JP3494787B2 - Image data interpolation calculation method and apparatus using the method - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image data interpolation calculation method and apparatus.

[0002]

2. Description of the Related Art Conventionally, in various fields, it is necessary to photoelectrically read an image recorded on a photographic film to obtain an image signal, perform appropriate image processing on the image signal, and then reproduce and record the image. Has been done. Also, once the radiation image information of the subject such as a human body is recorded in a sheet-shaped stimulable phosphor,
This stimulable phosphor sheet is scanned with excitation light such as laser light to generate stimulated emission light, and the obtained stimulated emission light is photoelectrically read to obtain an image signal, and based on this image data, the subject Radiation image recording material such as photographic light-sensitive material, CR
A radiation image recording / reproducing system for outputting a visible image on T or the like has already been put into practical use. This system has the practical advantage of being able to record images over a very wide radiation exposure area compared to conventional radiographic systems using silver halide photography.

In a system for obtaining an image signal and reproducing a visible image based on the image signal as described above, when it is desired to observe the region of interest to be observed in the visible image in more detail, the region is enlarged. May be replayed. In this case, if the number of pieces of image data to be enlarged and reproduced is enlarged and reproduced with the number of pieces of original image data corresponding to the original image, the sharpness of the enlarged image is higher than that of the original image due to human visual characteristics. Is also recognized as a relative decrease. For this reason, the sharpness is lowered and the image cannot be observed in detail only by simply enlarging and reproducing the image.

Therefore, a predetermined interpolation calculation is performed on the original image data obtained by reading the original image, and the number of data is different from the number of original image data. By obtaining the interpolated image data which is the secondary image data of the number of data and reproducing the visible image based on this interpolated image data, it is possible to prevent the sharpness of the image from being lowered even when the image is enlarged and reproduced. .

As described above, various methods have heretofore been proposed as the interpolation calculation method for performing the interpolation calculation on the image data, but in general, a method using a cubic spline interpolation function is often used. The method comprises digitally obtained original image data {Y _k} connected by a cubic function {f _k} for each interval, f _k in the setting position of the interpolation point (setting position in each section) Is used as interpolation image data.

As described above, the interpolation calculation which passes through the original image data is an interpolation method having a relatively high sharpness, and for example, a cubic spline interpolation calculation is known. The cubic spline interpolation calculation will be specifically described below.

Successive pixels X _k-2 , X _k-1 , X _k , X _{k + 1} , obtained by digitally reading from the original image,
The image data of X _{k + 2} , ... (Original image data) are respectively Y _k-2 , Y _k-1 , Y _k , Y _{k + 1} , as shown in FIG.
Let Y _{k + 2} , .... Here, the cubic spline interpolation function is used for each section X _{k-2 to} X _k-1 , X _{k-1 to} X _k , X _{k to} X.
_{k + 1} , X _{k + 1 to} X _{k + 2} are respectively set, and spline interpolation functions corresponding to the respective sections are f _k-2 , f _k-1 ,
Let f _k , f _{k + 1} , and f _{k + 2} . Each of these interpolation functions is a cubic function having the position of each section as a variable.

First, the points to be interpolated (hereinafter,
A case will be described in which X _{p (referred} to as an interpolation point) is in the range of section X _{k to} X _{k + 1} . The spline interpolation function f _k corresponding to the sections X _{k to} X _{k + 1} is represented by the following equation (6).

F _k (x) = A _k x ³ + B _k x ² + C _k x + D _k (6) In the cubic spline interpolation calculation, the spline interpolation function f _k passes through the original sample point (pixel) and It is necessary that the first-order differential coefficient be continuous between each section, and from these conditions, it is necessary to satisfy the following equations (7) to (10) f _k (X _k ) = Y _k (7) f _k (X _{k + 1} ) = Y _{k + 1} (8) f _k ′ (X _k ) = f _k−1 ′ (X _k ) (9) f _k ′ (X _{k + 1} ) = f _{k + 1} ′ ( X _{k + 1} ) (10) where f _k ′ is the first derivative (3A _k x ² +2) of the function f _k .
B _k x + C _k ).

Strictly speaking, the cubic spline interpolation calculation includes the continuation condition of the second derivative, but the continuity condition of the second derivative makes the arithmetic expression complicated. It is generally used in a simplified form.

[0011] In the cubic spline interpolating operation, the first-order differential coefficient at the pixel Xk is, for the X _k-1 and X _{k + 1} with respect to the picture elements X _k, these image data Y _{k- 1,} Y _{k + 1} gradient (Y _k + 1 -Y
_{Since the} condition is that ( _k-1 ) / ( _{Xk + 1-} Xk _-1 ), the following formula (11) must be satisfied.

F _k ′ (X _k ) = (Y _{k + 1} −Y _k−1 ) / (X _{k + 1} −X _k−1 ) (11) Similarly, the first derivative of the pixel X _{k + 1} . For coefficients X _k and X _{k + 2} that are the pixels before and after the pixel X _{k + 1} ,
Gradient (Y _{k + 2} − of these image data Y _k , Y _{k + 2}
The condition is that _Yk ) / (X _{k + 2-} X _k ), and therefore it is necessary to satisfy the following expression (12).

F _k ′ (X _{k + 1} ) = (Y _{k + 2} −Y _k ) / (X _{k + 2} −X _k ) (12) Here, each section X _{k−2 to} X _k−1 , X _{k-1 to} X _k , X _k to
The interval of X _{k + 1} , X _{k + 1 to} X _{k + 2} (called a grid interval) is 1
And then, if the position of the interpolation point X _p in the pixel X _{k + 1} directions from the pixel X _k and t (0 ≦ t ≦ 1) , the equation (6) ~ (12), f k (0) = D _k = Y _k f _k (1) = A _k + B _k + C _k + D _k = Y _{k + 1} f _k ′ (0) = C _k = (Y _{k + 1} −Y _k−1 ) / 2 f _k ′ (1) = 3A _k + 2B _k + C _k = (Y _{k + 2} −
Y _k ) / 2 Therefore, A _k = (Y _{k + 2} -3Y _{k + 1} + 3Y _k -Y _k-1 ) / 2 B _k = (-Y _{k + 2} + 4Y _{k + 1} -5Y _k + 2Y _k-1 ) / 2 C _k = (Y _{k + 1} −Y _k-1 ) / 2 D _k = Y _k Note that the spline interpolation function f _k (x) is X as described above.
Since the variable conversion of = t is performed, f _k (x) = f _k (t). Therefore, the interpolation image data Y at the interpolation point X _p
p can be represented by Y _p = f _k (t) = A _k t ³ + B _k t ² + C _k t + D _k (13). Here, the respective coefficients A _k , B _k , C
Substituting _k and D _k into the equation (13), Y _p = {(Y _{k + 2} −3Y _{k + 1} + 3Y _k −Y _k−1 ) / 2}
_{^{t 3 + {(- Y k}} + 2 + 4Y k + 1 -5Y k + 2Y k-1) /
2} t ² + {(Y _{k + 1} −Y _k−1 ) / 2} t + Y _k , which is the image data Y _k−1 , Y _k , Y _{k + 1} , Y.
_By rearranging _{k + 2} , it can be expressed by the following equation (14).

