Method for compensating for off-axis tilting of a lens
A method for compensating for off-axis tilting of a lens relative to an image sensor in an image acquisition device comprises acquiring a set of calibrated parameters n → ≡ ( n x n y n z ) corresponding to the tilting of said lens. P′ x and P′ y indicate a coordinate of a pixel in an acquired image. Image information is mapped from the acquired image to a lens tilt compensated image according to the formulae: P x ′ = s n z ( n z - 1 ) ( ( n x 2 + n z ( n z - 1 ) ) u x + n x n y u y ) P y ′ = s n z ( n z - 1 ) ( ( n y 2 + n z ( n z - 1 ) ) u y + n x n y u x ) where s comprises a scale factor given by s = n z u x n x + u y n y + n z and where u x and u y indicate the location of a pixel in the lens tilt compensated image.
1. A method comprising:
acquiring a set of calibrated parameters
n
→
≡
(
n
x
n
y
n
z
)
corresponding to tilting of a lens relative to an optical axis normal to an image sensor;
acquiring an image from the image sensor through the lens, where P x ′ and P y ′ indicate a coordinate of a pixel in the acquired image;
mapping image information from the acquired image to a lens tilt compensated image according to the formulae:
P
x
′
=
s
n
z
(
n
z
-
1
)
(
(
n
x
2
+
n
z
(
n
z
-
1
)
)
u
x
+
n
x
n
y
u
y
)
P
y
′
=
s
n
z
(
n
z
-
1
)
(
(
n
y
2
+
n
z
(
n
z
-
1
)
)
u
y
+
n
x
n
y
u
x
)
wherein s comprises a scale factor given by
s
=
n
z
u
x
n
x
+
u
y
n
y
+
n
z
,
and
wherein u x and u y indicate a location of a pixel in the lens tilt compensated image; and
storing the lens tilt compensated image in a memory.
2. A method according to claim 1 , wherein the mapping comprises:
selecting a pixel location u x , u y in the lens tilt compensated image, determining a corresponding coordinate P x ′, P y ′ in the acquired image,
determining a plurality of pixel locations in the acquired image surrounding the coordinate, and
interpolating pixel values for the surrounding pixel locations to determine a value for the pixel location in the lens tilt compensated image.
3. A method according to claim 1 , wherein acquiring the set of calibrated parameters
n
->
≡
(
n
x
n
y
n
z
)
comprises:
acquiring a pair of calibrated scalar parameters NX, NY;
determining a length d=sqrt(NX 2 +NY 2 +1); and
calculating the components of {right arrow over (n)} as follows:
n x =NX/d
n=NY/d
n z =1/ d.
4. A method according to claim 1 , wherein the lens is integrally formed into an image acquisition system.
5. A method according to claim 1 , wherein the lens is interchangeable with a camera body.
6. A method comprising:
acquiring a set of calibrated parameters
n
->
≡
(
n
x
n
y
n
z
)
corresponding to tilting of a lens relative to an optical axis normal to an image sensor;
acquiring an image from the image sensor through the lens, where p x and p y indicate a coordinate of a pixel in the acquired image;
mapping image information from the acquired image to a lens tilt compensated image according to the formulae:
p
x
↦
λ
n
z
(
1
+
n
z
)
(
(
n
x
2
+
n
z
(
1
+
n
z
)
)
p
x
+
n
x
n
y
p
y
)
p
y
↦
λ
n
z
(
1
+
n
z
)
(
(
n
y
2
+
n
z
(
1
+
n
z
)
)
p
y
+
n
x
n
y
p
x
)
wherein λ comprises a scale factor given by
λ
=
n
z
n
z
-
n
x
p
x
-
n
y
p
y
;
and
storing the lens tilt compensated image in a memory.
7. A method according to claim 6 , wherein the mapping comprises:
selecting a pixel location p x , p y in the lens tilt compensated image, determining a corresponding coordinate in the acquired image,
determining a plurality of pixel locations in the acquired image surrounding the coordinate, and
interpolating pixel values for the surrounding pixel locations to determine a value for the pixel location in the lens tilt compensated image.
8. A method according to claim 6 , wherein acquiring the set of calibrated parameters
n
->
≡
(
n
x
n
y
n
z
)
comprises:
acquiring a pair of calibrated scalar parameters NX, NY;
determining a length d=sqrt(NX 2 +NY 2 +1); and
calculating the components of {right arrow over (n)} as follows:
n x =NX/d
n=NY/d
n z =1/ d.
