Interpolating operation method and apparatus for image signals

An interpolating operation is carried out on original image signal components which make up an original image signal representing an original image and represent values of original picture elements arranged in a grid pattern at predetermined intervals to obtain interpolation image signal components representing values of interpolation picture elements arranged in a grid pattern at intervals different from those of the original picture elements. Each interpolation image signal component is operated by multiplying the image signal components for a plurality of original picture elements adjacent to the interpolation picture element by respective interpolation coefficients calculated from the image signal components for the adjacent original picture elements. The density vector at the interpolation picture element on the original image represented is calculated, distances of the respective adjacent original picture elements from a segment perpendicular to the density vector are calculated, the interpolation coefficient is corrected to be smaller as the density vector and/or the distance of the original picture element from the segment becomes larger, and the interpolating operation is carried out on the basis of the corrected interpolation coefficient.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to an interpolating operation method and apparatus 
for an image signal, and more particularly to an interpolating operation 
method and apparatus for an image signal applied at least to a portion of 
an image where an edge portion, in which change in density is sharp, 
extends obliquely. 
2. Description of the Related Art 
Techniques for photoelectrically reading out an image, which has been 
recorded on a radiation 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. For example, there has been put 
into practice a technique of reproducing a high quality image excellent in 
contrast, sharpness, graininess and the like by recording an X-ray image 
on X-ray film having a low .gamma. value designed to conform to subsequent 
image processing, photoelectrically reading out the X-ray image from the 
X-ray film, thereby obtaining an image signal, carrying out image 
processing on the image signal and reproducing a visible image as a 
photograph or the like by use of the processed image signal. See Japanese 
Patent Publication No. 61(1986)-5193. 
When certain kinds of phosphors are exposed to radiation such as X-rays, 
.alpha.-rays, .beta.-rays, .gamma.-rays, cathode rays or ultraviolet rays, 
they store a part of the energy of the radiation. Then, when the phosphor 
which has been exposed to the radiation is exposed to stimulating rays 
such as visible light, light is emitted from the phosphor in proportion to 
the stored energy of the radiation. A phosphor exhibiting such properties 
is referred to as "a stimulable phosphor". It has been proposed to use 
stimulable phosphors in radiation image recording and reproducing systems. 
Specifically, a radiation image of an object, such as a human body, is 
recorded on a sheet provided with a layer of the stimulable phosphor 
(hereinafter referred to as a stimulable phosphor sheet). The stimulable 
phosphor sheet, on which the radiation image has been stored, is then 
exposed to stimulating rays, such as a laser beam, which cause it to emit 
light in proportion to the amount of energy stored thereon during its 
exposure to the radiation. The light emitted by the stimulable phosphor 
sheet, upon stimulation thereof, is photoelectrically detected and 
converted into an electric image signal. The image signal is then 
processed and used for the reproduction of the radiation image of the 
object as a visible image on a recording material, such as photographic 
material, or on a display device such as a cathode ray tube (CRT) display 
device. See Japanese Unexamined Patent Publication No. 56(1981)-11395, 
U.S. Pat. Nos. 4,528,264, 4,315,318, 4,387,428, 4,276,473, and the like. 
Radiation image recording and reproducing systems, which use stimulable 
phosphor sheets, have been put into practice and are advantageous over 
conventional radiography using silver halide photographic materials, in 
that images can be recorded even when the energy intensity of the 
radiation, to which the stimulable phosphor sheet is exposed, varies over 
a wide range. 
In image recording and reproducing systems, in which an image signal is 
obtained in the manner described above 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. Such an enlarged image can be obtained by 
carrying out a predetermined interpolating operation on the original image 
signal, which has been obtained by reading out an original image, forming 
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, and reproducing a visible image from the 
interpolation image signal. 
In view of easiness to arrange an image input/output system, picture 
elements are generally arranged in a square grid pattern. In such a 
system, interpolated image signal components are obtained by carrying out 
linear interpolation on original image signal components of four original 
picture elements around each of points at which additional picture 
elements are to be set (interpolation points). 
For example, in FIG. 8A, x denotes of original picture elements P arranged 
in a square grid pattern and x denotes each of interpolation points P' 
which are arranged in a square grid pattern finer than that of original 
picture elements. The interpolated image signal component corresponding, 
for instance, to interpolation point P'0 can be obtained in the following 
manner. 
