JPH0927902A - Method and device for arithmetic operation for interpolation of image data - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make responses of an interpolated image reproduced by an image reproducing device nearly equal to each other regardless of a prescribed magnification factor in the interpolation arithmetic processing when original image data are magnified by the magnification. SOLUTION: Interpolation arithmetic processing is applied to original image data D to obtain interpolation image data whose picture element pitch differs from that of the original image data D, the interpolated image data are fed to a thermosensing recorder 28 in which the image is reproduced as a hard copy 29. In this case, different interpolation arithmetic processing is applied to the image data D depending on the magnification factor with respect to the original image by a method such as a Cubic spline and a B spline. Thus, the responses of the interpolated image are arranged nearly equal to each other regardless of the magnification.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and apparatus for interpolating image data, and more particularly to interpolating image data such that the responses of interpolated images can be made substantially equal regardless of the enlargement ratio of the original image. The present invention relates to a calculation method and device.

[0002]

2. Description of the Related Art Radiation (X-ray, α-ray,
(β-rays, γ-rays, electron beams, ultraviolet rays, etc.), a part of the energy of this radiation is accumulated in the phosphor, and then, when the phosphor is irradiated with excitation light such as visible light, it is accumulated. The phosphor emits stimulated emission depending on energy. A phosphor exhibiting such properties is referred to as a stimulable phosphor.

Using this stimulable phosphor, radiation image information of a subject such as a human body is once recorded on a stimulable phosphor sheet (hereinafter referred to as a stimulable phosphor sheet), and the sheet is excited with excitation light. A radiation image information recording / reproducing system is proposed in which scanning is performed to cause stimulated emission, the stimulated emission is photoelectrically read to obtain an image signal, and the image signal is processed to obtain a radiation image of a subject having a good diagnostic suitability. (For example,
55-12429, 55-116340, 55-163472, 56
-11395, 56-104645, etc.).

In the 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. This visible image is subjected to a predetermined interpolation operation on the original image data obtained by reading the original image to obtain interpolated image data which is two-dimensional image data having a data number different from the original image data number. , By reproducing a visible image based on the interpolated image data.

As an interpolation method of such image data,
Various methods such as a method using a quadratic or cubic spline interpolation function have been proposed in addition to a method using linear interpolation. For example, Cubic using cubic spline interpolation function
The spline interpolation calculation requires passing through the original sample points (pixels) and that the first-order differential coefficient thereof be continuous between each section, which results in a sharp sharpness with a relatively high sharpness.
It is for reproducing the next image (image obtained by interpolation). Also known is a B-spline interpolation calculation for obtaining interpolation image data for reproducing a smooth secondary image having a relatively low sharpness with respect to the Cubic spline interpolation calculation. In this way, if it is desired to reproduce the secondary image sharply with high sharpness, Cubic spline interpolation calculation is used, and if it is desired to reproduce smoothly with low sharpness, B spline interpolation calculation is used.

[0006]

However, when the interpolated image data is sent to the image reproducing apparatus and reproduced, the response of the reproduced interpolated image differs depending on the enlargement ratio with respect to the original image. That is, as the image is enlarged, the response of the high frequency component of the image decreases, and the image becomes blurred. Therefore, even if the image is enlarged in order to observe the region of interest to be observed in more detail, the image is rather difficult to see, and necessary image information may not be obtained.

In view of the above circumstances, it is an object of the present invention to provide an image data interpolation calculation method and apparatus capable of making the response of an image represented by interpolated image data substantially equal regardless of the enlargement ratio with respect to the original image. To do.

[0008]

SUMMARY OF THE INVENTION An image data interpolation calculation method and apparatus according to the present invention uses original image data indicating original pixel data indicating pixel values of respective pixels arranged in a grid at predetermined intervals. In the interpolation calculation method for the image data, the interpolation image data having a different interval from the original image data is obtained by an interpolation calculation process according to the enlargement ratio for the original image represented, and the interpolation image data is sent to the image reproducing apparatus. By performing different interpolation calculation processing on the original image data according to the rate, the response of the interpolated image data displayed on the image reproduction device is made substantially equal regardless of the enlargement rate. .