[0014] ^{_{Y p = {(- t 3}} + 2t 2 -t) / 2} Y k-1 + {(3t 3 -5t 2 +2) / 2} Y k + {(- 3t 3 + 4t 2 + t) / 2 _{} Y k + 1 + {(} t 3 -t 2) / 2} Y k + 2 (14) where the original image data Y _k-1, Y _k, the coefficients of _{Y k + 1, Y k +} 2 Are referred to as interpolation coefficients c _k-1 , c _k , c _{k + 1} , c _{k + 2} . That is, the original image data Y _k−1 in equation (14),
Interpolation coefficients c corresponding to Y _k , Y _{k + 1} , and Y _{k + 2} , respectively.
_k-1 , c _k , c _{k + 1} , c _{k + 2} are c _k-1 = (− t ³ + 2t ² −t) / 2 c _k = (3t ³ −5t ² +2) / 2 c _{k + 1} = (− 3t ³ + 4t ² + t) / 2 _{ck + 2} = (t ³ −t ² ) / 2.

The above calculation is performed for each section X _{k-2 to} X _k-1 , X
By repeating for _{k−1 to} X _k , X _{k to} X _{k + 1} , and X _{k + 1 to} X _{k + 2} , it is possible to obtain interpolated image data having a different interval from the original image data for the entire original image data. it can.

By the way, in the cubic spline interpolation calculation, as described above, it is necessary to pass through the original sample point (pixel) and the first-order differential coefficient thereof should be continuous between each section, which is sharp. This is an interpolation function for obtaining interpolated image data for reproducing a sharp secondary image (image obtained by interpolation) having a relatively high degree of sharpness. Is desirable to reproduce a relatively low but smooth secondary image. As an interpolation function for obtaining interpolation image data for reproducing a smooth secondary image having a relatively low sharpness as described above, for example, a B-spline (B-spline) interpolation calculation is known. This beespline interpolation operation does not require passing through the original sample points (pixels), but the first derivative and the second derivative (represented by f ″ (X)) are continuous between each section. Required to do.

That is, in f _k (x) = A _k x ³ + B _k x ² + C _k x + D _k (6), f _k ′ (X _k ) = f _k−1 ′ (X _k ) (9) f _k ′ (X _{k + 1} ) = f _{k + 1} ′ (X _{k + 1} ) (10) f _k ″ (X _k ) = f _k−1 ″ (X _k ) (15) f _k ″ (X _{k + 1} ) = F _{k + 1} ″ (X _{k + 1} ) (16). However, X _k-1 first-order differential coefficient at the picture element X _k is with respect to the picture elements X _k and X _{k + 1}
For and, the condition is that they match the gradient (Y _{k + 1} −Y _k−1 ) / (X _{k + 1} −X _k−1 ) of these image data Y _k−1 , Y _{k + 1.} , It is necessary to satisfy the following formula (11).

F _k ′ (X _k ) = (Y _{k + 1} −Y _k−1 ) / (X _{k + 1} −X _k−1 ) (11) Similarly, the first derivative of the pixel X _{k + 1} . For coefficients X _k and X _{k + 2} that are the pixels before and after the pixel X _{k + 1} ,
Gradient (Y _{k + 2} − of these image data Y _k , Y _{k + 2}
The condition is that _Yk ) / (X _{k + 2-} X _k ), and therefore it is necessary to satisfy the following expression (12).

F _k ′ (X _{k + 1} ) = (Y _{k + 2} −Y _k ) / (X _{k + 2} −X _k ) (12) The function f (X) is generally expressed by the following equation (17). It is approximated by things.

F (X) = f (0) + f ′ (0) X + {f ″ (0) / 2} X ² (17) Here, each section X _{k−2 to} X _k−1 , X _{k− 1} ~ X _k , X _k ~
The interval of X _{k + 1} , X _{k + 1 to} X _{k + 2} (called a grid interval) is 1
And then, if the position of the interpolation point X _p in the pixel X _{k + 1} directions from the pixel X _k and t (0 ≦ t ≦ 1) , equation (6), (9) -
(13), (15) from _{~ (17), f k '} (0) = C k = (Y k + 1 -Y k-1) / 2 f k' (1) = 3A k + 2B k + C k = (Y _{k + 2-}
Y _k ) / 2 f _k ″ (0) = Y _{k + 1} −2Y _k + Y _k−1 = 2B Therefore, A _k = (Y _{k + 2} −3Y _{k + 1} + 3Y _k −Y _k−1 ) / 6 B _k = (Y _{k + 1} −2Y _k + Y _k−1 ) / 2 C _k = (Y _{k + 1} −Y _k−1 ) / 2 Here, since D _k is unknown, D _k = (D ₁ Y _{k + 2} + D ₂ Y _{k + 1} + D ₃ Y _k + D ₄ Y
_k-1 ) / 6. In addition, since the spline interpolation function f _k (x) has undergone the variable conversion of X = t as described above, f _k (x) = f _k (t). _{Therefore, f k (t) = {} (Y k + 2 -3Y k + 1 + 3Y k -Y k-1)
^{/ 6} t 3 + {(} Y k + 1 -2Y k + Y k-1) / 2} t 2
_{+ {(Y k + 1 -Y} k-1) / 2} t + (D 1 Y k + 2 + D 2
Y _{k + 1} + D ₃ Y _k + D ₄ Y _k-1 ) / 6, which is the image data Y _k-1 , Y _k , Y _{k + 1} , Y
_By rearranging _{k + 2} , it can be expressed by the following equation (18).