The image signal components S.sub.A, S.sub.B, S.sub.C and S.sub.D of four 
original picture elements P.sub.A, P.sub.B, P.sub.C and P.sub.D around the 
interpolation point P'0 are used. 
Assuming that the interval of each of sections P.sub.A .about.P.sub.B, 
P.sub.C .about.P.sub.D, P.sub.A .about.P.sub.C and P.sub.B .about.P.sub.D 
is equal to 1, the distance of the interpolation point P'0 from the 
original picture element P.sub.A (P.sub.C) as measured in the direction of 
x-axis (in the transverse direction) is Tx and the distance of the 
interpolation point P'0 from the original picture element P.sub.A 
(P.sub.B) as measured in the direction of y-axis (in the longitudinal 
direction) is Ty as shown in FIG. 8B, interpolation image signal 
components S'm and S'n for interpolation points P'm and P'n aligned with 
the interpolation point P'0 in the direction of y-axis are first obtained 
by linear interpolation according to the following Formulas (17) and (18). 
EQU S'm=(1-Tx)S.sub.A +TxS.sub.B ( 17) 
EQU S'n=(1-Tx)S.sub.C +TxS.sub.D ( 18) 
Then with respect to the direction of y-axis, linear interpolating 
operation is carried out according to the following Formula (19) including 
the interpolation image signal components S'm and S'n, thereby obtaining 
interpolation image signal component S'0 for the interpolation point P'0. 
EQU S'0=(1-Ty)S'm+TyS'n (19) 
The operations described above are repeated for the other interpolation 
points P' in order to obtain interpolation image signal components S' for 
the interpolation points P'. 
As the interpolating operation methods for an image signal, there have been 
proposed various methods other than the linear interpolation described 
above, e.g., a method using a second- or third-order spline interpolating 
function. For example, in a cubic spline interpolating operation using a 
third-order spline interpolating function, it is necessary that the spline 
interpolating function passes through the original sampling points 
(pictures elements) and that the first-order differential coefficient of 
the spline interpolating function is continuous between adjacent sections. 
Under these conditions, interpolation coefficients by which the original 
imagine signal components for four picture elements around the 
interpolation point multiplied are calculated and the interpolation image 
signal component for the interpolation point is obtained by multiplying 
the original image signal components for four picture elements around the 
interpolation point by the interpolation coefficients. The cubic spline 
interpolating operation provide a secondary imagine (interpolation image) 
having a relatively high sharpness. As an interpolating operation method 
for obtaining an interpolation image signal for reproducing a secondary 
image which has a relatively low sharpness and is smooth, a B spline 
interpolating operation is known. Thus, when a second image having a high 
sharpness is to be reproduced, the cubic spline interpolating operation 
may be used while when a secondary image which is smooth and has a 
relatively low sharpness is to be reproduced, the B spline interpolating 
operation may be used. 
A reproduced visible image sometimes includes an edge portion where change 
in density (brightness) is sharp, e.g., bone in a radiation image and such 
an edge portion is sometimes enlarged. 
When such an edge portion extends obliquely with respect to the square grid 
pattern of the original picture elements and the linear interpolating 
operation according to said Formulas (16) to (18), the cubic spline 
interpolating operation or the B spline interpolating operation is carried 
out on the original image signal, the enlarged image of the oblique edge 
portion becomes remarkably zigzag. 
For example, in an image having an oblique edge portion as shown in FIG. 
9A, microscopically the oblique edge portion is a boundary between a 
region of higher density points (indicated at black dots) and lower 
density points (indicated at white dots) as shown in FIG. 9B. When 
interpolation image signal components are obtained by carrying out said 
interpolating operation on the edge portion, the obtained interpolation 
image signal component S'0 becomes an image signal representing an 
intermediate density slightly lower than that of the higher density 
picture elements P.sub.A, P.sub.B and P.sub.C as shown in FIG. 10B since 
the interpolation image signal component S'0 depends also on the original 
image signal component S.sub.D representing a lower density. Accordingly, 
when an enlarged image is reproduced from the interpolation image signal 
thus obtained, the zigzag line at the edge portion is enlarged as it is as 
shown by the broken line in FIG. 10B. Thus the edge portion which 
substantially looks like an oblique straight line in the whole image as 
shown in FIG. 9A clearly appears zigzag in the enlarged image as shown in 
FIG. 10A. 
