Interpolating operation method and apparatus for image signals

Claim 2

An interpolating operation method for an image signal as defined in Claim 1 wherein: a) a plurality of first look-up tables are prepared, each of said first look-up tables setting the frequencies and the corresponding responses R 1 with respect to one of said two interpolating functions and for each of a plurality of different image size enlargement scale factors, b) a plurality of second look-up tables are prepared, each of said second look-up tables setting the frequencies and the corresponding responses R 2 with respect to the other interpolating function and for each of a plurality of different image size enlargement scale factors, c) a response R 1 of said one interpolating function with respect to an image size enlargement scale factor, which is desired for an interpolation image, and a response R 2 of said other interpolating function with respect to said image size enlargement scale factor, which is desired for the interpolation image, are calculated by making reference to a first look-up table and a second look-up table, which correspond to said image size enlargement scale factor desired for the interpolation image, and d) said coefficient α is calculated from an operation carried out with Formula (5): α=(R-R 1 )/(R 2 -R 1 ) in accordance with a response R desired for the interpolation image, the calculated response R 1 of said one interpolating function, and the calculated response R 2 of said other interpolating function.

Claim 3

An interpolating operation method for an image signal as defined in Claim 1 wherein one of the two different interpolating functions for obtaining two interpolation images having different levels of sharpness is a B spline interpolating operation function, and the other interpolating function is a cubic spline interpolating operation function.

Claim 4

An interpolating operation method for an image signal as defined in Claim 2 wherein one of the two different interpolating functions for obtaining two interpolation images having different levels of sharpness is a B spline interpolating operation function, and the other interpolating function is a cubic spline interpolating operation function.

Claim 5

An interpolating operation method for an image signal as defined in Claim 1 wherein the original image is a radiation image.

Claim 6

An interpolating operation method for an image signal as defined in Claim 5 wherein the radiation image has been stored on a stimulable phosphor sheet.

Claim 7

An interpolating operation method for an image signal as defined in Claim 6 wherein the original image signal representing the radiation image is obtained by exposing the stimulable phosphor sheet to stimulating rays, which cause the stimulable phosphor sheet to emit light in proportion to the amount of energy stored thereon during its exposure to the radiation, and photoelectrically detecting the emitted light.

Claim 8

An interpolating operation method for an image signal as defined in Claim 1 wherein the original image has been recorded on photographic film.

Claim 9

An interpolating operation apparatus for an image signal, wherein: i) an original image signal, which represents an original image and is made up of a series of original image signal components Yij, is obtained, ii) interpolation coefficients Bij and Cij, which correspond to each other and are set for each of the original image signal components Yij, in two different interpolating functions f and g for obtaining two interpolation images having different levels of sharpness, which functions are represented by Formulas (1) and (2), are linearly combined with each other, said linear combination being carried out with Formula (3), a new interpolation coefficient Aij being obtained from said linear combination, and iii) an interpolating operation is carried out on the original image signal components Yij by using an interpolating function h having the new interpolation coefficient Aij, which function is represented by Formula (4), an interpolation image signal being obtained from said interpolating operation, said interpolation image signal being made up of a series of image signal components, which occur at intervals different from those of the original image signal components Yij, (1) f=ΣBij·Yij (2) g=ΣCij·Yij (3) Aij=(1-α)Bij+αCij (4) h=ΣAij·Yij in which i=1, 2, ..., and j=1, 2, ..., the apparatus comprising: 1) a storage means for storing information representing the interpolation coefficients Bij and Cij, 2) an input means for inputting the coefficient α as one of real numbers including a range smaller than 0 and/or a range larger than 1, the coefficient α determining the sharpness of a secondary image, which is reproduced from the interpolation image signal, 3) an interpolation coefficient operation means for calculating the interpolation coefficient Aij in accordance with the coefficient α, the calculation being carried out from the interpolation coefficients Bij and Cij, which are stored in said storage means, and the coefficient α inputted from said input means, and 4) an interpolating operation means for storing Formula (4) as the operation formula, and calculating the value of an interpolated image signal component Y p , which corresponds to an interpolation point X p , with Formula (4) in accordance with the interpolation coefficient Aij, which has been calculated by said interpolation coefficient operation means, and each of the original image signal components Yij.