F _k (t) = {(-t ³ + 3t ² -3t + D ₄ ) / 6} Y _k-1 + {(3t ³ -6t ² + D ₃ ) / 6} Y _k + {(-3t ³ + 3t ² + 3t + D ₂ ) / 6} Y _{k + 1} + {(t ³ + D ₁ ) / 6} Y _{k + 2} (18) Here, if t = 1, then f _k (1) = {(D ₄ − 1) / 6} Y _k-1 + {(D ₃ −
3) / 6} Y _k + {(D ₂ +3) / 6} Y _{k + 1} + {(D
₁ +1) / 6} Y _{k + 2} Next, the equation (18) for the sections X _{k + 1 to} X _{k + 2} is f _{k + 1} (t) = {(-t ³ + 3t ² -3t + D ₄ ) / _{6} Y k + {(3t} 3 -6t 2 + D 3) / 6} Y k + 1 + {(- 3t 3 + 3t 2 + 3t + D 2) / 6} Y k + 2 + {(t 3 + D 1) / 6 } Y _{k + 3} (19) wherein, if put as _{t = 0, f k + 1} (0) = (D 4/6) Y k + (D 3/6) Y k + 1
_{+ (D 2/6) Y} k + 2 + (D 1/6) Y k + 3 continuity conditions _{(f k (1) = f} k + 1 (0)), and corresponding to each original image data Under the condition that the coefficients are equal, D ₄ −1 = 0, D ₃ −3 = D ₄ , D ₂ + 3 =
D ₃ , D ₁ + 1 = D ₂ , D ₁ = 0, and therefore D _k = (Y _{k + 1} + 4Y _k + Y _k-1 ) / 6. _{Therefore, Y p = f k (t} ) = {(- t 3 + 3t 2 -3t + 1) / 6} Y k-1 + {(3t 3 -6t 2 +4) / 6} Y k + {(- 3t 3 + 3t ^{2 + 3t + 1) / 6} } Y k + 1 + {t 3/6} Y k + 2 (20) Therefore, the original image data _{Y k-1, Y k,} Y k + 1, Y
interpolation coefficients b _k-1 , b _k corresponding to _{k + 2} ,
b _{k + 1} and b _{k + 2} are: b _k-1 = (− t ³ + 3t ² −3t + 1) / 6 b _k = (3t ³ −6t ² +4) / 6 b _{k + 1} = (− 3t ³ + 3t a ^{2 + 3t + 1) / 6} b k + 2 = t 3/6.

The above calculation is performed for each section X _{k-2 to} X _k-1 , X
By repeating for _{k−1 to} X _k , X _{k to} X _{k + 1} , and X _{k + 1 to} X _{k + 2} , it is possible to obtain interpolated image data having a different interval from the original image data for the entire original image data. it can.

When it is desired to reproduce the secondary image (interpolated image) sharply with high sharpness, for example, cubic spline interpolation calculation is used. When it is desired to reproduce smoothly with low sharpness, bee spline interpolation calculation is used. Good.

Further, the applicant of the present application determines the sharpness of the interpolated image by weighting and adding the corresponding coefficients of two interpolation functions having different sharpnesses according to the desired sharpness of the interpolated image. An image data interpolation method that enables fine adjustment is proposed (see Japanese Patent Laid-Open No. 2-278478). According to this method, for example, when the cubic spline interpolation calculation and the beespline interpolation calculation are adopted as the two interpolation functions having different sharpness, the interpolation coefficients c _k-1 , c _k , c _{k of the} cubic spline interpolation calculation are adopted. ₊₁ and c _{k + 2} and the interpolation coefficients b _k-1 , b _k , b _{k + 1} and b _{k + 2 of the} beespline interpolation calculation are used as the original image data Y _k-1 , Y _k and Y _{k + 1.} , Y _{k + 2} corresponding to Y _{k + 2} , and by changing the weighting ratio (coefficient) α, an intermediate value in the range from the sharpest sharpness to the smoothest sharpness is obtained. A secondary image having a desired sharpness can be obtained.

That is, the interpolation coefficients for the cubic spline interpolation calculation are c _k-1 , c _k , c _{k + 1} , c _{k + 2} , and the interpolation coefficients for the bee spline interpolation calculation are b _k-1 , b _k , b _{k +. 1} ,
When b _{k + 2} is set, the weighted interpolation coefficients a _k-1 , a _k , a _{k + 1} , and a _{k + 2} are set as follows.

A _k-1 = (1-α) c _k-1 + αb _k-1 a _k = (1-α) c _k + αb _k a _{k + 1} = (1-α) c _{k + 1} + αb _{k + 1} a _{k + 2} = (1-α) c _{k + 2} + αb _{k + 2} (where 0 ≦ α ≦ 1) The new interpolation coefficients a _k−1 , a _k , obtained in this way
Interpolated image data Y _p is calculated by the following equation (21) based on a _{k + 1} and a _{k + 2} .

Y _p = a _k-1 Y _k-1 + a _k Y _k + a _{k + 1} Y _{k + 1} + a _{k + 2} Y _{k + 2} (21) In an actual image, pixels are arranged two-dimensionally. Therefore, the interpolation coefficient a _k is represented as an interpolation coefficient Bij or Cij for each of two different array directions (i direction and j direction).

[0028]

By the way, there are cases where more diverse expressions are required for the sharpness of such an interpolated image. For example, an interpolated image with sharper sharpness than an interpolated image obtained by cubic cubic spline interpolation calculation alone, or an interpolated image with smoother sharpness compared to an interpolated image obtained by beep spline interpolation calculation alone may be required. is there.

However, in the image data interpolation method disclosed in JP-A-2-278478, when the cubic spline interpolation calculation and the beespline interpolation calculation are adopted,
The sharpness can be adjusted only within the range from the sharpness corresponding to the sharpest image by the cubic spline interpolation calculation to the sharpness corresponding to the smoothest image by the bee spline interpolation calculation. We cannot meet your needs.

The present invention has been made in view of the above circumstances, and has a high degree of freedom in adjusting the sharpness of an interpolated image obtained by linearly combining two interpolation operations having different sharpnesses from each other. An object of the present invention is to provide an interpolation calculation method and device.

[0031]

A method of interpolating image data according to the present invention is based on the following equation (1) for obtaining two interpolated images having different sharpness with respect to a large number of original image data Yij representing an image. ) And (2) which are different from each other
Expression by interpolation function h having new interpolation coefficient Aij obtained by linearly combining corresponding interpolation coefficients Bij, Cij for each image data Yij in one interpolation function f, g as shown in the following expression (3) In the image data interpolation calculation method for performing interpolation calculation according to (4) to obtain interpolation image data having a different interval from the original image data, f = ΣBij · Yij (1) g = ΣCij · Yij (2) Aij = (1-α) Bij + αCij (3) h = ΣAij · Yij (4) (where i = 1, 2, ..., j = 1, 2, ...) The coefficient α in the equation (3) is smaller than 0. A real number including a range and / or a range larger than 1 is used.

