Facsimile and static presentation processing – Static presentation processing – Attribute control
Reexamination Certificate
1999-06-29
2004-11-23
Rogers, Scott (Department: 2626)
Facsimile and static presentation processing
Static presentation processing
Attribute control
C358S003260, C358S003240, C358S519000
Reexamination Certificate
active
06822758
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to an image processing apparatus, image processing method, image sensing apparatus, control method for the image sensing apparatus, and a memory and, more particularly, to an image processing apparatus and method which improve a defective image (degraded image), image sensing apparatus suitably combined with the image processing apparatus, control method for the image sensing apparatus, and memory for controlling the execution of the methods. In this specification, an image called a degraded image indicates a poor-quality image that is out of focus or blurred due to inappropriate movement of a camera or inappropriate image sensing conditions such as an exposure instead of indicating an image having undergone a change from a good image to a degraded image due to a change in quality over time or the like.
As methods of improving a degraded image, e.g., an out-of-focus image or blurred image, into an image with little degradation (ideal image), methods using a Wiener filter, general inverted filter, projection filter, and the like are available. To use these methods, a degradation function must be determined first. An ideal method of determining such a degradation function is a method of analytically obtaining a degradation function from physical factors such as image sensing conditions or estimating a degradation function on the basis of an output from a measuring device (e.g., an acceleration sensor) mounted in an image sensing apparatus.
A degradation function will be described below. The relationship between an ideal image f(x, y), a degraded image g(x, y), a degradation function h(x, y, x′, y′), and random noise on output image &ngr;(x, y) is expressed as
∫∫
h
(
x,y,x′,y′
)
f
(
x′,y′
)
dx′dy′+&ngr;
(
x,y
) (1)
If an image having a degraded point is not located at the point, except for translation, a point spread function (PSF) is expressed by h(x−x′, y−y′), and mathematical expression (1) is rewritten into
∫∫
h
(
x−x′,y−y′
)
f
(
x′,y′
)
dx′dy′+&ngr;
(
x,y
) (2)
If there is no noise, a Fourier transform of the two sides of mathematical expression (2) is performed, and a convolution theorem is applied to the resultant expression, equation (3) is obtained:
G
(
u,v
)=
H
(
u,v
)
F
(
u,v
) (3)
where G(u, V) H(u, v), and F(u, V) are the Fourier transforms of g(x, y), f(x, y), and h(x, y).
H(u, v) is the transfer function of a system for transforming the ideal image f(x, y) into the degraded image g(x, y).
A degradation model in degradation (blur) due to a relative movement between a camera and a scene (object) will be described below as an example. Assume that an image on the image sensing element of the camera remains unchanged over time except this relative movement. If the relative movement is approximately equal to the movement of the image sensing element in the same plane, the total exposure light amount at one point on the image sensing element can be obtained by integrating an instantaneous exposure light amount with respect to an exposure time. Assume that the time required to open/close the shutter can be neglected. Letting &agr;(t) and &bgr;(t) be the x and y components of the displacement, equation (4) can be established:
g
(
x,y
)=∫
−T/2
T/2
f
(
x−&agr;
(
t
),
y−&bgr;
(
t
))
dt
(4)
where T is the exposure time, and the integration range is set from t=−T/2 to t=T/2 for the sake of convenience.
A Fourier transform of the two sides of equation (4) yields equation (5):
G
(
u
,
v
)
=
∫
ⅆ
x
∫
ⅆ
y
exp
[
-
j2
π
(
ux
-
vy
)
]
∫
-
T
/
2
T
/
2
ⅆ
tf
(
x
-
α
(
t
)
,
y
-
β
(
t
)
)
=
∫
-
T
/
2
T
/
2
ⅆ
t
∫
ⅆ
x
∫
ⅆ
yf
(
x
-
α
(
t
)
,
y
-
β
(
t
)
)
exp
[
-
j2
π
(
ux
-
vy
)
]
(
5
)
If x−&agr;(t)=&xgr; and y−&bgr;(t)=&eegr;, equation (5) is rewritten into equation (6):
G
(
u
,
v
)
=
∫
ⅆ
x
∫
∫
ⅆ
ξ
ⅆ
η
f
(
ξ
,
η
)
×
exp
[
-
j2
π
(
u
ξ
-
v
η
)
]
exp
[
-
j2
π
(
α
(
t
)
u
+
β
(
t
)
v
)
]
=
F
(
u
,
v
)
∫
-
T
/
2
T
/
2
exp
[
-
j2
π
(
u
α
(
t
)
+
v
β
(
t
)
)
]
ⅆ
t
=
F
(
u
,
v
)
H
(
u
,
v
)
(
6
)
According to equation (6), the degradation is modeled by equation (3) or mathematical expression (2) which is equivalent to equation (3). The transfer function H(u, v) for this degradation is given by
H
(
u, v
)=∫
−T/2
T/2
exp[−
j
2&pgr;(
u&agr;
(
t
)+
v&bgr;
(
t
))]
dt
(7)
In this case, if camera shake occurs in a direction at an angle &thgr; with respect to the x-axis at a predetermined speed V for a time T, a point response function is given as
H
(
u
,
v
)
=
sin
πω
T
πω
(
8
)
where &ohgr; is given by equation (9)
&ohgr;—(
u−u
o
)
V
cos &thgr;+(
v−v
o
)
V
sin &thgr; (9)
where u
o
and v
o
are the center coordinates of the image. When &ohgr; is minimum, H(u, v)=T is approximately established.
Likewise, a degradation model of degradation due to a blur can be expressed by a function. Assume that a phenomenon of blurring is based on a normal (Guassian) distribution rule. In this case, letting r be the distance from a central pixel and &sgr;
2
is an arbitrary parameter in the normal distribution rule, a degradation function h(r) is given by
h
(
r
)
=
1
σ
2
π
exp
(
-
r
2
σ
2
)
(
10
)
Processing for improving a degraded image using an inverted filter will be described next. Assume that the degraded image g(x, y) and the ideal image f(x, y) are based on the model expressed by mathematical expression (2). If there is no noise, the Fourier transforms of g(x, y), f(x, y), PSF, and h(x, y) satisfy equation (3). In this case, equation (3) is modified into
F
(
u,v
)=
G
(
u,v
)/
H
(
u,v
) (11)
According to equation (11), if H(u, v) is known, the ideal image f (x, y) can be improved by multiplying the Fourier transform G(u, v) of the degraded image by 1/H(u, v) and performing an inverse Fourier transform of the product. In other words, the transfer function of the filter is 1/H(u, v).
In practice, the application of equation (3) poses various problems. For example, in consideration of noise, mathematical expression (2) can be written into
G
(
u,v
)=
H
(
u,v
)
F
(
u,v
)+
N
(
u,v
) (12)
where N(u, v) is the Fourier transform of &ngr;(x, y).
According to equation (12), when the filter (1/H) (u, v)) is applied to the Fourier transform of the degraded image, equation (13) is established:
G
(
u
,
v
)
H
(
u
,
v
)
=
F
(
u
,
v
)
+
N
(
u
,
v
)
H
(
u
,
v
)
(
13
)
Consider a system in which the degraded image recorded by the digital camera is loaded into an information processing apparatus by an image receiving unit controlled by a TWAIN driver or the like, and the degraded image is improved to generate an ideal image. In this case, a technique of determining a degradation function obtained by modeling the process of generating a degraded image, and improving the degraded image by using an image improving algorithm generally called deconvolution using a Wiener filter or the like is considered as the most effective improving technique.
In such a conventional technique, however, since no consideration
Canon Kabushiki Kaisha
Morgan & Finnegan , LLP
Rogers Scott
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