Claim 10

An interpolating operation apparatus for an image signal as defined in Claim 9 wherein said input means is provided with: a) a response input means for inputting a response R desired for the interpolation image, b) a plurality of first look-up tables, each of said first look-up tables setting the frequencies and the corresponding responses R 1 with respect to one of said two interpolating functions and for each of a plurality of different image size enlargement scale factors, c) a plurality of second look-up tables, each of said second look-up tables setting the frequencies and the corresponding responses R 2 with respect to the other interpolating function and for each of a plurality of different image size enlargement scale factors, and d) a coefficient calculating means for calculating a response R 1 of said one interpolating function with respect to an image size enlargement scale factor, which is desired for an interpolation image, and a response R 2 of said other interpolating function with respect to said image size enlargement scale factor, which is desired for the interpolation image, by making reference to a first look-up table and a second look-up table, which correspond to said image size enlargement scale factor desired for the interpolation image, and for calculating said coefficient α from an operation carried out with Formula (5): α=(R-R 1 )/(R 2 -R 1 ) in accordance with the response R desired for the interpolation image, the calculated response R 1 of said one interpolating function, and the calculated response R 2 of said other interpolating function.

Claim 11

An interpolating operation apparatus for an image signal as defined in Claim 9 wherein one of the two different interpolating functions for obtaining two interpolation images having different levels of sharpness is a B spline interpolating operation function, and the other interpolating function is a cubic spline interpolating operation function.

Claim 12

An interpolating operation apparatus for an image signal as defined in Claim 10 wherein one of the two different interpolating functions for obtaining two interpolation images having different levels of sharpness is a B spline interpolating operation function, and the other interpolating function is a cubic spline interpolating operation function.

Claim 13

An interpolating operation apparatus for an image signal as defined in Claim 9 wherein the original image is a radiation image.

Claim 14

An interpolating operation apparatus for an image signal as defined in Claim 13 wherein the radiation image has been stored on a stimulable phosphor sheet.

Claim 15

An interpolating operation apparatus for an image signal as defined in Claim 14 wherein the original image signal representing the radiation image is obtained by exposing the stimulable phosphor sheet to stimulating rays, which cause the stimulable phosphor sheet to emit light in proportion to the amount of energy stored thereon during its exposure to the radiation, and photoelectrically detecting the emitted light.

Claim 16

An interpolating operation apparatus for an image signal as defined in Claim 9 wherein the original image has been recorded on photographic film.

Claim 17

A spline interpolating operation method for an image signal, wherein an interpolating operation using a third-order spline interpolating function is carried out on an original image signal, which represents an original image and is made up of a series of original image signal components, and an interpolation image signal is obtained with Formula (6), said interpolation image signal being made up of a series of image signal components, which occur at intervals different from those of the original image signal components, Y p =a k-1 Y k-1 +a k Y k +a k+1 Y k+1 +a k+2 Y k+2 in which Y k-1 , Y k , Y k+1 , and Y k+2 represent the original image signal components representing picture elements X k-1 , X k , X k+1 , and X k+2 in the original image, Y p represents the interpolated image signal component corresponding to an interpolation point X p located between the picture elements X k and X k+1 , and a k-1 , a k , a k+1 , and a k+2 represent the interpolation coefficients, the method comprising the steps of: i) calculating the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 respectively corresponding to the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 such that, in cases where the original image signal components representing the two picture elements X k-1 and X k located before the interpolation point X p , which is located between the picture elements X k and X k+1 in the original image, are represented by Y k-1 and Y k , the original image signal components representing the two picture elements X k+1 and X k+2 located after the interpolation point X p are represented by Y k+1 and Y k+2 , the third-order spline interpolating function between the picture elements X k and X k+1 is represented by f k , the third-order spline interpolating function between the picture elements X k-1 and X k is represented by f k-1 , and the third-order spline interpolating function between the picture elements X k+1 and X k+2 is represented by f k+1 : a) the spline interpolating function f k at the picture elements X k and X k+1 may satisfy the original image signal components Y k and Y k+1 , as represented by Formulas (7) and (8): (7) f k (X k )=Y k (8) f k (X k+1 )=Y k+1 b) the first-order differential coefficient of the spline interpolating function f k at the picture element X k may coincide with the first-order differential coefficient of the spline interpolating function f k-1 at the picture element X k , as represented by Formula (9): f k '(X k )=f k-1 '(X k ) c) the first-order differential coefficient of the spline interpolating function f k at the picture element X k+1 may coincide with the first-order differential coefficient of the spline interpolating function f k+1 at the picture element X k+1 , as represented by Formula (10): f k '(X k+1 )=f k+1 '(X k+1 ) d) the first-order differential coefficient of the spline interpolating function f k at the picture element X k may have an inclination of an arbitrary parameter α with respect to the gradient of the original image signal components Y k-1 and Y k+1 representing the picture elements X k-1 and X k+1 , which are located before and after the picture element X k , as represented by Formula (11), the arbitrary parameter α being selected previously and determining the sharpness of a secondary image represented by the interpolation image signal, f k '(X k )=α(Y k+1 -Y k-1 )/(X k+1 -X k-1 ) and e) the first-order differential coefficient of the spline interpolating function f k at the picture element X k+1 may have an inclination of said parameter α with respect to the gradient of the original image signal components Y k and Y k+2 representing the picture elements X k and X k+2 , which are located before and after the picture element X k+1 , as represented by Formula (12): f k '(X k+1 )=α(Y k+2 -Y k )/(X k+2 -X k ) and ii) calculating the interpolated image signal component Y p corresponding to the interpolation point X p in accordance with the calculated interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , and the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 .