[0009]

According to the interpolation image data calculation method and apparatus of the present invention, when performing interpolation calculation processing on original image data, different interpolation calculation processing is performed in accordance with the enlargement ratio and reproduced by the image reproducing apparatus. Since the response of the interpolated image is substantially equal regardless of the enlargement ratio, the response of the interpolated image displayed on the image reproduction device is substantially equal regardless of the enlargement ratio of the original image. Therefore, it is possible to prevent the response of the reproduced interpolated image from being different depending on the enlargement ratio and making the image difficult to see as compared with the original image.

If the present invention is applied to a radiation image information recording / reproducing system using the above-mentioned stimulable phosphor sheet, a radiation image having extremely high diagnostic suitability can be reproduced, but such radiation image information is preferable. Needless to say, even when it is applied to a system other than the recording / reproducing system, the above-described actions and effects can be obtained.

[0011]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described in detail based on embodiments shown in the drawings. FIG. 1 shows an example of a radiation image information recording / reproducing system including an apparatus for performing interpolation calculation according to the present invention. This system reads the radiation image information recorded on the above-mentioned stimulable phosphor sheet and reproduces and records the read radiation image by a thermal recording device as an example.

For example, a stimulable phosphor sheet 10 in which transmission radiation image information of a subject is accumulated and recorded by irradiating a subject such as a human body with radiation such as X-rays. , And is conveyed in the arrow Y direction for sub-scanning. Excitation light source such as semiconductor laser
A laser beam 13 as excitation light (reading light) emitted from 12 is reflected and deflected by a rotating polygon mirror 14 that rotates at high speed, focused by a scanning lens 18 which is usually an f.theta. Lens, and reflected by a mirror 19. The stimulable phosphor sheet 10 is main-scanned in the direction of arrow X, which is substantially perpendicular to the sub-scanning direction Y.

From the portion of the sheet 10 irradiated with the laser beam 13 in this way, stimulated emission light 15 having a light amount corresponding to the radiation image information accumulated and recorded is diverged, and this stimulated emission light 15 is collected. The light is condensed by 16 and photoelectrically detected by a photomultiplier (photomultiplier tube) 17 as a photodetector.

The light collector 16 is formed by molding a light guide material such as an acrylic plate, and has a linear incident end surface.
The emission end face 16b is arranged so as to extend along the beam scanning line on the stimulable phosphor sheet 10 and is formed in an annular shape.
The light receiving surface of the photomultiplier 17 is connected to the photomultiplier 17. The stimulated emission light 15 entering the condenser 16 from the incident end face 16a travels through the interior of the condenser 16 by repeating total reflection, exits from the exit end face 16b, and exits from the photomultiplier.
The photomultiplier 17 detects the amount of photostimulated light 15 received by the photodetector 17 and carrying the radiation image information.

The analog output signal (image signal) S of the photomultiplier 17 is amplified by the logarithmic amplifier 20,
It is digitized by the A / D converter 21 with a predetermined recording scale factor. The digital image data D carrying the two-dimensional image thus obtained is subjected to interpolation calculation processing in the image processing device 27 so as to be enlarged at a predetermined enlargement ratio. Image data D that has undergone interpolation calculation processing
Undergoes image processing such as gradation processing and frequency enhancement processing.
The image data D ′ subjected to this image processing is input to the thermal recording device 28 using the thermal head 28a, and the two-dimensional image represented by the image data D ′ is reproduced and recorded on the hard copy 29 in the thermal recording device 28.

Next, the interpolation calculation process in the image processing device 27 will be described in detail. This image processing device 27
Is a buffer memory 23 for temporarily storing digital image data indicating pixel values for one image, a memory 24 for storing interpolation coefficients and the like, which will be described later, an interpolation calculator 25 and an image processor 26. Become.