Here, as the two interpolation functions having different sharpness, the interpolation function corresponding to an image having a relatively low sharpness is a beespline interpolation calculation function, and the interpolation function corresponding to an image having a higher sharpness than this. Is preferably a cubic spline interpolation calculation function. This is because the first-order differential coefficient is continuous in the case of the combination of both.

However, the interpolation calculation method of the image data of the present invention is not limited to these combinations, and various types such as a bee spline interpolation calculation function, a cubic spline interpolation calculation function, a linear interpolation function, a Lagrange interpolation calculation function, etc. Interpolation operation functions can be used, and any two of these interpolation operation functions can be combined.

The interpolation coefficients Bij and Cij mean the interpolation coefficients for each of two mutually different array directions (i direction and j direction) of pixels forming an image (described in the section of the prior art). Interpolation coefficients a _k-1 , a _k , a _{k + 1} , a
Corresponds to the coefficient by which each original image data such as _{k + 2} is multiplied).

In the image data interpolation calculation method of the present invention, the spatial frequency and the response R _{1 of} one of the two interpolation functions are previously associated with each other for a plurality of different image enlargement magnifications. A plurality of first look-up tables set according to the above, and a plurality of second look-up tables set in advance by associating the spatial frequency and the response R ₂ of the other interpolation function with a plurality of different image enlargement magnifications. Of the look-up tables, the first look-up table and the second look-up table corresponding to the desired image enlargement ratio for the interpolated image are referred to, and the response R of the one interpolation function at the image enlargement ratio is obtained. ₁ and obtains a response R ₂ of said other interpolating function, desired response R for the interpolation image, the one By calculation according to the following equation on the basis of the response R ₂ of the response R ₁ and the other interpolation function interpolation function (5) may be obtained the coefficient alpha.

Α = (R−R ₁ ) / (R ₂ −R ₁ ) (5) Here, an example of the first lookup table and the second lookup table corresponding to a predetermined enlargement ratio is shown in FIG. Shown in. From this figure 5, for example, 1cycl which is most sensitive to human eyes
By using e / mm as the frequency of interest, the responses R ₁ and R ₂ at a frequency of 1 cycle / mm are obtained from each look-up table, and these are linearly interpolated according to R = αR ₂ + (1-α) R ₁ Since the response R is obtained, the equation (5) can be obtained by rearranging this equation for the coefficient α. For the frequency of interest, 1 cycl
The spatial frequency is not limited to e / mm, but may be another spatial frequency or two or more different spatial frequencies depending on the type of image, etc., and is representative of one obtained by averaging responses at two or more spatial frequencies. It can be used as a value.

In the method of directly designating the response R as a desired value in this way, the degree of change in the sharpness can be easily grasped as the change of the response of the image, so that the value of α as a simple mere coefficient is designated. It is possible to obtain an interpolated image with a sharpness closer to that of a real feeling.

In the case of the method of designating the response R as described above, when enlarging the image, it is necessary to designate the enlargement magnification of the image by using some known means. And the first matching the specified magnification
If the look-up table and the second look-up table are present in the plurality of look-up tables, the look-up table may be selected. However, if there is no look-up table matching the specified enlargement ratio, , Two look-up tables corresponding to the two magnifying powers closest to the specified magnifying power are selected from the respective look-up table groups, and the response obtained from each look-up table is obtained by linear interpolation. You can do it like this.

For example, both the first and second lookup tables have enlargement magnifications of 1.0, 1.2, ..., 1.8.
When 6 types of 2x and 2.0x are prepared and the specified magnification is 1.3x, the response R obtained from the 1.2x lookup table and the 1.4x lookup table respectively. ₁ (1.2) and R ₁ (1.
4) and linearly interpolated and the response R ₁ (1.3) = 0.5R
It should be ₁ (1.2) + 0.5R ₁ (1.4). Similarly, for the response R ₂ of the other interpolation function, R ₂ (1.3) = 0.
It should be 5R ₂ (1.2) + 0.5R ₂ (1.4).

That is, in general, the enlargement ratios n ₁ , n ₂ , n
_When the look-up tables of ₃ , ..., _Ni , _{ni + 1} , ... Are prepared, the specified enlargement factor is n _j (i ≦ j
When ≦ i + 1), based on the n _i response R obtained from the lookup table ₁ (n _i) and n _{i + 1} of the look-response R ₁ obtained from up table (n i _{+ 1)} R ₁ (n _j ) = s using a real number s such that 0 ≦ s ≦ 1.
The response R ₁ of _one interpolation function may be obtained according to R ₁ (n _i ) + (1−s) · R ₁ (n _{i + 1} ).
The response R ₂ of the other interpolation function can be similarly obtained.

The image data interpolation calculation device of the present invention is expressed by the following equations (1) and (2) for obtaining two interpolated images having different sharpness with respect to a large number of original image data representing an image. The corresponding interpolation coefficient B for each of the image data Yij in the two different interpolation functions f and g
ij and Cij are linearly combined as shown in the following equation (3) to perform interpolation calculation according to the equation (4) by the interpolation function h having a new interpolation coefficient Aij, and the original image data is In an image data interpolation calculation device for obtaining interpolated image data with different intervals, f = ΣBij · Yij (1) g = ΣCij · Yij (2) Aij = (1-α) Bij + αCij (3) h = ΣAij · Yij (4) ) Storage means for storing the interpolation coefficients Bij and Cij, and a coefficient α for determining the sharpness of the secondary image reproduced based on the interpolation image data in a range smaller than 0 and / or a range larger than 1 Input means for inputting as a real number including the interpolation coefficients Bij and Cij stored in the storage means
And an interpolation coefficient calculation means for obtaining an interpolation coefficient Aij corresponding to the coefficient α based on the coefficient α inputted from the input means, and the calculation formula of the formula (4) is stored in advance, and the interpolation coefficient calculation is performed. And an interpolation calculation means for calculating the interpolation image data Y _p at the interpolation point X _p according to the equation (4) based on the interpolation coefficient Aij and the original image data Yij calculated by the means. Is.

Also in this apparatus, as the two interpolation functions having different sharpness, an interpolation function corresponding to an image having a low sharpness corresponds to a beespline interpolation calculation function, and an image having a sharpness higher than this is used. It is desirable to use the cubic spline interpolation calculation function as the interpolation function,
The invention is not limited to the combination of the two, but various interpolation calculation functions such as a bee spline interpolation calculation function, a cubic spline spline interpolation calculation function, a linear interpolation function, and a Lagrange interpolation calculation function can be used. Any two interpolation operation functions can be combined.