Claim 18

A spline interpolating operation method for an image signal as defined in Claim 17 wherein the calculated interpolation coefficients a k-1 , a k , a k+1 , and a k+2 are respectively represented by Formulas (13), (14), (15), and (16): (13) a k-1 =-(α/2)t(t-1) 2 (14) a k =(2-α/2)t 3 -(3-α/2)t 2 +1 (15) a k+1 =(α/2-2)t 3 +(3-α)t 2 +(α/2)t (16) a k+2 =(α/2)t 2 (t-1) in which t, where 0≦t<1, represents the position of the interpolation point X p , the position being taken with respect to the picture element X k , that serves as a reference position, and in the direction heading toward the picture element X k+1 , the lattice interval of the original image signal components being set to be equal to 1.

Claim 19

A spline interpolating operation method for an image signal as defined in Claim 17 wherein the original image is a radiation image.

Claim 20

A spline interpolating operation method for an image signal as defined in Claim 19 wherein the radiation image has been stored on a stimulable phosphor sheet.

Claim 21

A spline interpolating operation method for an image signal as defined in Claim 20 wherein the original image signal representing the radiation image is obtained by exposing the stimulable phosphor sheet to stimulating rays, which cause the stimulable phosphor sheet to emit light in proportion to the amount of energy stored thereon during its exposure to the radiation, and photoelectrically detecting the emitted light.

Claim 22

A spline interpolating operation method for an image signal as defined in Claim 17 wherein the original image has been recorded on photographic film.