Such zigzag in the edge portion is obstructive in diagnostic observation 
and deteriorates diagnostic performances of the image. 
SUMMARY OF THE INVENTION 
In view of the foregoing observations and description, the primary object 
of the present invention is to provide an interpolating operation method 
and apparatus for an image signal which can provide an enlarged image in 
which an oblique edge portion can be reproduced as a smooth and sharp 
image. 
In accordance with the present invention, an interpolating operation is 
carried out on original image signal components which make up an original 
image signal representing an original image and represent values of 
original picture elements arranged in a grid pattern at predetermined 
intervals in vertical and horizontal directions to obtain interpolation 
image signal components representing values of interpolation picture 
elements arranged in a grid pattern at intervals different from those of 
the original picture elements. In the interpolating operation, the 
interpolation image signal component for each of the interpolation picture 
elements is operated by multiplying the image signal components for a 
plurality of adjacent original picture elements adjacent to the 
interpolation picture element by respective interpolation coefficients 
which are calculated from the image signal components for the adjacent 
original picture elements. The density vector at the interpolation picture 
element on the original image represented by the original image signal is 
calculated, distances of the respective adjacent original picture elements 
from a straight segment perpendicular to the density vector are 
calculated, the interpolation coefficient for each of the adjacent 
original picture elements is corrected to be smaller as the density vector 
and/or the distance of the original picture element from the straight 
segment perpendicular to the density vector becomes larger, and then the 
interpolating operation is carried out on the basis of the corrected 
interpolation coefficient. 
Specifically the adjacent original picture elements are a plurality of 
(e.g., four) original picture elements nearest to the interpolation 
picture element. 
The interpolation coefficient may be represented by various functions 
including linear, third-order or higher functions. 
Since the density vector in the original image becomes larger in a portion 
where change in density is larger, when the density vector is relatively 
large, the segment perpendicular to the density vector represents an edge 
portion where change in density is sharp in the image. When considering 
the magnitude of the density vector at the interpolation picture element 
and the distance between the segment perpendicular to the density vector 
and the original picture element adjacent to the interpolation picture 
element, it may be considered that the interpolation picture element is on 
a edge portion and the segment perpendicular to the density vector 
represents the edge when the density vector is large. Accordingly, when 
the interpolation coefficient for the original image signal component for 
an original picture element distant from the segment is used as 
calculated, the interpolation image signal component is affected by a 
picture element with a density different from that of the edge in case 
where the edge portion extends obliquely to the pattern of the picture 
elements, which results in an interpolation image signal component 
representing a density different from that of the edge. Accordingly, when 
an image is reproduced from an interpolation image signal made up of 
interpolation image signal components thus obtained, the reproduced image 
has an oblique edge portion contoured by an enlarged zigzag line. 
Accordingly, in accordance with the present invention, the interpolation 
coefficient calculated is not applied as calculated but applied after 
corrected according to the magnitude of the density vector at the 
interpolation picture element and/or the distance of the interpolation 
picture element from the segment perpendicular to the density vector. That 
is, the interpolation coefficient is corrected to be smaller as the 
density vector becomes larger and/or the distance from the segment 
perpendicular to the density vector increases. Accordingly when an edge 
portion extends obliquely, the interpolation image signal component for an 
interpolation picture element on the edge portion less depends upon the 
image signal components for picture elements distant from the edge as 
compared with those for picture elements near the edge, or picture 
elements disposed along the edge. Accordingly the interpolation picture 
elements on the edge portion are given substantially the same density as 
the edge portion and the zigzag on the edge portion in the original image 
is not enlarged in the interpolation image, whereby the oblique edge 
portion in the enlarged image can have a smooth contour. 
The density vector at an interpolation picture element in a portion other 
than an edge portion is relatively small and accordingly the interpolation 
coefficient is not corrected so largely even if the original picture 
element is relatively distant from the segment perpendicular to the 
density vector, whereby the interpolation image signal component is 
calculated with the interpolation coefficient substantially unchanged. 