The image data interpolating operation apparatus of the present invention further comprises a response input means for inputting a desired response R for the interpolated image, a spatial frequency and a response R ₁ for one of the two interpolating functions. With a plurality of first look-up tables set in advance in correspondence with a plurality of different image enlargement magnifications, and the spatial frequency and the response R ₂ of the other interpolation function for a plurality of different image enlargement magnifications. The image enlargement ratio is referred to by referring to a plurality of second look-up tables set in advance in association with each other, and the first look-up table and the second look-up table corresponding to a desired image enlargement ratio for the interpolated image. Response R ₁ of one interpolation function and response R ₁ of the other interpolation function in
₂ is obtained, and based on the obtained response R ₁ of one interpolation function and the response R ₂ of the other interpolation function and the desired response R, the coefficient α is calculated by the following equation (5). It is also possible to adopt a configuration having a coefficient calculating means to be obtained.

Α = (R−R ₁ ) / (R ₂ −R ₁ ) (5) In this case, the image enlargement ratio, which is the enlargement ratio of the interpolated image with respect to the original image, is input from an independent enlargement ratio input means or the like. Alternatively, the response input means may have this function.

As the first and second lookup tables, for example, the one shown in FIG. 5 can be applied. Also, regarding the correspondence when the input image enlargement ratio is a ratio for which a lookup table is not prepared in advance, as with the case of the interpolation calculation method of the present invention described above, it is the closest to the input ratio. The two response values respectively obtained from the look-up tables corresponding to the two magnifications may be obtained by linear interpolation.

[0046]

The image data interpolation calculation method and apparatus according to the present invention provides a first interpolation function f for obtaining an interpolated image having a first sharpness for a large number of original image data representing an image.
And a second interpolation function g for obtaining an interpolated image having a second sharpness different from the first sharpness, the corresponding interpolation coefficients for each image data are linearly combined and new interpolation is performed. Find the coefficient. 2 by the linear combination at this time
The weighting coefficient for each interpolation coefficient is not limited to one in the range of 0 to 1
It is possible to obtain an interpolated image having various sharpnesses in a range not limited to the sharpness within the range between the sharpness and the second sharpness.

That is, specifically, the first interpolation function f
And the second interpolation function g is as shown below, f = ΣBij · Yij, g = ΣCij · Yij (where Yij is the original image data and Bij and Cij are the interpolation coefficients) Image data The linear combination of the corresponding interpolation coefficients for
For example, regarding the interpolation coefficient B12 in the interpolation function f and the interpolation function C12 in the interpolation function g for the image data Y12 (when i = 1, j = 2), A12 = (1−α) B12 + αC12 (where α is all real numbers) Means to perform an operation.

Interpolation coefficients Bij, C of other original image data Yij
Also for ij, a new interpolation coefficient Aij is obtained by performing linear combination with the arithmetic expression shown in the following expression (3).

Aij = (1-α) Bij + αCij (3) Here, in the conventional linear combination, the coefficient α is 0 to 1
However, in the method and apparatus of the present invention, since the coefficient α can take a value less than 0 or a value greater than 1, the sharpness of the interpolation functions f and g A sharper image having a higher sharpness than the interpolation image obtained by the interpolation function capable of obtaining a sharper interpolation image having a higher sharpness, or a smoother image having a lower sharpness than the interpolation functions f and g. It is also possible to obtain a smooth image with a sharpness lower than that of the interpolation image obtained by the interpolation function that can obtain a different interpolation image, and the sharpness of the interpolation image can be selected according to the image type and the enlargement ratio. The degree of freedom can be greatly expanded. For example, since a very sharp image is desired in a radiation image of a blood vessel shadow, if a weighting coefficient for an interpolation coefficient (for example, Cij) for an interpolation function having a higher sharpness is set to a value exceeding 1. It is possible to obtain an interpolated image with extremely high sharpness, while it is desirable to reproducibly blur the stepwise density change portion that may occur due to low CT resolution in the CT scanner image of the liver. Because
By setting the weighting coefficient for the interpolation coefficient (for example, Bij) for the interpolation function with the lower sharpness to a value exceeding 1, it is possible to obtain an interpolated image with extremely low sharpness, and meet these various needs. be able to.

Further, the input means includes a response input means for inputting a desired response R, a plurality of first look-up tables for one interpolation function and a plurality of second look-up tables for the other interpolation function. ,
In the case of the interpolation calculation device having the configuration including the coefficient calculation means, the method and device of the present invention directly specify the response R of the image, which is easy to grasp the degree of change in sharpness, as a desired value. Since the coefficient α corresponding to the response is obtained by the first and second look-up tables, it is possible to obtain an interpolated image with a sharpness closer to that of a device that specifies α as an inorganic simple coefficient.

[0051]

BEST MODE FOR CARRYING OUT THE INVENTION An embodiment of an interpolation calculation method for image data according to the present invention will be described below.

FIG. 1 is an interpolation calculation apparatus which is a concrete embodiment for carrying out the image data interpolation calculation method of the present invention.
FIG. 3 is a schematic block diagram showing an image reproduction system including 30. The illustrated image reproduction system includes an image data storage device 10 storing image data representing an image, and image data stored in the image data storage device 10 so as to conform to a predetermined reproduction format (hereinafter referred to as primary image data or A multi-formatter 20 that performs a predetermined signal processing on Sorg (hereinafter referred to as original image data) and image data (hereinafter referred to as secondary image data or interpolation image data) S ′ subjected to a predetermined signal processing by the multi-formatter 20 Based on the above, a CRT for reproducing a visible image in the desired reproduction format
And a reproducing means 40 such as a printer.

The multi-formatter 20 divides, for example, one film into four small areas which are different from each other, and prints a reduced image of four different images in each area, and one format on one film. The primary image data Sorg is adapted so as to be compatible with various formats for reproducing an image, such as a format for printing a large image as it is or a format for enlarging a part of the image and printing the enlarged part on the film. The signal processing is performed, and in particular, when the image is enlarged or reduced, the interpolation calculation device 30 of the present invention for calculating secondary image data (interpolation image data) having a different number of data from the primary image data Sorg is included. It is what

Here, the primary image data Sorg used in this embodiment is the sampling points (pixels) X _k-2 , arranged in one direction, which are sampled at evenly-spaced intervals.
_{X k-1, X k,} X k + 1, X k + 2, the digital image data Y _k-2 corresponding to _{..., Y k-1, Y} k, Y k + 1, Y k + 2, ...
Is.