Claim 23

A spline interpolating operation method for an image signal, wherein an interpolating operation using a third-order spline interpolating function is carried out on an original image signal, which represents an original image and is made up of a series of original image signal components, and an interpolation image signal is obtained with Formula (6), said interpolation image signal being made up of a series of image signal components, which occur at intervals different from those of the original image signal components, Y p =a k-1 Y k-1 +a k Y k +a k+1 Y k+1 +a k+2 Y k+2 in which Y k-1 , Y k , Y k+1 , and Y k+2 represent the original image signal components representing picture elements X k-1 , X k , X k+1 , and X k+2 in the original image, Y p represents the interpolated image signal component corresponding to an interpolation point X p located between the picture elements X k and X k+1 , and a k-1 , a k , a k+1 , and a k+2 represent the interpolation coefficients, the method comprising the steps of: i) calculating the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 respectively corresponding to the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 such that, in cases where the original image signal components representing the two picture elements X k-1 and X k located before the interpolation point X p , which is located between the picture elements X k and X k+1 in the original image, are represented by Y k-1 and Y k , the original image signal components representing the two picture elements X k+1 and X k+2 located after the interpolation point X p are represented by Y k+1 and Y k+2 , the third-order spline interpolating function between the picture elements X k and X k+1 is represented by f k , the third-order spline interpolating function between the picture elements X k-1 and X k is represented by f k-1 , and the third-order spline interpolating function between the picture elements X k+1 and X k+2 is represented by f k+1 : a) the spline interpolating function f k at the picture elements X k and X k+1 may slightly deviate from the original image signal components Y k and Y k+1 in accordance with an arbitrary parameter β, as represented by Formulas (17) and (18), the arbitrary parameter β being selected previously and determining the sharpness of a secondary image represented by the interpolation image signal, (17) f k (X k )=-0.5βY k-1 +(1+β)Y k -0.5βY k+1 (18) f k (X k+1 )=-0.5βY k +(1+β)Y k+1 -0.5βY k+2 b) the first-order differential coefficient of the spline interpolating function f k at the picture element X k may coincide with the first-order differential coefficient of the spline interpolating function f k-1 at the picture element X k , as represented by Formula (9): f k '(X k )=f k-1 '(X k ) c) the first-order differential coefficient of the spline interpolating function f k at the picture element X k+1 may coincide with the first-order differential coefficient of the spline interpolating function f k+1 at the picture element X k+1 , as represented by Formula (10): f k '(X k+1 )=f k+1 '(X k+1 ) d) the first-order differential coefficient of the spline interpolating function f k at the picture element X k may coincide with the gradient of the original image signal components Y k-1 and Y k+1 representing the picture elements X k-1 and X k+1 , which are located before and after the picture element X k , as represented by Formula (19): f k '(X k )=(Y k+1 -Y k-1 )/(X k+1 -X k-1 ) and e) the first-order differential coefficient of the spline interpolating function f k at the picture element X k+1 may coincide with the gradient of the original image signal components Y k and Y k+2 representing the picture elements X k and X k+2 , which are located before and after the picture element X k+1 , as represented by Formula (20): f k '(X k+1 )=(Y k+2 -Y k )/(X k+2 -X k ) and ii) calculating the interpolated image signal component Y p corresponding to the interpolation point X p in accordance with the calculated interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , and the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 .

Claim 24

A spline interpolating operation method for an image signal as defined in Claim 23 wherein the calculated interpolation coefficients a k-1 , a k , a k+1 , and a k+2 are respectively represented by Formulas (21), (22), (23), and (24): (21) a k-1 =-(β+1/2)t 3 +(3β/2+1)t 2 -(1/2)t-β/2 (22) a k =3(β+1/2)t 3 -(9β/2+5/2)t 2 +β+1 (23) a k+1 =-3(β+1/2)t 3 +(9β/2+2)t 2 +(1/2)t-β/2 (24) a k+2 =(β+1/2)t 3 -(3β/2+1/2)t 2 in which t, where 0≦t<1, represents the position of the interpolation point X p , the position being taken with respect to the picture element X k , that serves as a reference position, and in the direction heading toward the picture element X k+1 , the lattice interval of the original image signal components being set to be equal to 1.

Claim 25

A spline interpolating operation method for an image signal as defined in Claim 23 wherein the original image is a radiation image.

Claim 26

A spline interpolating operation method for an image signal as defined in Claim 25 wherein the radiation image has been stored on a stimulable phosphor sheet.

Claim 27

A spline interpolating operation method for an image signal as defined in Claim 26 wherein the original image signal representing the radiation image is obtained by exposing the stimulable phosphor sheet to stimulating rays, which cause the stimulable phosphor sheet to emit light in proportion to the amount of energy stored thereon during its exposure to the radiation, and photoelectrically detecting the emitted light.

Claim 28

A spline interpolating operation method for an image signal as defined in Claim 23 wherein the original image has been recorded on photographic film.