Here, the response characteristic of the interpolated image data depending on the enlargement ratio is as shown in FIG. In FIG. 2, the spatial frequency at which the response is desired to be aligned regardless of the enlargement ratios a, b, and c is α, and the MTF (Modulation Transfer Functi) of the interpolated image data corresponding to this spatial frequency α is set.
on, frequency-dependent characteristic) are m, m ′, and m ″, respectively, in order to make the responses at the spatial frequency α uniform, the response at the magnification rate b becomes m / m ′ with respect to the response at the magnification rate a. One-dimensional interpolation of various functions,
The one-dimensional interpolation of the function such that the response of the enlargement ratio c is m / m ″ with respect to the response of the enlargement ratio a is performed on the image data D.
Need to be applied to. Therefore, for this reason, in the interpolation calculation unit 25, the response of the interpolated image is calculated at each enlargement ratio a, b, c.
The interpolation calculation processing is performed on the image data D so as to be substantially equal to each other.

In this embodiment, the enlargement ratio a
The interpolation calculation of the enlargement factor b with respect to
The description of the interpolation calculation of the enlargement factor c with respect to? As shown in FIG. 2, the response of the enlargement rate a is the enlargement rate b.
Since the response is higher than the response of, the B-spline interpolation operation is performed on the image data D in the case of the enlargement ratio a to perform smooth interpolation with a low sharpness, and the Cubic spline is performed in the image data D in the case of the enlargement ratio b. By the interpolation calculation, sharp interpolation is performed with high sharpness.

The Cubic spline interpolation calculation and the B spline interpolation calculation will be described in detail below.

Successive pixels X _k-2 , X _k-1 , X _k , X _{k + 1} , X obtained by digitally reading the original image
Image data (original image data) of _{k + 2} , ... _Yk-2 , _Yk-1 , _Yk , _{Yk + 1} , _{Yk + 2} , respectively, as shown in FIG.
... 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.
_The spline interpolation functions, which are respectively set for _{k + 1 to} X _{k + 2} and correspond to the respective sections, are f _k-2 , f _k-1 , f _k ,
Let 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 point 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 expressed by the following equation (1).

F _k (x) = A _k x ³ + B _k x ² + C _k x + D _k (1) 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 (2) to (5).

F _k (X _k ) = Y _k (2) f _k (X _{k + 1} ) = Y _{k + 1} (3) f _k ′ (X _k ) = f _k−1 ′ (X _k ) (4 ) F _k ′ (X _{k + 1} ) = f _{k + 1} ′ (X _{k + 1} ) (5) Note that f _k ′ is the first derivative (3A _k x ² +2) of the function f _k .
B _k x + C _k ).

[0024] In the Cubic spline interpolating operation, the first-order differential coefficient at the picture element X _k is the pixel X _k
For the X _k-1 and X _{k + 1} is the preceding and succeeding pixels, these image data _{Y k-1, Y k +} 1 gradient _{(Y k + 1 -Y k-} 1)
Since the condition is that it matches / (X _{k + 1} −X _k−1 ), it is necessary to satisfy the following expression (6).

F _k ′ (X _k ) = (Y _{k + 1} −Y _k−1 ) / (X _{k + 1} −X _k−1 ) (6) 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}
Since the condition is that Y _k ) / (X _{k + 2-} X _k ), the following formula (7) must be satisfied.

F _k ′ (X _{k + 1} ) = (Y _{k + 2} −Y _k ) / (X _{k + 2} −X _k ) (7) Here, each section X _{k−2 to} X _k−1 , X _{k-1 to} X _k , X _k to
The interval between X _{k + 1} , X _{k + 1 to} X _{k + 2} (referred to as lattice 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 (1) to (4) and (6), (7) Therefore, 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 (8). Here, the respective coefficients A _k , B _k , C
Substituting _k and D _k into the equation (8), 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 becomes, which original image data _{Y k-1, Y k,} Y k ₊₁ and Y
_{If k + 2} is arranged, it can be expressed by the following equation (9).

[0027] ^{_{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} (9).