The interpolation calculation device 30 included in the multi-formatter 20 uses the original sampling points X _{k to} X _{k + 1.}
The first secondary image data Y _p of the interpolation point X _p provided between
Cubic cubic spline interpolation calculation formula (2
The original image data Y _k-1 , Y _k , Y _{k + 1} , Y in 2)
interpolation coefficients c _k-1 , c _k corresponding to _{k + 2} ,
The cubic spline interpolation coefficient storage means 32 storing c _{k + 1} and c _{k + 2} as shown below, and Y _p 1 = c _k-1 Y _k-1 + c _k Y _k + c _{k + 1} Y _{k +1} + c _{k + 2} Y _{k + 2} (22) c _k-1 = (− t ³ + 2t ² −t) / 2 c _k = (3t ³ −5t ² +2) / 2 c _{k + 1} = (− 3t ³ + 4t ² + t) / 2 c _{k + 2} = (t ³ −t ² ) / 2 (where t (0 ≦ t ≦ 1) is a grid interval of 1 and the interpolation point is based on the pixel X _k ) The position of X _{p in} the pixel X _{k + 1} direction is shown.) 3 representing the second secondary image data Y _p 2 of the interpolation point X _p provided between the original sampling points X _{k to} X _{k + 1} Interpolation coefficients b _k-1 , b _k , b _{k + 1} corresponding to the respective original image data Y _k-1 , Y _k , Y _{k + 1} , Y _{k + 2} in the following B-spline interpolation calculation formula (23). , B _{k + 2} are stored as shown below, respectively. B spline interpolation coefficient storage means 31 and Y _p 2 = b _k-1 Y _k-1 + b _k Y _k + b _{k +} 1 Y _{k + 1} + b _{k + 2} Y _{k + 2} (23) b _k-1 = (- ^{t 3 + 3t 2 -3t + 1} ) / 6 b k = (3t 3 -6t 2 +4) / 6 b k + 1 = (- 3t 3 + 3t 2 + 3t + 1) / 6 b k + 2 = t 3/6 ( provided that, t (0.ltoreq.t.ltoreq.1) indicates the position of the interpolation point _{Xp in} the direction of the pixel _{Xk + 1} when the grid interval is 1 and the pixel _Xk is a reference.) Stored in the cubic spline interpolation coefficient storage means 32. Interpolation coefficients (hereinafter referred to as cubic spline interpolation coefficients) c _k−1 , c _k , c _{k + 1} , c _{k + 2} and the interpolation coefficients stored in the bee spline interpolation coefficient storage means 31 (hereinafter, bee spline interpolation). Called coefficients) b _k-1 , b _k , b _{k + 1} , b
and _{k + 2,} according to the following equation (24) to (27), the interpolation coefficients and adding the weighted each corresponding to the original image data _{Y k-1, Y k,} Y k + 1, Y k + 2 The calculation means 33 and a _k-1 = (1-α) c _k-1 + αb _k-1 = {(2α-3) t ³ − (3α-6) t ² −3t + α} / 6 (24) a _k = (1-α) c _k + αb _k = {(9-6α) t ³ + (9α-15) t ² + (6-2α)} / 6 (25) _{ak + 1} = (1-α) c _{k + 1} + αb _{k + 1} = {(6α-9) t ^3- (9α-12) t ² + 3t + α} / 6 (26) _{ak + 2} = (1-α) c _{k + 2} + αb _{k + 2} = {(3-2α) t ³ + (3α-3) t ² } / 6 (27) Input means 35 for inputting an arbitrary parameter α for determining the weighting ratio to the interpolation coefficient calculation means 33, and the following in advance. Store the cubic spline interpolation function calculation formula of the formula (21),
The interpolation coefficients a _k-1 , a _k , a _{k + 1} , a _{k + 2} and the original image data Y _k-1 , Y _k , Y _{k + 1} according to the parameter α obtained by the interpolation coefficient calculation means 33. This is a configuration including an interpolation calculation means 34 for obtaining the interpolated image data Y _p of the interpolation point X _p based on Y _{k + 2} according to the equation (21).

Y _p = a _k-1 Y _k-1 + a _k Y _k + a _{k + 1} Y _{k + 1} + a _{k + 2} Y _{k + 2} (21) Incidentally, the interpolation coefficient a _k stored in the storage means 31. _-1 , a _k ,
a _{k + 1} and a _{k + 2} are obtained in advance by the above-described algorithm. Further, the parameter α can take all real numbers including a range exceeding 1 and a range less than 0.

Further, since an actual image is formed by arranging pixels in a two-dimensional array, the above interpolation coefficients a _k-1 , a _k , a
_{k + 1} and a _{k + 2} are two different pixels of the image.
It is obtained for each of the two array directions (i-direction and j-direction), and the thus-obtained one is referred to as an interpolation coefficient Aij, and similarly, a beespline interpolation coefficient b _k-1 ,
Bij is a cubic spline interpolation coefficient c that is obtained for each of the i direction and the j direction of b _k , b _{k + 1} , and b _{k + 2.
A value} obtained for each of the i direction and the j direction of _k-1 , c _k , c _{k + 1} , and c _{k + 2} may be referred to as Cij.

Further, the interpolation coefficient calculation means 33 may store the above equations (24) to (27) in advance, and can replace the beespline interpolation coefficient storage means 31 and the cubic spline interpolation coefficient storage means 32.

Here, the image reproducing system of the present embodiment not only outputs the interpolated image data S ′, but also makes the interval of the array of the interpolated image data S ′ the same as the array interval of the original image data Sorg. By expanding, the interpolated image is reproduced as an enlarged version of the original image. This processing is usually performed by the function of the multi-formatter 20. Therefore, the multi-formatter 20 is configured so that a desired enlargement ratio can be input from an input means (not shown).

Next, the operation of the image reproducing system of this embodiment will be described.

First, the multi-formatter 20 determines the primary image data Sorg stored in advance in the image data storage device 10.
Read out. Further, the multi-formatter 20 interpolates the read primary image data Sorg in the multi-formatter 20 in order to obtain secondary image data representing an enlarged image corresponding to the enlargement magnification input from the input means (not shown). Input to the arithmetic unit 30.

The primary image data Sorg input to the interpolation calculation device 30 is input to the interpolation calculation means 34.