9. A method according to claim 6 , wherein the lens is integrally formed into an image acquisition system.
10. A method according to claim 6 , wherein the lens is interchangeable with a camera body.
11. A non-transitory computer-readable storage medium storing instructions that, when executed, cause a processor to perform operations comprising:
acquiring a set of calibrated parameters
n
->
≡
(
n
x
n
y
n
z
)
corresponding to tilting of a lens relative to an optical axis normal to an image sensor;
acquiring an image from the image sensor through the lens, where P x ′ and P y ′ indicate a coordinate of a pixel in the acquired image;
mapping image information from the acquired image to a lens tilt compensated image according to the formulae:
P
x
′
=
s
n
z
(
n
z
-
1
)
(
(
n
x
2
+
n
z
(
n
z
-
1
)
)
u
x
+
n
x
n
y
u
y
)
P
y
′
=
s
n
z
(
n
z
-
1
)
(
(
n
y
2
+
n
z
(
n
z
-
1
)
)
u
y
+
n
x
n
y
u
x
)
wherein s comprises a scale factor given by
s
=
n
z
u
x
n
x
+
u
y
n
y
+
n
z
,
and
wherein u x and u y indicate a location of a pixel in the lens tilt compensated image; and
storing the lens tilt compensated image in a memory.
12. A non-transitory computer-readable storage medium according to claim 11 , wherein the mapping comprises:
selecting a pixel location u x , u y in the lens tilt compensated image,
determining a corresponding coordinate P x ′, P y ′ in the acquired image,
determining a plurality of pixel locations in the acquired image surrounding the coordinate, and
interpolating pixel values for the surrounding pixel locations to determine a value for the pixel location in the lens tilt compensated image.
13. A non-transitory computer-readable storage medium according to claim 11 , wherein acquiring the set of calibrated parameters
n
->
≡
(
n
x
n
y
n
z
)
comprises:
acquiring a pair of calibrated scalar parameters NX, NY;
determining a length d=sqrt(NX 2 +NY 2 +1); and
calculating the components of {right arrow over (n)} as follows:
n x =NX/d
n=NY/d
n z =1/ d.
14. A non-transitory computer-readable storage medium according to claim 11 , wherein the lens is integrally formed into an image acquisition system.
15. A non-transitory computer-readable storage medium according to claim 11 , wherein the lens is interchangeable with a camera body.
16. A non-transitory computer-readable storage medium storing instructions that, when executed, cause a processor to perform operations comprising:
acquiring a set of calibrated parameters
n
->
≡
(
n
x
n
y
n
z
)
corresponding to tilting of a lens relative to an optical axis normal to an image sensor;
acquiring an image from the image sensor through the lens, where p x and p y indicate a coordinate of a pixel in the acquired image;
mapping image information from the acquired image to a lens tilt compensated image according to the formulae:
p
x
↦
λ
n
z
(
1
+
n
z
)
(
(
n
x
2
+
n
z
(
1
+
n
z
)
)
p
x
+
n
x
n
y
p
y
)
p
y
↦
λ
n
z
(
1
+
n
z
)
(
(
n
y
2
+
n
z
(
1
+
n
z
)
)
p
y
+
n
x
n
y
p
x
)
wherein λ comprises a scale factor given by
λ
=
n
z
n
z
-
n
x
p
x
-
n
y
p
y
;
and
storing the lens tilt compensated image in a memory.
17. A non-transitory computer-readable storage medium according to claim 16 , wherein the mapping comprises:
selecting a pixel location p x , p y in the lens tilt compensated image, determining a corresponding coordinate in the acquired image,
determining a plurality of pixel locations in the acquired image surrounding the coordinate, and
interpolating pixel values for the surrounding pixel locations to determine a value for the pixel location in the lens tilt compensated image.
18. A non-transitory computer-readable storage medium according to claim 16 , wherein acquiring the set of calibrated parameters
n
->
≡
(
n
x
n
y
n
z
)
comprises:
acquiring a pair of calibrated scalar parameters NX, NY;
determining a length d=sqrt(NX 2 +NY 2 +1); and
calculating the components of {right arrow over (n)} as follows:
n x =NX/d
n=NY/d
n z =1/ d.
19. A non-transitory computer-readable storage medium according to claim 16 , wherein the lens is integrally formed into an image acquisition system.
20. A non-transitory computer-readable storage medium according to claim 16 , wherein the lens is interchangeable with a camera body.