Method and apparatus for obtaining rectilinear images using rotationally symmetric wide-angle lens
View Patent ↗The present invention provides mathematically accurate image processing algorithms for extracting natural looking panoramic images and distortion-free rectilinear images from images acquired using a camera equipped with a wide-angle lens which is rotationally symmetric about an optical axis and devices implementing such algorithms. Imaging systems using this method can be used not only in security•surveillance applications for indoor and outdoor environments, but also in diverse areas such as video phone for apartment entrance door, rear view camera for vehicles, visual sensor for unmanned aerial vehicles and robots, camera phone, PC camera, and broadcasting camera. Also, it can be used to obtain panoramic or rectilinear photographs using a digital camera.
1. An imaging system comprising:
an image acquisition means configured for acquiring an uncorrected image plane using a wide-angle lens rotationally symmetric about an optical axis,
an image processing means configured for extracting a rectilinear image plane from the uncorrected image plane; and
an image display means configured for displaying the rectilinear image plane on a rectangular screen,
wherein,
if a coordinate of an image point on the rectangular screen corresponding to an object point having a coordinate (X, Y, Z) in a world coordinate system, which has a nodal point of the wide-angle lens as an origin and a vertical line passing through the origin as an Y-axis, is given as (x″, y″),
arbitrary straight lines in the world coordinate system appear as straight, lines on the screen,
wherein,
the uncorrected image plane is a two dimensional array with K max rows and L max columns,
a pixel coordinate of the optical axis on the uncorrected image plane is (K o , L o ),
a real projection scheme of the lens is an image height r obtained as a function of a zenith angle θ of a corresponding incident ray and given as r=r(θ),
a magnification ratio g of the camera is given as
g
≡
r
′
r
=
1
p
,
wherein r′ is a pixel distance on the uncorrected image plane corresponding to the image height r,
and p is a linear dimension of a square pixel in the image sensor plane,
the processed image plane is a two dimensional array with I max rows and J max columns,
a pixel coordinate of the optical axis on the processed image plane is (I o −ΔI, J o −ΔJ),
wherein (I o , J o ) is given as
(
I
o
,
J
o
)
=
(
1
+
I
m
a
x
2
,
1
+
J
m
a
x
2
)
,
and ΔI and ΔJ are arbitrary pixel distances,
a video signal value for the pixel having a coordinate (I, J) on the processed image plane is given as a video signal value of an imaginary pixel on the uncorrected image plane having a coordinate (x′ I,J , y′ I,J ),
wherein the pixel coordinate (x′ I,J , y′ I,J ) of the imaginary pixel is given by a following set of equations.
s
″
=
J
m
a
x
-
1
2
tan
(
Δ
ψ
2
)
θ
i
,
j
=
tan
-
1
{
(
I
-
I
o
+
Δ
I
)
2
+
(
J
-
J
o
+
Δ
J
)
2
s
″
}
ϕ
i
,
j
=
tan
-
1
(
I
-
I
o
+
Δ
I
J
-
J
o
+
Δ
J
)
x
i
,
j
′
=
L
o
+
gr
(
θ
i
,
j
)
cos
(
ϕ
i
,
j
)
y
i
,
j
′
=
K
o
+
gr
(
θ
i
,
j
)
sin
(
ϕ
i
,
j
)
.
2. A method of obtaining a rectilinear image, the method comprising:
acquiring an uncorrected image plane using a camera equipped with a wide-angle lens rotationally symmetric about an optical axis; and
extracting a processed image plane from the uncorrected image plane,
wherein,
the uncorrected image plane is a two dimensional array with K max rows and L max columns,
a pixel coordinate of the optical axis on the uncorrected image plane is (K o , L o )
a real projection scheme of the lens is an image height r obtained as a function of a zenith angle θ of a corresponding incident ray and given as r=r(θ),
a magnification ratio g of the camera is given as
g
≡
r
′
r
=
1
p
,
wherein r′ is a pixel distance on the uncorrected image plane corresponding to the image height r,
and p a linear dimension of a square pixel ire the image sensor plane,
the processed image plane is a two dimensional array with I max rows and J max columns,
a pixel coordinate of the optical axis on the processed image plant is (I o −ΔI, J o −ΔJ),
wherein (I o , J o ) is given as
(
I
o
,
J
o
)
=
(
1
+
I
m
a
x
2
,
1
+
J
m
a
x
2
)
,
and ΔI and ΔJ are arbitrary pixel distances,
a video signal value for the pixel having a coordinate (I, J) on the processed image plane is given as a video signal value of an imaginary pixel on the uncorrected image plane having a coordinate (x′ I,J , y′ I,J ),
wherein the pixel coordinate (x′ I,J , y′ I,J ) of the imaginary pixel is given by a following set of equations,
s
″
=
J
m
a
x
-
1
2
tan
(
Δ
ψ
2
)
θ
i
,
j
=
tan
-
1
{
(
I
-
I
o
+
Δ
I
)
2
+
(
J
-
J
o
+
Δ
J
)
2
s
″
}
ϕ
i
,
j
=
tan
-
1
(
I
-
I
o
+
Δ
I
J
-
J
o
+
Δ
J
)
x
i
,
j
′
=
L
o
+
gr
(
θ
i
,
j
)
cos
(
ϕ
i
,
j
)
y
i
,
j
′
=
K
o
+
gr
(
θ
i
,
j
)
sin
(
ϕ
i
,
j
)
.