When edge portions have been distinguished from other portions by some 
suitable method, the interpolation coefficient may be corrected solely on 
the basis of the distance from the segment perpendicular to the density 
vector without taking into account the magnitude of the density vector.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
In FIG. 1, an interpolating operation apparatus 1 in accordance with an 
embodiment of the present invention comprises an interpolation coefficient 
operation means 3 which calculates interpolation coefficients at 
interpolation picture elements on the basis of original image signal 
components input from an image input means 2, a vector/distance 
calculating means 4 which calculates the density vector at each 
interpolation picture element in the original image and the distance 
between the segment perpendicular to the density vector and the original 
picture element used in the interpolation, an correction term calculating 
means 5 which calculates the correction term for correcting the 
interpolation coefficient, calculated by the interpolation coefficient 
operation means 3, on the basis of the magnitude of the density vector 
and/or the distance between the segment perpendicular to the density 
vector and the original picture element used in the interpolation 
calculated by the vector/distance calculating means 4, a correcting means 
6 which corrects the interpolation coefficient on the basis of the 
correction term calculated by the correction term calculating means 5, an 
interpolation image signal operation means 7 which operates interpolation 
image signal components on the basis of the interpolation coefficients 
corrected by the correcting means 6 and operates an interpolation image 
signal made up of the interpolation image signal components and an image 
output means 8 for reproducing a visible image from the interpolation 
image signal operated by the interpolation image signal operation means 7. 
The image input means 2 may be, for instance, a radiation image read-out 
apparatus shown in FIG. 2. Specifically, with the image read-out apparatus 
illustrated in FIG. 2, an X-ray image of an object, which has been stored 
on a stimulable phosphor sheet 10, is read from the stimulable phosphor 
sheet 10. The stimulable phosphor sheet 10 has been exposed to radiation 
such as X-rays through an object such as a human body and transmission 
radiation image information has been stored on the stimulable phosphor 
sheet 10. The stimulable phosphor sheet is conveyed in a sub-scanning 
direction, which is indicated by the arrow Y, by a conveyor means 11 such 
as an endless belt. A laser beam 13, which serves as stimulating rays 
(read-out rays), is emitted from a laser 12 such as a semiconductor laser. 
The laser beam 13 is reflected and deflected by a rotating polygon mirror 
14 which is quickly rotated. The laser beam 13 then passes through a 
scanning lens 18, which may be generally constituted of an f.theta. lens. 
The direction of the optical path of the laser beam 13 is then changed by 
a mirror 19, and the laser beam 13 impinges upon the stimulable phosphor 
sheet 10 and scans it in a main scanning direction indicated by the arrow 
X, which direction is approximately normal to the sub-scanning direction 
indicated by the arrow Y. 
When the stimulable phosphor sheet 10 is exposed to the laser beam 13, the 
exposed portion of the stimulable phosphor sheet 10 emits light 15 in an 
amount proportional to the amount of energy stored thereon during its 
exposure to the radiation. The emitted light 15 is guided by a light guide 
member 16 and photoelectrically detected by a photomultiplier 17. 
The light guide member 16 is made of a light guiding material, such as an 
acrylic plate. The light guide member 16 has a linear light input face 
16a, which is positioned to extend along the main scanning line on the 
stimulable phosphor sheet 10, and a ring-shaped light output face 16b, 
which is positioned in close contact with a light receiving face of the 
photomultiplier 17. The emitted light 15, which has entered the light 
guide member 16 at its light input face 16a, is guided through repeated 
total reflection inside of the light guide member 16, emanates from the 
light output face 16b, and is received by the photomultiplier 17. In this 
manner, the amount of the emitted light 15, which amount represents the 
radiation image is converted into an electric signal by the 
photomultiplier 17. 
An analog output signal S output from the photomultiplier 17 is 
logarithmically amplified by a logarithmic amplifier 20, and digitized by 
an analog-to-digital converter 21 at a predetermined reading scale factor. 
In this manner, an digital original image signal bearing thereon a 
two-dimensional image is obtained and is input into the aforesaid 
interpolating operation apparatus 1. 
In the interpolating operation apparatus 1, interpolation coefficients are 
first calculated by the interpolation coefficient operation means 3. 
Calculation of the interpolation coefficient will be described, 
hereinbelow. In this particular embodiment, the interpolation coefficient 
is calculated by a third-order cubic spline interpolating operation. 
Though the original picture elements are arranged in a square grid pattern 
in this embodiment, the original picture elements are assumed here to be 
linearly arranged for the purpose of simplicity of description. 