Claim 29

A spline interpolating operation method for an image signal, wherein an interpolating operation using a third-order spline interpolating function is carried out on an original image signal, which represents an original image and is made up of a series of original image signal components, and an interpolation image signal is obtained with Formula (6), said interpolation image signal being made up of a series of image signal components, which occur at intervals different from those of the original image signal components, Y p =a k-1 Y k-1 +a k Y k +a k+1 Y k+1 +a k+2 Y k+2 in which Y k-1 , Y k , Y k+1 , and Y k+2 represent the original image signal components representing picture elements X k-1 , X k , X k+1 , and X k+2 in the original image, Y p represents the interpolated image signal component corresponding to an interpolation point X p located between the picture elements X k and X k+1 , and a k-1 , a k , a k+1 , and a k+2 represent the interpolation coefficients, the method comprising the steps of: i) calculating the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 respectively corresponding to the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 such that, in cases where the original image signal components representing the two picture elements X k-1 and X k located before the interpolation point X p , which is located between the picture elements X k and X k+1 in the original image, are represented by Y k-1 and Y k , the original image signal components representing the two picture elements X k+1 and X k+2 located after the interpolation point X p are represented by Y k+1 and Y k+2 , the third-order spline interpolating function between the picture elements X k and X k+1 is represented by f k , the third-order spline interpolating function between the picture elements X k-1 and X k is represented by f k-1 , and the third-order spline interpolating function between the picture elements X k+1 and X k+2 is represented by f k+1 : a) the spline interpolating function f k at the picture elements X k and X k+1 may satisfy the original image signal components Y k and Y k+1 , as represented by Formulas (7) and (8): (7) f k (X k )=Y k (8) f k (X k+1 )=Y k+1 b) the first-order differential coefficient of the spline interpolating function f k at the picture element X k may coincide with the first-order differential coefficient of the spline interpolating function f k-1 at the picture element X k , as represented by Formula (9): f k '(X k )=f k-1 '(X k ) c) the first-order differential coefficient of the spline interpolating function f k at the picture element X k+1 may coincide with the first-order differential coefficient of the spline interpolating function f k+1 at the picture element X k+1 , as represented by Formula (10): f k '(X k+1 )=f k+1 '(X k+1 ) d) the first-order differential coefficient of the spline interpolating function f k at the picture element X k may have an inclination of an arbitrary parameter α with respect to the gradient of the original image signal components Y k-1 and Y k+1 representing the picture elements X k-1 and X k+1 , which are located before and after the picture element X k , as represented by Formula (11), the arbitrary parameter α being selected previously and determining the sharpness of a secondary image represented by the interpolation image signal, f k '(X k )=α(Y k+1 -Y k-1 )/(X k+1 -X k-1 ) and e) the first-order differential coefficient of the spline interpolating function f k at the picture element X k+1 may have an inclination of said parameter α with respect to the gradient of the original image signal components Y k and Y k+2 representing the picture elements X k and X k+2 , which are located before and after the picture element X k+1 , as represented by Formula (12): f k '(X k+1 )=α(Y k+2 -Y k )/(X k+2 -X k ) ii) calculating interpolation coefficients b k-1 , b k , b k+1 , and b k+2 respectively corresponding to the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 such that: f) the spline interpolating function f k at the picture elements X k and X k+1 may slightly deviate from the original image signal components Y k and Y k+1 in accordance with an arbitrary parameter β, as represented by Formulas (17) and (18), the arbitrary parameter β being selected previously and determining the sharpness of the secondary image represented by the interpolation image signal, (17) f k (X k )=-0.5βY k-1 +(1+β)Y k -0.5βY k+1 (18) f k (X k+1 )=-0.5βY k +(1+β)Y k+1 -0.5βY k+2 g) the first-order differential coefficient of the spline interpolating function f k at the picture element X k may coincide with the first-order differential coefficient of the spline interpolating function f k-1 at the picture element X k , as represented by Formula (9): f k '(X k )=f k-1 '(X k ) h) the first-order differential coefficient of the spline interpolating function f k at the picture element X k+1 may coincide with the first-order differential coefficient of the spline interpolating function f k+1 at the picture element X k+1 , as represented by Formula (10): f k '(X k+1 )=f k+1 '(X k+1 ) i) the first-order differential coefficient of the spline interpolating function f k at the picture element X k may coincide with the gradient of the original image signal components Y k-1 and Y k+1 representing the picture elements X k-1 and X k+1 , which are located before and after the picture element X k , as represented by Formula (19): f k '(X k )=(Y k+1 -Y k-1 )/(X k+1 -X k-1 ) and j) the first-order differential coefficient of the spline interpolating function f k at the picture element X k+1 may coincide with the gradient of the original image signal components Y k and Y k+2 representing the picture elements X k and X k+2 , which are located before and after the picture element X k+1 , as represented by Formula (20): f k '(X k+1 )=(Y k+2 -Y k )/(X k+2 -X k ) iii) calculating a mean value of the set of the interpolation coefficients a k-1 and b k-1 , a mean value of the set of the interpolation coefficients a k and b k , a mean value of the set of the interpolation coefficients a k+1 and b k+1 , and a mean value of the set of the interpolation coefficients a k+2 and b k+2 , which sets respectively correspond to the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 , the calculated mean values being taken as the values of new interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , and iv) calculating the interpolated image signal component Y p corresponding to the interpolation point X p in accordance with the calculated new interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , and the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 .