Here, the original image data Y _k-1 , Y _k , Y
Interpolation coefficients a _k-1 , a _k , and _{k + 1} and Y _{k + 2
They} are called a _{k + 1} and a _{k + 2} . That is, the interpolation coefficients a _k-1 , a _k , a _{k + 1} , a _{k + 2} corresponding to the original image data Y _k-1 , Y _k , Y _{k + 1} , Y _{k + 2} in the equation (9), respectively. _{is, a k-1 = (-} t 3 + 2t 2 -t) / 2 a k = (3t 3 -5t 2 +2) / 2 a k + 1 = (- 3t 3 + 4t 2 + t) / 2 a k + 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, the Cubic spline interpolation calculation requires passing through the original sample points (pixels) and that the first-order differential coefficient is continuous between each section as described above. It is intended to obtain interpolated image data for reproducing a sharp secondary image having a high sharpness (an image obtained by interpolation), but on the other hand, for reproducing a smooth secondary image having a relatively low sharpness. B-spline interpolation calculation for obtaining interpolated image data is also known. This B-spline interpolation operation does not need to go through the original sample points (pixels), but instead the first derivative and second
The differential coefficient (represented by f ″ (X)) is required to be continuous between each section.

That is, in f _k (x) = A _k x ³ + B _k x ² + C _k x + D _k (1), f _k ′ (X _k ) = f _k−1 ′ (X _k ) (10) f _k ′ (X _{k + 1} ) = f _{k + 1} ′ (X _{k + 1} ) (11) f _k ″ (X _k ) = f _k−1 ″ (X _k ) (12) f _k ″ (X _{k + 1} ) = F _{k + 1} ″ (X _{k + 1} ) (13). 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 (14).

F _k ′ (X _k ) = (Y _{k + 1} −Y _k−1 ) / (X _{k + 1} −X _k−1 ) (14) 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}
Since the condition is that Y _k ) / (X _{k + 2-} X _k ), the following formula (15) must be satisfied.

F _k ′ (X _{k + 1} ) = (Y _{k + 2-} Y _k ) / (X _{k + 2-} X _k ) (15) Further, the function f (X) is generally expressed by the following equation (16). It is approximated by things.

F (X) = f (0) + f ′ (0) X + {f ″ (0) / 2} X ² (16) Here, each section X _{k−2 to} X _k−1 , X _{k− 1} ~ X _k , X _k ~
The interval between X _{k + 1} , X _{k + 1 to} X _{k + 2} (referred to as lattice 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 (10) to (13) and (16), 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 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. Further, as described above, the spline interpolation function f _k (x) performs the variable transformation of X = t, so that 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 , and the this Image data Y _k-1 , Y _k , Y _{k + 1} , Y
_By rearranging _{k + 2} , it can be expressed by the following equation (17).

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} (17) 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 expression (17) 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} (18) where if you put the _{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 (19) 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.

The interpolation coefficients a _k-1 , a _k , a _{k + 1} , a _{k + 2} and b _k-1 , b _k , b thus obtained.
_{The k + 1} and b _{k + 2} are stored in the memory 24. When the image data D is input to the interpolation calculation unit 25, the interpolation calculation unit 25
Reads the interpolation coefficient from the memory 24 and performs interpolation calculation of the image data D based on this interpolation coefficient. That is, in the case of the enlargement ratio a, the B-spline interpolation operation is performed on the image data D to perform smooth interpolation with a low sharpness, and in the case of the enlargement ratio b, the high sharpness is performed on the image data D by the Cubic spline interpolation operation. Sharp interpolation is performed depending on the degree.

Interpolation calculation processing is performed in this way,
The image data enlarged to a predetermined enlargement ratio is processed by the image processing unit 26.
Image data D ′ that has been subjected to image processing such as frequency processing and further subjected to image processing is input to the thermal recording device 28.
Is reproduced as a hard copy 29.

In the interpolated image reproduced in this manner, the difference in response due to the enlargement ratio is compensated, and the response of the reproduced image is made substantially equal regardless of the enlargement ratio. This makes it possible to prevent the response from changing depending on the enlargement ratio.

