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. An image acquisition system comprising a lens assembled to project an image onto an image sensor, where the lens is tilted relative to the image sensor, the image acquisition system including a calibration module configured to:
acquire a set of calibrated parameters
n
→
≡
(
n
x
n
y
n
z
)
corresponding to said tilting of said lens, where z is the optical axis relative to which said lens is tilted;
acquire an image from said image sensor through said lens, where P x ′ and P y ′ indicate a coordinate of a pixel in said acquired image;
map image information from said 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
x
′
=
s
n
z
(
n
z
-
1
)
(
(
n
x
2
+
n
z
(
n
z
-
1
)
)
u
x
+
n
x
n
y
u
y
)
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 said lens tilt compensated image;
and store said lens tilt compensated image in a memory.
2. An image acquisition system according to claim 1 wherein said calibration module is configured to map image information by: selecting a pixel location u x , u y in said lens tilt compensated image, determining a corresponding coordinate P x ′, P y ′ in said acquired image, determining a plurality of pixel locations in said acquired image surrounding said coordinate, and interpolating pixel values for said surrounding pixel locations to determine a value for the pixel location in said lens tilt compensated image.
3. An image acquisition system according to claim 1 wherein said calibration module is configured to acquire said set of calibrated parameters
n
→
≡
(
n
x
n
y
n
z
)
by:
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 y =NY/d
n z =1/ d.
4. An image acquisition system comprising a lens assembled to proiect an image onto an image sensor, while the lens is tilted relative to the image sensor, the image acquisition system including a calibration module configured to:
acquire a set of calibrated parameters
n
→
≡
(
n
x
n
y
n
z
)
corresponding to said tilting of said lens, where z is the optical axis relative to which said lens is tilted;
acquire an image from said image sensor through said lens, where p x and p y indicate a location of a pixel in a lens tilt compensated image;
map image information from said lens tilt compensated image to said acquired 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
)
where λ comprises a scale factor given by:
λ
=
n
z
n
z
-
n
x
p
x
-
n
y
p
y
;
and
store said lens tilt compensated image in a memory.
5. An image acquisition system according to claim 4 wherein said calibration module is configured to map image information by: selecting a pixel location p x , p y in said lens tilt compensated image, determining a corresponding coordinate in said acquired image, determining a plurality of pixel locations in said acquired image surrounding said coordinate, and interpolating pixel values for said surrounding pixel locations to determine a value for the pixel location in said lens tilt compensated image.
6. An image acquisition system according to claim 4 wherein said calibration module is configured to acquire said set of calibrated parameters
n
→
≡
(
n
x
n
y
n
z
)
by:
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 y =NY/d
n z =1/ d.