Facsimile and static presentation processing – Natural color facsimile – Interpolation
Reexamination Certificate
1998-12-03
2002-05-21
Coles, Edward (Department: 2722)
Facsimile and static presentation processing
Natural color facsimile
Interpolation
C382S300000, C358S426010, C358S518000
Reexamination Certificate
active
06392765
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to an interpolating operation method and apparatus for an image signal.
2. Description of the Prior Art
Techniques for photoelectrically reading out an image, which has been recorded on a photographic film, in order to obtain an image signal, carrying out appropriate image processing on the image signal, and then reproducing a visible image by use of the processed image signal have heretofore been known in various fields. In image recording and reproducing systems, in which an image signal is obtained and a visible image is reproduced from the image signal, in cases where the region of interest in the visible image is to be viewed in more detail, the region of interest is often enlarged and reproduced. In such cases, if the enlargement of the image size is carried out such that the number of the image signal components of the image signal representing the enlarged image may be identical with the number of the image signal components of the original image signal representing the original image, the sharpness of the enlarged image will be recognized to be lower than the sharpness of the original image due to the visual characteristics of persons. Therefore, if the image is merely enlarged and reproduced, an enlarged image having a high sharpness cannot be obtained, and the details of the image cannot be viewed accurately.
In order for the aforesaid problems to be eliminated, a predetermined interpolating operation may be carried out on the original image signal, which has been obtained by reading out an original image, and an interpolation image signal, which is a secondary image signal and is made up of a number of image signal components different from that of the original image signal, may thereby be formed. Specifically, in cases where an enlarged image is to be reproduced, an interpolation image signal, which is made up of a number of image signal components larger than that of the original image signal, may be formed from the interpolating operation. A visible image may then be reproduced from the interpolation image signal. In this manner, the sharpness of the enlarged image can be prevented from becoming low.
As the interpolating operation methods for carrying out interpolating operations on image signals, various methods have heretofore been proposed. Among such methods, the method using third-order spline interpolating functions is popular. With the interpolating operation method using the third-order spline interpolating functions, digital original image signal components {Z
k
} in each section are connected by a third-order function {f
k
}, and the value of f
k
corresponding to a position, at which an interpolation point is set, (i.e., a setting position in each section) is taken as the value of the interpolated image signal component.
The interpolating operations, which pass through the original image signal in the manner described above, can yield an image having a comparatively high sharpness. As such interpolating operations, cubic spline interpolating operations, and the like, are known. How the cubic spline interpolating operations are carried out will be described hereinbelow.
FIG. 18
is an explanatory graph showing how interpolated image signal components are obtained with a cubic spline interpolating operation from original image signal components, which are sampled with a period of an equal interval and represent sampling points (picture elements) arrayed in one direction. As illustrated in
FIG. 18
, the image signal components (the original image signal components), which have been detected as digital signal components from an original image and represent a series of picture elements X
k−2
, X
k−1
, X
k
, X
k+1
, X
k+2
, . . . , are respectively represented by Z
k−2
, Z
k−1
, Z
k
, Z
k+1
, Z
k+2
, . . . A third-order spline interpolating function is set for each of sections X
k−2
~X
k−1
, X
k−1
~X
k
, X
k
~X
k+1
, and X
k+1
~X
k+2
. The spline interpolating functions corresponding to the respective sections are represented by f
k−2
, f
k−1
, f
k
, f
k+1
, and f
k+2
. The interpolating functions are the third-order functions, in which the position in each section serves as a variable.
Firstly, how the interpolating operation is carried out when a point taken for interpolation (hereinbelow referred to as the interpolation point) X
p
falls within the section X
k
~X
k+1
will be described hereinbelow. The spline interpolating function f
k
corresponding to the section X
k
~X
k+1
is represented by Formula (1) shown below.
f
k
(x)=A
k
x
3
+B
k
x
2
+C
k
x+D
k
(1)
In the cubic spline interpolating operation, it is necessary that the spline interpolating function f
k
passes through the original sampling points (picture elements), and that the first-order differential coefficient of the spline interpolating function f
k
is continuous between adjacent sections. Therefore, it is necessary for Formulas (2), (3), (4), and (5) shown below to be satisfied.
f
k
(X
k
)=Z
k
(2)
f
k
(X
k+1
)=Z
k+1
(3)
f
k
′(X
k
)=f
k−1
′(X
k
) (4)
f
k
′(X
k+1
)=f
k+1
′(X
k+1
) (5)
In these formulas, f
k
′ represents the first-order differentiation (3A
k
x
2
+2B
k
x+C
k
) of the function f
k
.
In the strict sense, the cubic spline interpolating operation contains the continuity conditions of the second-order differential coefficient. However, with continuity conditions of the second-order differential coefficient, the operation formulas become complicated. Therefore, the cubic spline interpolating operation is popularly carried out in the form simplified in the manner described above.
Also, in the cubic spline interpolating operation, it is necessary for the first-order differential coefficient at the picture element X
k
to satisfy the condition with respect to the picture elements X
k−1
and X
k+1
, which are located before and after the picture element X
k
, in that the first-order differential coefficient at the picture element X
k
should coincide with the gradient (Z
k+1
−Z
k−1
)/(X
k+1
−X
k−1
) of the image signal components Z
k−1
and Z
k+1
representing the picture elements X
k−1
and X
k+1
. Therefore, it is necessary for Formula (6) shown below to be satisfied.
f
k
′(X
k
)=(Z
k+1
−Z
k−1
)/(X
k+1
−X
k−1
) (6)
Also, it is necessary for the first-order differential coefficient at the picture element X
k+1
to satisfy the condition with respect to the picture elements X
k
and X
k+2
, which are located before and after the picture element X
k+1
, in that the first-order differential coefficient at the picture element X
k+1
should coincide with the gradient (Z
k+2
−Z
k
)/(X
k+2
−X
k
) of the image signal components Z
k
and Z
k+2
representing the picture elements X
k
and X
k+2
. Therefore, it is necessary for Formula (7) shown below to be satisfied.
f
k
′(X
k+1
)=(Z
k+2
−Z
k
)/(X
k+2
−X
k
) (7)
It is herein assumed that the interval (i.e., the lattice interval) of each of sections X
k−2
~X
k−1
, X
k−1
~X
k
, X
k
~X
k+1
, and X
k+1
~X
k+2
is equal to 1, and the position of the interpolation point X
p
, which is taken from the picture element X
k
toward the picture element X
k+1
, is represented by t (0≦t≦1). In such cases, from Formulas (1) through (7), the formulas shown below obtain.
f
k
(0)=D
k
=Z
k
f
k
(1)=A
k
+B
k
+C
k
+D
k
=Z
k+1
f
k
′(0)=C
k
=(Z
k+1
−Z
k−1
)/2
f
k
′(1)=3A
k
+2B
k
+C
k
=(Z
k+2
−Z
Carter Tia A.
Coles Edward
Fuji Photo Film Co. , Ltd.
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