In the above embodiment, the B spline interpolation calculation is performed when the enlargement ratio is a, and the Cubic spline interpolation calculation is performed when the enlargement ratio is b. Spline interpolation and Cubi
Both c-spline interpolation may be used to weight each interpolation coefficient according to the enlargement ratio to perform the interpolation calculation. That is, the following formula (20) F = α · A + (1-α) · B (20) where F: new interpolation coefficient A, B: interpolation coefficient α: range smaller than 0 and / or range larger than 1 In the weighting coefficient including, A is an interpolation coefficient for Cubic spline interpolation, B is an interpolation coefficient for B spline interpolation, and the interpolation coefficient is changed by changing the value of the weighting coefficient t so that the responses of the interpolated images are substantially equal. For example, the original image data Y _k-1 , Y _k , Y
_The Cubic spline interpolation coefficient for _{k + 1} and _{Yk + 2} is a
_{When k-1} , _ak , _{ak + 1} , _{ak + 2} and B spline interpolation coefficients are _bk-1 , _bk , _{bk + 1} , _{bk + 2} , the interpolation value S '
Is S ′ = {α · a _k-1 + (1-α) · b _k-1 } Y _k-1 + {α · a _k + (1-α) · b _k } Y _k + {α · It becomes _{ak + 1} + (1- (alpha)) * _{bk + 1} } _{Yk + 1} + {(alpha * _{ak + 2} + (1- (alpha)) * _{bk + 2} } _{Yk + 2} (21).

Then, in the case of the enlargement ratio a, the value of the weighting factor t is reduced to perform the interpolation operation so that the weighting of the interpolation coefficient of the B-spline interpolation becomes large, and in the case of the enlargement ratio b, the Cubic The value of the weighting coefficient t is increased to perform the interpolation calculation so that the weighting of the interpolation coefficient of the spline interpolation is increased. Thus, Cubic spline interpolation and B
Weight each interpolation coefficient of spline interpolation,
By performing the interpolation calculation process, the responses of the reproduced interpolated images can be made equal regardless of the enlargement ratio.

Further, when the original image data is subjected to the interpolation calculation processing according to the enlargement ratio, for example, Japanese Patent Laid-Open No. 55-16347.
It is also possible to perform frequency processing such as the blur mask processing described in Japanese Patent Publication No. 2) to adjust the response of the interpolated image according to the enlargement ratio.

This is the original image data Dor depending on the enlargement ratio.
The filtering process corresponding to the following calculation process D ′ = Dorg + β (Dorg−Dus) is performed on g. In addition, β is an emphasis coefficient, Dus is blur mask data corresponding to an ultra-low spatial frequency for each pixel, and when the mask size is N and the sum of pixel values of pixels in the mask size is Σ,
Dus = Σ / N.

[0044] For example, the N = 3, the original image data of three pixels arranged in the X direction is x _1, x _2, x _3, the original image data x ₂ in the center of the pixel, D '= x ₂ + Β {x ₂ − (x ₁ + x ₂ + x ₃ ) / 3} = (− β / 3) x ₁ + (1 + 2β / 3) x ₂ + (− β / 3) x ₃ Therefore, x ₂ ′ = Filtering processing is performed to replace ax ₁ + bx ₂ + cx ₃ (b = 1 + 2β / 3, a = c = −β / 3) (22).

As described above, when the interpolation calculation processing is performed on the original image data according to the enlargement ratio, the frequency processing is performed so that the responses of the interpolated images are substantially equal to each other regardless of the enlargement ratio. Similar to the form, the difference in the response of the interpolated image depending on the enlargement ratio is compensated, and the responses of the reproduced images are made substantially equal regardless of the enlargement ratio. This makes it possible to prevent the response from changing depending on the enlargement ratio.

Further, in the present embodiment, instead of the above equations (6) and (7) for performing the Cubic spline interpolation calculation, the following equations (6 ') and (7') to which a parameter α is added are given. ) F _k ′ (X _k ) = α (Y _{k + 1} −Y _k−1 ) / (X _{k + 1} −X _k−1 ) (6 ′) f _k ′ (X _{k + 1} ) = α (Y _{k + 2 -Y k) / (} X k + 2 -X k) with (7 '), may be performed interpolation processing by variously changing the parameters alpha.