Claim 30

A spline interpolating operation method for an image signal in as defined in Claim 29 wherein the calculated new interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , which represent the mean values, are respectively represented by Formulas (25), (26), (27), and (28): (25) a k-1 =-{(α+2β+1)/4}t 3 +{(2α+3β+2)/4}t 2 -{(α+1)/4}t-β/4 (26) a k ={(-α+6β+7)/4}t 3 +{(α-9β-11)/4}t 2 +β/2+1 (27) a k+1 ={(α-6β-7)/4}t 3 +{(-2α+9β+10)/4}t 2 +{(α+1)/4}t-β/4 (28) a k+2 ={(α+2β+1)/4}t 3 -{(α+3β+1)/4}t 2 in which t, where 0≦t<1, represents the position of the interpolation point X p , the position being taken with respect to the picture element X k , that serves as a reference position, and in the direction heading toward the picture element X k+1 , the lattice interval of the original image signal components being set to be equal to 1.

Claim 31

A spline interpolating operation method for an image signal as defined in Claim 29 wherein the original image is a radiation image.

Claim 32

A spline interpolating operation method for an image signal as defined in Claim 31 wherein the radiation image has been stored on a stimulable phosphor sheet.

Claim 33

A spline interpolating operation method for an image signal as defined in Claim 32 wherein the original image signal representing the radiation image is obtained by exposing the stimulable phosphor sheet to stimulating rays, which cause the stimulable phosphor sheet to emit light in proportion to the amount of energy stored thereon during its exposure to the radiation, and photoelectrically detecting the emitted light.

Claim 34

A spline interpolating operation method for an image signal as defined in Claim 29 wherein the original image has been recorded on photographic film.

Claim 35

A spline interpolating operation apparatus for an image signal, wherein an interpolating operation using a third-order spline interpolating function is carried out on an original image signal, which represents an original image and is made up of a series of original image signal components, and an interpolation image signal is obtained with Formula (6), said interpolation image signal being made up of a series of image signal components, which occur at intervals different from those of the original image signal components, Y p =a k-1 Y k-1 +a k Y k +a k+1 Y k+1 +a k+2 Y k+2 in which Y k-1 , Y k , Y k+1 , and Y k+2 represent the original image signal components representing picture elements X k-1 , X k , X k+1 , and X k+2 in the original image, Y p represents the interpolated image signal component corresponding to an interpolation point X p located between the picture elements X k and X k+1 , and a k-1 , a k , a k+1 , and a k+2 represent the interpolation coefficients, the apparatus comprising: 1) a storage means for storing information representing the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , which respectively correspond to the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 representing the picture elements X k-1 , X k , X k+1 , and X k+2 in the original image, and which are set to be respectively represented by Formulas (13), (14), (15), and (16): (13) a k-1 =-(α/2)t(t-1) 2 (14) a k =(2-α/2)t 3 -(3-α/2)t 2 +1 (15) a k+1 =(α/2-2)t 3 +(3-α)t 2 +(α/2)t (16) a k+2 =(α/2)t 2 (t-1) in which α represents the parameter determining the sharpness of a secondary image represented by the interpolation image signal, and t, where 0≦t<1, represents the position of the interpolation point X p , the position being taken with respect to the picture element X k , that serves as a reference position, and in the direction heading toward the picture element X k+1 , the lattice interval of the original image signal components being set to be equal to 1, 2) an input means for inputting the arbitrary parameter α, which determines the sharpness of the secondary image reproduced from the interpolation image signal, 3) an interpolation coefficient operation means for calculating the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 in accordance with the parameter α, the calculation being carried out from the interpolation coefficients, which are stored in said storage means, and the parameter α inputted from said input means, and 4) an interpolating operation means for storing Formula (6) as the operation formula, and calculating the value of the interpolated image signal component Y p , which corresponds to the interpolation point X p , with Formula (6) in accordance with the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , which have been calculated by said interpolation coefficient operation means, and the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 .