As illustrated in FIG. 3, 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.sub.k-2, X.sub.k-1, X.sub.k, 
X.sub.k+1, X.sub.k+2, . . . , are respectively represented by Y.sub.k-2, 
Y.sub.k-1, Y.sub.k, Y.sub.k+1, Y.sub.k+2, . . . A third-order spline 
interpolating function is set for each of sections X.sub.k-2 
.about.X.sub.k-1, X.sub.k-1 .about.X.sub.k, X.sub.k .about.X.sub.k+1, and 
X.sub.k+1 .about.X.sub.k+2. The spline interpolating functions 
corresponding to the respective sections are represented by f.sub.k-2, 
f.sub.k-1, f.sub.k, f.sub.k+1, and f.sub.k+2. The interpolating functions 
are the third-order functions, in which the position in each section 
serves as a variable. 
How the interpolating operation is carried out when a point taken for 
interpolation (hereinbelow referred to as "the interpolation point") 
X.sub.p falls within the section X.sub.k .about.X.sub.k+1 will be 
described hereinbelow. The spline interpolating function f.sub.k 
corresponding to the section X.sub.k .about.X.sub.k+1 is represented by 
Formula (1). 
EQU f.sub.k (X)=A.sub.k X.sup.3 +B.sub.k X.sup.2 +C.sub.k X+D.sub.k(1) 
In the cubic spline interpolating operation, it is necessary that the 
spline interpolating function f.sub.k passes through the original sampling 
points (picture elements), and that the first-order differential 
coefficient of the spline interpolating function f.sub.k is continuous 
between adjacent sections. Therefore, it is necessary for Formulas (2) to 
(5) to be satisfied. 
EQU f.sub.k (X.sub.k)=Y.sub.k (2) 
EQU f.sub.k (X.sub.k+1)=Y.sub.k+1 (3) 
EQU f.sub.k '(X.sub.k)=f.sub.k-1 '(X.sub.k) (4) 
EQU f.sub.k '(X.sub.k+1)=f.sub.k+1 '(X.sub.k+1) (5) 
In these formulas, f.sub.k ' represents the first-order differentiation 
(3A.sub.k x.sup.2 +2B.sub.k x+C.sub.k) of the function f.sub.k. 
Also, in the cubic spline interpolating operation, it is necessary for the 
first-order differential coefficient at the picture element X.sub.k to 
satisfy the condition with respect to the picture elements X.sub.k-1 and 
X.sub.k+1, which are located before and after the picture element X.sub.k, 
in that the first-order differential coefficient at the picture element 
X.sub.k should coincide with the gradient (Y.sub.k+1 
-Y.sub.k-1)/(X.sub.k+1 -X.sub.k-1) of the image signal components 
Y.sub.k-1 and Y.sub.k+1 representing the picture elements X.sub.k-1 and 
X.sub.k+1. Therefore, it is necessary for Formula (6) to be satisfied. 
EQU f.sub.k '(X.sub.k)=(Y.sub.k+1 -Y.sub.k-1)/(X.sub.k+1 -X.sub.k-1)(6) 
Also, it is necessary for the first-order differential coefficient at the 
picture element X.sub.k+1 to satisfy the condition with respect to the 
picture elements X.sub.k and X.sub.k+2, which are located before and after 
the picture element X.sub.k+1, in that the first-order differential 
coefficient at the picture element X.sub.k+1 should coincide with the 
gradient (Y.sub.k+2 -Y.sub.k)/(X.sub.k+2 -X.sub.k) of the image signal 
components Y.sub.k and Y.sub.k+2 representing the picture elements X.sub.k 
and X.sub.k+2. Therefore, it is necessary for Formula (7) to be satisfied. 
EQU f.sub.k '(X.sub.k+1)=(Y.sub.k+2 -Y.sub.k)/(X.sub.k+2 -X.sub.k)(7) 
It is herein assumed that the interval (i.e., the lattice interval) of each 
of sections X.sub.k-2 .about.X.sub.k-1, X.sub.k-1 .about.X.sub.k, X.sub.k 
.about.X.sub.k+1, and X.sub.k+1 .about.X.sub.k+2 is equal to 1, and the 
position of the interpolation point X.sub.p, which is taken from the 
picture element X.sub.k toward the picture element X.sub.k+1, is 
represented by t (0.ltoreq.t.ltoreq.1). In such cases, from Formulas (2) 
to (7), the formulas shown below obtain. 