That is, in the conventional Cubic spline interpolation calculation, the parameter α in equations (6 ') and (7') is used.
However, since it was fixed at "1", when this Cubic spline interpolation calculation was performed alone or when the B spline interpolation calculation was performed independently, only a secondary image of one response was always obtained, and Cu shown in Kaihei 2-278478
In the spline interpolation calculation that combines the bic spline interpolation calculation and the B spline interpolation calculation, the response can be adjusted only within the range between the response obtained by the Cubic spline interpolation calculation and the response obtained by the B spline interpolation calculation. It is possible to change, for example, by setting the parameter α larger than “1”, it is possible to obtain a secondary image with a higher response than the response obtained by the conventional Cubic spline interpolation calculation,
The response can be increased as the parameter α is increased. Also, set the parameter α to “1”
By setting it smaller, the response is lower than the response obtained by the conventional Cubic spline interpolation calculation.
The next image can be obtained, and the response can be lowered as the parameter α is reduced. Therefore, it is possible to arbitrarily change the value of the parameter α and obtain interpolated image data of a desired response.

As described above, by setting the parameter α for adjusting the response when performing the interpolation calculation on the original image data according to the enlargement ratio, the enlargement ratio is the same as in the above-described embodiment. The difference in response due to is compensated, and the responses of the reproduced images are made substantially equal regardless of the enlargement ratio. This makes it possible to prevent the response from changing depending on the enlargement ratio.

[Brief description of drawings]

FIG. 1 is a schematic configuration diagram showing an example of an apparatus for performing a method of the present invention.

FIG. 2 is a graph showing a response characteristic of an interpolated image according to a magnification rate.

FIG. 3 is a graph illustrating a method of obtaining interpolated image data from original image data of sampling points (pixels) arranged in one direction sampled at evenly-spaced intervals.

[Explanation of symbols]

 10 Accumulative phosphor sheet 11 Sheet conveying means 12 Excitation light source 13 Laser beam 14 Rotating polygon mirror 15 Excited emission light 16 Condenser 17 Photomultiplier 23 Buffer memory 24 Memory 25 Interpolation calculation processing section 26 Image processing section 27 Image processing Device 28 Thermal recording device 29 Hard copy

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[Procedure amendment]

[Submission date] October 2, 1996

[Procedure amendment 1]

[Document name to be amended] Statement

[Correction target item name] 0023

[Correction method] Change

[Correction contents]

F _k (X _k ) = Y _k (2) f _k (X _{k + 1} ) = Y _{k + 1} (3) f _k ′ (X _k ) = f _k−1 ′ (X _k ) (4 ) F _k ′ (X _{k + 1} ) = f _{k + 1} ′ (X _{k + 1} ) (5) Note that 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 continuous condition of the second derivative, but since the formula becomes complicated, it is generally simplified and used as described above.

[Procedure amendment 2]

[Document name to be amended] Statement

[Correction target item name] 0026

[Correction method] Change

[Correction contents]

F _k ′ (X _{k + 1} ) = (Y _{k + 2} −Y _k ) / (X _{k + 2} −X _k ) (7) Here, each section X _{k−2 to} X _k−1 , X _{k-1 to} X _k , X _k to
The interval between X _{k + 1} , X _{k + 1 to} X _{k + 2} (referred to as lattice 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 (1) to (5) and (6), (7) Therefore, 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 (8). Here, the respective coefficients A _k , B _k , C
Substituting _k and D _k into the equation (8), 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 becomes, which original image data _{Y k-1, Y k,} Y k ₊₁ and Y
_{If k + 2} is arranged, it can be expressed by the following equation (9).

