Pixel interpolating device capable of preventing noise...

Details Pixel interpolating device capable of preventing noise... Pixel interpolating device capable of preventing noise...

1999-01-25

2003-05-20

Mehta, Bhavesh (Department: 2625)

Image analysis

Image transformation or preprocessing

Changing the image coordinates

C358S525000

Reexamination Certificate

active

06567568

ABSTRACT:

This application is based on applications Nos. 10-012532 and 10-029691 filed in Japan, the contents of which is hereby incorporated by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to pixel interpolating devices and more particularly to a pixel interpolating device using the IM-GPDCT method for interpolating a pixel while restoring a high frequency component of an image.
2. Description of the Related Art
In converting a pixel density (interpolating a pixel) of an image based on image information included in a sampled original image, a method (“IM-GPDCT method”) is conventionally known which restores a spatial high frequency component, which is lost during a sampling process, under the two restrictive conditions that information on a passing frequency band is correct and an expanse of an image is limited in a process in which normal transformation and inverse transformation of the image are repeated by orthogonal transformation.
The principle of the method will be described in the following. An operation is known which restores an original signal that is lost because a frequency band is limited when an original image is sampled. Such an operation is generally accompanied by the super-resolution problem.
In any observation system that can physically be implemented, a high frequency component of at least a certain frequency cannot be observed.
For example, an image pick-up system has a limited size of an entrance aperture, and the image pick-up system itself functions as a low pass filter (LPF). Thus, a large number of frequency components that can be propagated are lost, and resolution is lowered.
The lost resolution can be obtained only by bandwidth extrapolation (super-resolution problem) in which an original signal prior to passage through the image pick-up system is found from an image signal that can be obtained through the image pick-up system.
The super-resolution problem is mathematically formulated for a function of one variable as described below. When an original signal in a real space region is f(x), a signal that is formed by limiting the frequency component band of original signal f(x) to cut-off frequency u
0
at most and that actually passes through an image pick-up system is g(x), and the process for carrying out band limitation is expressed as A, the expression (1) below is derived.
g
(
x
)=
Af
(
x
)  (1)
The process A corresponds to actual application of an LPF by passing the original signal through the image pick-up system.
The functions that correspond to Fourier transform of signals f(x) and g(x) above are assumed to be F(u) and G(u), and a window function W(u) in a frequency region is defined by the following expressions (2) and (3).
W
(
u
)=1(|
u|≦u
0
)  (2)
W
(
u
)=0(|
u|>u
0
)  (3)
Performance of window function W(u) corresponds to application of an ideal LPF.
Further, the expression (1) above is expressed in a frequency region as the expression (4) below.
G
(
u
)=
W
(
u
)
F
(
u
)  (4)
The super-resolution problem is intended to find original signal f(x) from band-limited signal g(x) by the expression (1) in a real space region and to find F(u) from G(u) of the expression (4) in a frequency region.
If original signal f(x) is not limited at all, however, F(u) cannot be found.
Accordingly, the super-resolution problem can be solved by applying a process in which unlimited resolution can be obtained in principle when original signal f(x) is subjected to spatial region limitation so that an object has a limited size, and f(x) only exists in a certain region, a region between −x
0
and +x
0
, for example, and it does not exist outside the region.
Conventionally, the Gerchberg-Papoulis iteration method (GP iteration method) is used to solve the super-resolution problem.
FIG. 14
illustrates the principle of the GP iteration method. In FIG.
14
(A), (C), (E) and (G) correspond to a frequency region while (B), (D), (F) and (H) correspond to a real space region. FIG.
14
(B) shows original signal f(x) of which region is limited to a space |x|≦x
0
. FIG.
14
(A) shows Fourier transform F(u) of original signal f(x), and F(u) includes even an unlimitedly high frequency component because the region of original signal f(x) is limited.
FIG.
14
(C) indicates that only G(u), which is the part of the space |u|≦u
0
of F(u), is observed. In other words, the expression (4) using a window function such as the expressions (2) and (3) above is formed.
Inverse Fourier transform of G(u) is g(x) in FIG.
14
(D). Solving the super-resolution problem is to find F(u) or f(x) from G(u) above.
The operation in the GP iteration method will be described in the following. Since the band of G(u) is limited to |u|≦u
0
, g(x) extends unlimitedly.
Since it is known that the region of original signal f(x) is limited to the interval |x|≦x
0
, however, the same region limitation is performed even on g(x).
In short, only the part of interval |x|≦x
0
in g(x) is extracted to obtain f
1
(x). When f
1
(x) is expressed as an expression that uses a window function w(x) expressed by the following expressions (5) and (6), the expression (7) is obtained. This is function f
1
(x) shown in FIG.
14
(F).
w
(
x
)=1(|
x|≦x
0
)  (5)
w
(
x
)=0(|
x|>x
0
)  (6)
f
1
(
x
)=
w
(
x
)
g
(
x
)  (7)
Fourier transform of f
1
(x) results in F
1
(u) in FIG.
14
(E). Since the region of f
1
(x) is limited, F
1
(u) extends unlimitedly. However, a correct value of G(u)=F(u) is already known for space |u|≦u
0
, and therefore the portion of |u|=≦u
0
in F
1
(u) is substituted by G(u).
The waveform formed in this manner is G
1
(u) in FIG.
14
(G). The relations are expressed by the expressions (8) to (10). Inverse Fourier transform of G
1
(u) above is g
1
(x) in FIG.
11
(H).
G
1
(
u
)=
G
(
u
)+(1
−W
(
u
))
F
1
(
u
)  (8)
G
1
(
u
)=
G
(
u
)(|
u|≦u
0
)  (9)
G
1
(
u
)=
F
1
(
u
)(|
u|>u
0
)  (10)
The processing from (C), (D) to (G), (H) in
FIG. 14
is the first round of the GP iteration method. Then, the operation of extracting only the portion of interval |x|=≦u
0
from g
1
(x) in FIG.
14
(H), carrying out Fourier transform on f
2
(x) (not shown) corresponding to f
1
(x) in FIG.
14
(F), and finding F
2
(u) (not shown) corresponding to FIG.
14
(E) is repeatedly performed. Thus, an original signal can perfectly be restored.
Conventionally, an operation load is reduced by substituting Fourier transform in the GP iteration method by discrete cosine transform (DCT). This is called the “IM-GPDCT” method.
FIG. 15
is a flow chart schematically showing a processing flow carried out in image magnification processing (an example of pixel interpolation processing) using the conventional IM-GPDCT method, and
FIG. 16
illustrates the processing of the flow chart in FIG.
15
.
It is assumed here that an original image consisting of N×N pixels shown in FIG.
16
(A) is magnified m times to produce an image of (N×m)
2
pixels. In
FIG. 16
, the numbers in parenthesis correspond to the step numbers of the flow chart in FIG.
15
.
Referring to
FIG. 15
, the number of iteration times in the GP iteration method and the value of a magnification rate (resolution conversion rate) are set in step S
1
. In step S
2
, an original image to be magnified, shown in FIG.
16
(A), is read. In step S
3
, an image of interest (herein, an image shown in FIG.
16
(A)) is extracted.
In step S
4
, an image extending around the image of interest of N×N pixels (extension region) is found to limit the spatial expanse of the image. Conventionally, the data of an image to be extended is fixed to a particular value, and calculation of extension region data

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