On the other hand, the bee spline interpolation coefficient storage means 3
1. The cubic spline interpolation coefficient storage means 32 sets the value of t in each interpolation coefficient according to the enlargement ratio input from the input means to the multi-formatter 20 not shown. For example, when a magnification of 2 times is input, 0.5 and 1.0 are set as the value of t, and when it is 4 times, 0.25,
Each value of 0.5, 0.75, 1.0 is set, 0.1, 0 when 10 times.
Each value of 2, ..., 1.0 is set as the value of t. The beespline interpolation coefficient for each value of t set in this way,
The cubic spline interpolation coefficient is the interpolation coefficient calculation means 33.
Entered in.

Further, the value of the parameter (coefficient) α corresponding to the desired sharpness of the secondary image is input to the input means 35, and the value of this parameter α is also input to the interpolation coefficient calculation means 33.

Regarding the parameter α, the operator may directly input the parameter α from the outside, or the response R corresponding to the sharpness of the interpolation image desired by the operator.
By inputting, the response R may be converted into the corresponding parameter α inside the input means 35.

In order for the input means 35 to have the function of receiving the input of the response R and converting it into the parameter α in this way, the input means 35 may be configured as shown in FIG.

That is, the input means 35 shown in FIG. 3 includes the response input means 35a for inputting the response R desired by the operator for the interpolated image and the spatial frequency for the cubic spline interpolation function represented by the equation (22). And response R ₁ are different from each other in a plurality of image enlargement magnifications (for example, enlargement magnifications 1.0 times, 1.2 times, ...
For example, six kinds of first look-up tables 35b having a function shape as shown in FIG. 5 (A), which are set in advance in association with each other, and the spatial frequency of the beespline interpolation function represented by the equation (23), The response R ₂ and a plurality of image enlargement factors different from each other (for example, an enlargement factor of 1.0,
1.2 times, ..., 1.8 times, 2.0 times), and 6 types of second look-up tables 35c having function shapes as shown in FIG. magnification to see the first look-up table 35b and a second lookup table 35c corresponding, calculated the response R ₂ of the response R ₁ and Bee spline interpolation function of the cubic spline interpolation function of the image magnification of, Based on the obtained two responses R ₁ and R ₂ and the desired response R, the parameter α is calculated by the calculation according to the following equation (5).
And a coefficient calculating means 35d for obtaining

Α = (R−R ₁ ) / (R ₂ −R ₁ ) (5) The first lookup table 35b and the second lookup table 35c are stored in one database.

By configuring the input means 35 as described above, it becomes possible to specify by the response R, which makes it easy to grasp the degree of change in sharpness as a real feeling.

[0070] Note that the image magnification at the time of the coefficient calculation means 35d seek a response R ₂ of the response R ₁ and Bee spline interpolation function of the cubic spline interpolating function, multi-formatter 20 from the input means (not shown)
Is the desired enlargement ratio input to.

The parameter α directly input in this way or calculated based on the input response R
Is input to the interpolation coefficient calculation means 33.

The interpolation coefficient calculation means 33 creates a new value for each t value corresponding to the value of the parameter α, based on the input α bespline interpolation coefficient and cubic cubic spline interpolation coefficient for each value of t and the parameter α. The interpolation coefficients a _k-1 , a _k , a _{k + 1} , a _{k + 2} are calculated according to the equations (24) to (27).

The calculated new interpolation coefficients a _k-1 , a _k ,
The a _{k + 1} and a _{k + 2} are input to the interpolation calculation means 34.

The interpolation calculation means 34 is provided with the interpolation coefficients a _k-1 , a _k , a _{k + 1} and a _{k + 2} inputted from the interpolation coefficient calculation means 33 and the original image data inputted from the image data storage device 10. Y
_{Based on k-1} , Y _k , Y _{k + 1} , and Y _{k + 2} , the interpolated image of the interpolation point X _p for each t according to the stored third-order spline interpolation function calculation formula of the formula (21). The data Y _p is calculated.

The interpolated image data S ′ of all the interpolated points thus obtained are output to the reproducing means 40.

The reproducing means 40 reproduces an image based on the input interpolation image data S'as a visible image. The sharpness of the reproduced visible image is easily adjusted only by changing the value of the input parameter α. Then, if the input parameter α is set to a negative value less than 0, a sharp image having a higher sharpness than the secondary image obtained by the normal cubic spline interpolation calculation can be obtained, and the parameter α exceeds 1 If the value is set to a value, a smooth image having a sharpness lower than that of the secondary image obtained by the normal bee spline interpolation calculation can be obtained. If the parameter α is set to a value of 0 or more and 1 or less, the bee spline interpolation calculation is performed. It is possible to obtain an image having an intermediate sharpness between the secondary image obtained by the above method and the secondary image obtained by the cubic spline interpolation calculation. Of course, when the input means 35 is configured to input the desired response R described above, if the desired response R is changed and input to the response input means 35a, the value of the parameter α similarly changes. The sharpness can be easily adjusted.

The interpolation calculation device 30 used in the image reproduction system of this embodiment has been described as one using the primary image data previously stored in the image data storage device 10. However, the interpolation calculation device of the present invention is not limited to this. The present invention is not limited to this form, and may be a form using image data representing an image read by an image reading device as shown in FIG. 2, for example.

That is, the image reading device shown in FIG. 2 is a device for reading the accumulated and recorded transmission X-ray image as image information from the stimulable phosphor sheet 100 in which the transmission X-ray image of the subject is accumulated and recorded. .

Accumulative phosphor sheet on which an X-ray image is recorded
100 is set at a predetermined position of the reading unit 50 of the X-ray image reading apparatus. When the stimulable phosphor sheet 100 is set at a predetermined position of the reading unit 50, the sheet 100 is conveyed (sub-scanned) in the arrow Y direction by the endless belt 52 driven by the motor 51. On the other hand, the light beam 54 emitted from the laser light source 53 is reflected and deflected by a rotating polygon mirror 56 driven by a motor 55 and rotating at a high speed in the direction of the arrow f,
After passing through a converging lens 57 such as a θ lens, the optical path is changed by a mirror 58 to enter the sheet 100, and main scanning is performed in an arrow X direction substantially perpendicular to the sub-scanning direction (arrow Y direction). From the portion of the sheet 100 irradiated with the excitation light 54, a quantity of stimulated emission light 59 according to the accumulated and recorded X-ray image information is emitted, and this stimulated emission light 59 is guided by the light guide 60. , Photomultiplier (photomultiplier tube) 61 detects photoelectrically.

