity homography for the selected image pair from the known infinity homography further comprises:
solving
c
jk
[
e
ik
]
x
H
jk
+
[
e
ik
]
x
e
jk
z
jk
T
=
c
ik
F
ik
H
ij
∞
-
1
,
where H jk is a homography for images j,k, c jk is a scalar multiple for the homography H jk , e jk are epipoles for images j,k,
z
jk
T
is a transpose of an unknown vector multiple for the epipoles e jk , [e ik ] z is derived from the epipoles e ik for images i,k, c ik is a scalar multiple for a homography H ik for images i,k, F ik is a fundamental matrix for images i,k, and
H
ij∞
-
1
is an inverse of the known infinity homography.