[Procedure 3]

[Document name to be amended] Statement

[Correction target item name] 0034

[Correction method] Change

[Correction contents]

F (X) = f (0) + f ′ (0) X + {f ″ (0) / 2} X ² (16) Here, each section X _{k−2 to} X _k−1 , X _{k− 1} ~ X _k , X _k ~
The interval between X _{k + 1} , X _{k + 1 to} X _{k + 2} (referred to as lattice 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 formula (1), (10) -
From (13) and (14) to (16), f _k ′ (0) = C _k = (Y _{k + 1} −Y _k−1 ) / 2 f _k ′ (1) = 3 A _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 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. Further, as described above, the spline interpolation function f _k (x) performs the variable transformation of X = t, so that 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 , and the this Image data Y _k-1 , Y _k , Y _{k + 1} , Y
_By rearranging _{k + 2} , it can be expressed by the following equation (17).

[Procedure amendment 4]

[Document name to be amended] Statement

[Correction target item name] 0040

[Correction method] Change

[Correction contents]

In the above embodiment, the B spline interpolation calculation is performed when the enlargement ratio is a, and the Cubic spline interpolation calculation is performed when the enlargement ratio is b. Spline interpolation and Cubi
Both c-spline interpolation may be used to weight each interpolation coefficient according to the enlargement ratio to perform the interpolation calculation. That is, the following formula (20) F = α · A + (1-α) · B (20) where F: new interpolation coefficient A, B: interpolation coefficient α: range smaller than 0 and / or range larger than 1 In the weighting coefficient including, the interpolation coefficient is changed by changing the value of the weighting coefficient α so that A is the Cubic spline interpolation interpolation coefficient and B is the B spline interpolation interpolation coefficient. For example, the original image data Y _k-1 , Y _k , Y
_The Cubic spline interpolation coefficient for _{k + 1} and _{Yk + 2} is a
_{When k-1} , _ak , _{ak + 1} , _{ak + 2} and B spline interpolation coefficients are _bk-1 , _bk , _{bk + 1} , _{bk + 2} , the interpolation value S '
Is S ′ = {α · a _k-1 + (1-α) · b _k-1 } Y _k-1 + {α · a _k + (1-α) · b _k } Y _k + {α · It becomes _{ak + 1} + (1- (alpha)) * _{bk + 1} } _{Yk + 1} + {(alpha * _{ak + 2} + (1- (alpha)) * _{bk + 2} } _{Yk + 2} (21).

[Procedure Amendment 5]

[Document name to be amended] Statement

[Correction target item name] 0041

[Correction method] Change

[Correction contents]

In the case of the enlargement ratio a, the value of the weighting factor α is decreased to perform the interpolation operation so that the weighting of the interpolation coefficient of the B-spline interpolation becomes large, and in the case of the enlargement ratio b, the Cubic Interpolation calculation is performed by increasing the value of the weighting coefficient α so that the weighting of the interpolation coefficient of the spline interpolation becomes large. Thus, Cubic spline interpolation and B
Weight each interpolation coefficient of spline interpolation,
By performing the interpolation calculation process, the responses of the reproduced interpolated images can be made equal regardless of the enlargement ratio.

Claims (2)

[Claims] 1. Original image data showing pixel values for each of pixels arranged in a grid at predetermined intervals,
Interpolation image data having an interval different from that of the original image data is obtained by interpolation calculation processing according to the enlargement ratio of the original image represented by the original image data, and the interpolation image data is sent to the image reproducing apparatus. In the method, by performing different interpolation calculation processing on the original image data according to the enlargement ratio, the response of the interpolated image data displayed on the image reproduction device is made substantially equal regardless of the enlargement ratio. Image data interpolation calculation method. 2. Original image data showing pixel values for each of pixels arranged in a grid at predetermined intervals,
Interpolation image data having an interval different from the original image data is obtained by an interpolation calculation processing unit according to the enlargement ratio of the original image represented by the original image data, and the interpolation image data is sent to the image reproducing apparatus. In the calculation device, the interpolation calculation processing means performs different interpolation calculation processing on the original image data according to the enlargement ratio, thereby making a response of the interpolation image data displayed on the image reproduction device to the enlargement ratio. An image data interpolation calculation device characterized in that it is a means for making them substantially equal regardless of each other.