The light guide 60 is made by molding a light guide material such as an acrylic plate, and the linear incident end face 60a extends along the main scanning line on the stimulable phosphor sheet 100. End face 60b, which is annularly formed
Is connected to the light receiving surface of the photomultiplier 61.
The stimulated emission light 59 that has entered the light guide 60 from the incident end face 60a.
Travels through the light guide 60 by repeating total reflection, is emitted from the emission end face 60b and is received by the photomultiplier 61, and the stimulated emission light 59 representing an X-ray image is converted into an electric signal by the photomultiplier 61. To be converted.

The analog output signal S output from the photomultiplier 61 is logarithmically amplified by the log amplifier 62,
The signal is converted into a digital signal by the A / D converter 63, whereby the original primary image data Sorg is obtained and input to the above-mentioned multi-formatter 20.

As described above, the primary image data used in the interpolation calculation device 30 of the present invention may be stored in the image data storage device 10 in advance, or an image reading device as shown in FIG. It may be one obtained by reading.

[Brief description of drawings]

FIG. 1 is a schematic block diagram showing an image reproduction system including a specific interpolation calculation device for carrying out an image data interpolation calculation method of the present invention.

FIG. 2 is a block diagram showing an image reading device.

FIG. 3 is a diagram showing an input unit configured to have a response input unit, first and second look-up tables, and a coefficient calculation unit.

FIG. 4 is a graph for explaining a conventional operation of obtaining interpolated image data by cubic spline interpolation calculation from original image data of sampling points (pixels) arrayed in one direction sampled at evenly-spaced intervals.

FIG. 5 is a schematic graph showing a correspondence relationship between a spatial frequency and a response, showing examples of first and second lookup tables.

[Explanation of symbols]

10 Image data storage 20 Multi formatter 30 Interpolation calculation device 31 B-spline interpolation coefficient storage means 32 Cubic spline interpolation coefficient storage means 33 Interpolation coefficient calculation means 34 Interpolation calculation means 35 Input means 40 means of reproduction Sorg primary image data (original image data) S'Secondary image data (interpolated image data)

Claims (6)

(57) [Claims] 1. A plurality of different original image data Yij representing images, which are expressed by the following equations (1) and (2) for obtaining two interpolated images having different sharpnesses.
Expression by interpolation function h having new interpolation coefficient Aij obtained by linearly combining corresponding interpolation coefficients Bij, Cij for each image data Yij in one interpolation function f, g as shown in the following expression (3) In the image data interpolation calculation method for performing interpolation calculation according to (4) to obtain interpolation image data having a different interval from the original image data, f = ΣBij · Yij (1) g = ΣCij · Yij (2) Aij = (1-α) Bij + αCij (3) h = ΣAij · Yij (4) (where i = 1, 2, ..., j = 1, 2, ...) The coefficient α in the equation (3) is smaller than 0. An interpolation calculation method for image data, wherein the range and / or a real number including a range larger than 1 is used. 2. A plurality of first look-up tables in which the spatial frequency and the response R ₁ for one of the two interpolation functions are set in advance in association with each other for a plurality of different image enlargement magnifications. , And a plurality of second look-up tables in which the spatial frequency and the response R ₂ of the other interpolation function are set in advance in association with each other for each of a plurality of different image enlargement magnifications.
With reference to the first lookup table and the second lookup table corresponding to the desired image enlargement ratio for the interpolated image, the response R _{1 of the one} interpolation function at the image enlargement ratio and the other interpolation The response R ₂ of the function is obtained, and based on the desired response R for the interpolated image, the response R ₁ of the one interpolation function, and the response R ₂ of the other interpolation function, an operation according to the following equation (5) is performed. The interpolation calculation method for image data according to claim 1, wherein the coefficient α is obtained. _{α = (R-R 1)} / (R 2 -R 1) (5) 3. The interpolation of image data according to claim 1, wherein one of the two interpolation functions having different sharpnesses is a bee spline interpolation operation function and the other is a cubic spline interpolation operation function. Calculation method. 4. Two different interpolation functions f represented by the following formulas (1) and (2) for obtaining two interpolated images having different sharpness with respect to a large number of original image data representing an image. , G corresponding to the respective image data Yij for each of the image data Yij are linearly combined as shown in the following equation (3) to obtain an equation (4) by an interpolation function h having a new interpolation coefficient Aij. Accordingly, in the image data interpolation calculation device for performing interpolation calculation to obtain interpolation image data having a different interval from the original image data, f = ΣBij · Yij (1) g = ΣCij · Yij (2) Aij = (1 -Α) Bij + αCij (3) h = ΣAij · Yij (4) (where i = 1, 2, ..., j = 1, 2, ...) Storage means for storing the interpolation coefficients Bij, Cij; Of the secondary image reproduced based on the interpolated image data Input means for inputting a coefficient α for determining the sharpness as a real number including a range smaller than 0 and / or a range larger than 1, and the interpolation coefficients Bij and Cij stored in the storage means and the input from the input means. An interpolation coefficient calculation means for obtaining an interpolation coefficient Aij corresponding to the coefficient α based on the coefficient α; and an interpolation coefficient Aij obtained by the interpolation coefficient calculation means for storing the calculation expression of the equation (4) in advance. and on the basis of the original image data Yij, interpolating operation apparatus for an image data characterized by including an interpolation arithmetic means for obtaining an interpolated image data Y _p of the interpolation point X _p in accordance with formula (4). 5. The response input means for inputting a desired response R for the interpolated image, and the spatial frequency and the response R ₁ for one of the two interpolation functions are different from each other. A plurality of first look-up tables set in advance for each of a plurality of image enlargement factors, and a spatial frequency and a response R ₂ of the other interpolation function are previously corresponded to a plurality of different image enlargement factors. With reference to a plurality of second look-up tables that are additionally set, and a first look-up table and a second look-up table corresponding to a desired image enlarging ratio for the interpolated image, the image enlarging ratio calculated response R ₂ of the response R ₁ and the other interpolation function interpolation function of the one in this calculated et al One of the based on the responses R ₂ with the desired response R of the response R ₁ and the other interpolation function interpolation function, and a coefficient calculating means for determining the coefficient α by calculating according to the following formula (5) The interpolation calculation device for image data according to claim 4, wherein. _{α = (R-R 1)} / (R 2 -R 1) (5) 6. The interpolation of image data according to claim 4, wherein one of the two interpolation functions having different sharpnesses is a bee spline interpolation operation function and the other is a cubic spline interpolation operation function. Arithmetic unit.