EQU f.sub.k (0)=D.sub.k =Y.sub.k 
EQU f.sub.k (1)=A.sub.k +B.sub.k +C.sub.k +D.sub.k =Y.sub.k+1 
EQU f.sub.k '(0)=C.sub.k =(Y.sub.k+1 -Y.sub.k-1)/2 
EQU f.sub.k '(1)=3A.sub.k +2B.sub.k +C.sub.k =(Y.sub.k+2 -Y.sub.k)/2 
Therefore, the formulas shown below obtain. 
EQU A.sub.k =(Y.sub.k+2 -3Y.sub.k+1 +3Y.sub.k -Y.sub.k-1)/2 
EQU B.sub.k =(-Y.sub.k+2 +4Y.sub.k+1 -5Y.sub.k +2Y.sub.k-1)/2 
EQU C.sub.k =(Y.sub.k+1 -Y.sub.k-1)/2 
EQU D.sub.k =Y.sub.k 
As described above, the variable conversion of X=t is carried out, and 
therefore the spline interpolating function f.sub.k (X) is represented by 
the formula shown below. 
EQU f.sub.k (X)=f.sub.k (t) 
Therefore, an interpolated image signal component Y.sub.p corresponding to 
the interpolation point X.sub.p may be represented by Formula (8). 
EQU Y.sub.p =f.sub.k (t)=A.sub.k t.sup.3 +B.sub.k t.sup.2 +C.sub.k t+D.sub.k(8) 
Substituting the coefficients A.sub.k, B.sub.k, C.sub.k, and D.sub.k into 
Formula (8) yields 
##EQU1## 
Arranging this formula with respect to the image signal components 
Y.sub.k-1, Y.sub.k, Y.sub.k+1, and Y.sub.k+2 yields Formula (9). 
##EQU2## 
The coefficients for the original image signal components Y.sub.k-1, 
Y.sub.k, Y.sub.k+1, and Y.sub.k+2 are referred to as the interpolation 
coefficients a.sub.k-1, a.sub.k, a.sub.k+1, and a.sub.k+2. Specifically, 
the interpolation coefficients a.sub.k-1, a.sub.k, a.sub.k+1, and 
a.sub.k+2, which respectively correspond to the original image signal 
components Y.sub.k-1, Y.sub.k, Y.sub.k+1, and Y.sub.k+2 in Formula (9), 
may be represented by the Formulas shown below. 
EQU a.sub.k-1 =(-t.sup.3 +2t.sup.2 -t)/2 
EQU a.sub.k =(3t.sup.3 -5t.sup.2 +2)/2 
EQU a.sub.k+1 =(-3t.sup.3 +4t.sup.2 +t)/2 
EQU a.sub.k+2 =(t.sup.3 t.sup.2)/2 
The operations described above are repeated for the sections X.sub.k-2 
.about.X.sub.k-1, X.sub.k-1 .about.X.sub.k, X.sub.k .about.X.sub.k+1, and 
X.sub.k+1 .about.X.sub.k+2. In this manner, an interpolation image signal 
can be obtained, which is made up of image signal components occurring at 
intervals different from those of the image signal components of the 
entire original image signal. 
In the vector/distance calculating means 4, the density vector at the 
interpolation picture element (interpolation point) and the distance 
between the segment perpendicular to the density vector and the original 
picture element represented by the original image signal component used in 
the interpolating operation are calculated. That is, as shown in FIG. 4, 
the vector/distance calculating means 4 allocates sixteen picture elements 
in the vicinity of interpolation picture element P0', whose interpolation 
image signal component is to be calculated, to four regions a, b, c and d, 
and calculates the sums Wa, Wb, Wc and Wd of the original image signal 
components in the respective regions. Then density vector Pv is calculated 
as follows. 
EQU Pv=(Wb-Wa, Wd-Wc) 
Alternatively, as shown in FIG. 5, the density vector Pv may be calculated 
on the basis of the original image signal components Sa, Sb, Sc and Sd of 
four picture elements Pa, Pb, Pc and Pd around the interpolation picture 
element P.sub.0 ', whose interpolation image signal component is to be 
calculated, according to the following formula. 
EQU Pv=(Sb-Sa, Sd-Sc) 
Then the segment lv perpendicular to the density vector Pv is obtained. The 
interpolation image signal component S0' is calculated by multiplying the 
original image signal components Sa, Sb, Sc and Sd of the four original 
picture elements Pa, Pb, Pc and Pd adjacent to the interpolation picture 
element P.sub.0 ' by the respective interpolation coefficients, which are 
corrected according to the magnitude of the density vector Pv and the 
distances of the original picture elements Pa, Pb, Pc and Pd from the 
segment lv in accordance with the present invention. The correction is 
carried out as follows. 
It is assumed that the co-ordinates of an original picture element shown in 
FIG. 6 be (u,v), the interpolation coefficient at (u,v) be Au,v , the 
coordinates of the interpolation picture element P0' by (dx,dy) and the 
density vector Pv at (u,v) be (Px,Py). The corrected interpolation 
coefficient Au,v' is obtained from the following Formula (10). 
EQU A.sub.u,v '=A.sub.u,v /{k.multidot.f(Pv, t)+1} (10) 
wherein k is a constant, f(Pv, t) is the product (correction term) of the 
density vector Pv and the distance of (u,v) from the segment lv 
perpendicular to the density vector Pv. 
Specifically calculation of Formula (10) is carried out as follows. 
That is, in the correcting term calculating means 5, the magnitude 
.vertline.Pv.vertline. of the density vector (Px,Py) obtained in the 
vector/distance calculating means 4 is obtained according to the following 
Formula (11). 
EQU .vertline.Pv.vertline.=.sqroot. (Px.sup.2 +Py.sup.2) (11) 
Then the distance t between the segment lv, which passes through the 
interpolation picture element (dx,dy) and extends perpendicular to the 
density vector Pv, and the original picture element (u,v) is calculated 
according to the following Formula (12). 
EQU t=.vertline.Px(u-dx)+Py(v-dy).vertline./.sqroot. (Px.sup.2 +Py.sup.2)(12) 
Accordingly, the correction term f(Pv, t) is as follows. 
EQU f(Pv, t)=.vertline.Px(u-dx)+Py(v-dy).vertline. (13) 
In the correcting means 6, the interpolation coefficient calculated in the 
correction term calculating means 5 is corrected on the basis of the 
correction term f(Pv, t). That is, by substituting Formula (13) in Formula 
(10), the following Formula (10') is obtained. 
EQU A.sub.u,v '=A.sub.u,v 
/(k.multidot..vertline.Px(u-dx)+Py(v-dy).vertline.+1)(10') 
This correction of the interpolation coefficient A.sub.u,v is carried out 
on the four original picture elements Pa, Pb, Pc and Pd around the 
interpolation picture element P0', thereby obtaining four corrected 
interpolation coefficients A.sub.u,v ', and final interpolation 
coefficients 
EQU A.sub.u,v '/.SIGMA.A'ij 
are obtained by normalizing the corrected interpolation coefficients 
A.sub.u,v '. 
The final interpolation coefficient thus corrected becomes smaller as the 
inclination of the density vector Pv at the interpolation picture element 
P0' becomes larger and the distance of the original picture element from 
the segment perpendicular to the density vector Pv becomes larger. That 
is, where the density vector Pv becomes large in the original image is an 
edge portion where change in density is large and in such case, the 
segment perpendicular to the density vector Pv corresponds to the edge 
portion. The present invention is to prevent, when an edge where the 
density vector Pv is relatively extends obliquely to the square grid 
pattern of the original picture elements, the edge portion from appearing 
zigzag in an enlarged image. 
Specifically when the density vector Pv is relatively large, using the 
interpolation coefficient for an original picture element distant from the 
segment perpendicular to the density vector as calculated results in use 
of the original image signal component for an original picture element 
distant from the edge, and the interpolation image signal component S0' 
obtained is affected by the original picture element different from the 
edge in density and comes to represent the density different from that of 
the edge. Accordingly when an enlarged visible image is reproduced from an 
interpolation image signal made up of a series of interpolation image 
signal components SO' the fine zigzag in the original image is enlarged to 
be visible in the enlarged image. 
In accordance with the present invention, the interpolation coefficient is 
therefore not applied to the original image signal component as calculated 
but applied thereto after corrected so that it becomes smaller as the 
density vector Pv becomes larger and the distance from the segment lv 
perpendicular to the density vector Pv becomes larger. Accordingly, when 
an edge portion extends obliquely, the interpolation image signal 
component S0' for an interpolation picture element on the edge portion 
comes to less depend upon the original image signal component for an 
original picture element distant from the edge as compared with the 
original image signal component for an original picture element along the 
edge portion. With this arrangement, interpolation picture elements on the 
edge portion are interpolated to a density substantially equal to that of 
the edge portion and the zigzag in the original image is not enlarged, 
whereby the oblique edge portion can be enlarged without zigzag. 
Then in the interpolation image signal operation means 7, the interpolation 
image signal component So' for the interpolation picture element P0' is 
calculated on the basis of the final interpolation coefficient according 
to the aforesaid Formula (9). That is, 
EQU S0'=Aa'.multidot.Sa+Ab'.multidot.Sb+Ac'.multidot.Sc+Ad'.multidot.Sd(9') 
wherein Aa', Ab', Ac' and Ad' represent the corrected interpolation 
coefficients. This operation is carried out for all the interpolation 
picture elements. 
Then an interpolation image signal made up of a series of the interpolation 
image signal components S0' thus obtained is input into the image output 
means 8 such as a CRT and a visible image is reproduced from the 
interpolation image signal. In the visible image reproduced by the image 
output means 8, even an oblique edge has a sharp and smooth edge without 
zigzag. 
Though, in the embodiment described above, the interpolation coefficient is 
corrected according to Formula (10), the interpolation coefficient may be 
corrected according to the following Formula (14). 
EQU A.sub.u,v '=A.sub.u,v /{F(Pv, t)} (14) 
wherein F(Pv,t) is a function which monotonously increases with increase in 
f(Pv, t) as shown in FIG. 7. 
Further, though, in the embodiment described above, the interpolating 
operation is carried out on an image detected by a radiation image 
read-out apparatus such as shown in FIG. 2, the interpolating operation 
may be carried out on an original image signal which has been stored in a 
storing means. 
Further, though, in the embodiment described above, being carried out by a 
cubic spline interpolation, the interpolating operation may be carried 
out, for instance, by a B spline interpolation without being limited to 
the cubic spline interpolation. Different from the cubic spline 
interpolation, in the B spline interpolating operation, it is not 
necessary that the spline interpolating function passes through the 
original sampling points (picture elements) but it is necessary that the 
first-order differential coefficient of the spline interpolating function 
is continuous between adjacent sections. Under the condition, 
interpolation coefficients b.sub.k-1, b.sub.k, b.sub.k+1 and b.sub.k+2 for 
the original image signal components Y.sub.k-1, Y.sub.k, Y.sub.k+1 and 
Y.sub.k+2 are calculated. 
Further the interpolating operation may be carried out on the original 
image signal by both the B spline interpolation and the cubic spline 
interpolation. In this case, the interpolation coefficients obtained by 
the B spline interpolation and the cubic spline interpolation are 
differently weighted according to a desired scale factor and added to each 
other. That is, the interpolating operation is carried out according to 
the following Formula (15) with the value of t varied. 
EQU F=t.multidot.A+(1-t).multidot.B (15) 
wherein F represents an interpolation image signal component, A represents 
the interpolation coefficient by the cubic spline interpolation, B 
represents the interpolation coefficient by the B spline interpolation and 
t represents the weighting coefficient. For example, when the cubic spline 
interpolation coefficients for the original image signal components 
Y.sub.k-1, Y.sub.k, Y.sub.k+ and Y.sub.k+2 are represented by a.sub.k-1, 
a.sub.k, a.sub.k+ and a.sub.k+2 and the B spline interpolation 
coefficients for the original image signal components Y.sub.k-1, Y.sub.k, 
Y.sub.k+ and Y.sub.k+2 are represented by, b.sub.k, b.sub.k+ and 
b.sub.k+2, the interpolation image signal component F is as follows. 
##EQU3## 
Further, though, in the embodiment described above, the interpolation 
coefficient is corrected according to both the magnitude of the density 
vector and the distance of the original picture element from the segment 
perpendicular to the density vector, the interpolating operation method of 
the present invention may be applied only to edge portions by separating 
edge portions from other portions in advance. In such a case, the 
operation may be simplified by employing a fixed value as the magnitude of 
the density vector .vertline.Pv.vertline..