Claim 36

A spline interpolating operation apparatus for an image signal as defined in Claim 35 wherein the original image is a radiation image.

Claim 37

A spline interpolating operation apparatus for an image signal as defined in Claim 36 wherein the radiation image has been stored on a stimulable phosphor sheet.

Claim 38

A spline interpolating operation apparatus for an image signal as defined in Claim 37 wherein the original image signal representing the radiation image is obtained by exposing the stimulable phosphor sheet to stimulating rays, which cause the stimulable phosphor sheet to emit light in proportion to the amount of energy stored thereon during its exposure to the radiation, and photoelectrically detecting the emitted light.

Claim 39

A spline interpolating operation apparatus for an image signal as defined in Claim 35 wherein the original image has been recorded on photographic film.

Claim 40

A spline interpolating operation apparatus for an image signal, wherein an interpolating operation using a third-order spline interpolating function is carried out on an original image signal, which represents an original image and is made up of a series of original image signal components, and an interpolation image signal is obtained with Formula (6), said interpolation image signal being made up of a series of image signal components, which occur at intervals different from those of the original image signal components, Y p =a k-1 Y k-1 +a k Y k +a k+1 Y k+1 +a k+2 Y k+2 in which Y k-1 , Y k , Y k+1 , and Y k+2 represent the original image signal components representing picture elements X k-1 , X k , X k+1 , and X k+2 in the original image, Y p represents the interpolated image signal component corresponding to an interpolation point X p located between the picture elements X k and X k+1 , and a k-1 , a k , a k+1 , and a k+2 represent the interpolation coefficients, the apparatus comprising: 1) a storage means for storing information representing the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , which respectively correspond to the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 representing the picture elements X k-1 , X k , X k+1 , and X k+2 in the original image, and which are set to be respectively represented by Formulas (21), (22), (23), and (24): (21) a k-1 =-(β+1/2)t 3 +(3β/2+1)t 2 -(1/2)t-β/2 (22) a k =3(β+1/2)t 3 -(9β/2+5/2)t 2 +β+1 (23) a k+1 =-3(β+1/2)t 3 +(9β/2+2)t 2 +(1/2)t-β/2 (24) a k+2 =(β+1/2)t 3 -(3β/2+1/2)t 2 in which β represents the parameter determining the sharpness of a secondary image represented by the interpolation image signal, and t, where 0≦t<1, represents the position of the interpolation point X p , the position being taken with respect to the picture element X k , that serves as a reference position, and in the direction heading toward the picture element X k+1 , the lattice interval of the original image signal components being set to be equal to 1, 2) an input means for inputting the arbitrary parameter β, which determines the sharpness of the secondary image reproduced from the interpolation image signal, 3) an interpolation coefficient operation means for calculating the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 in accordance with the parameter β, the calculation being carried out from the interpolation coefficients, which are stored in said storage means, and the parameter β inputted from said input means, and 4) an interpolating operation means for storing Formula (6) as the operation formula, and calculating the value of the interpolated image signal component Y p , which corresponds to the interpolation point X p , with Formula (6) in accordance with the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , which have been calculated by said interpolation coefficient operation means, and the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 .

Claim 41

A spline interpolating operation apparatus for an image signal as defined in Claim 40 wherein the original image is a radiation image.

Claim 42

A spline interpolating operation apparatus for an image signal as defined in Claim 41 wherein the radiation image has been stored on a stimulable phosphor sheet.

Claim 43

A spline interpolating operation apparatus for an image signal as defined in Claim 42 wherein the original image signal representing the radiation image is obtained by exposing the stimulable phosphor sheet to stimulating rays, which cause the stimulable phosphor sheet to emit light in proportion to the amount of energy stored thereon during its exposure to the radiation, and photoelectrically detecting the emitted light.

Claim 44

A spline interpolating operation apparatus for an image signal as defined in Claim 40 wherein the original image has been recorded on photographic film.

Claim 45

A spline interpolating operation apparatus for an image signal, wherein an interpolating operation using a third-order spline interpolating function is carried out on an original image signal, which represents an original image and is made up of a series of original image signal components, and an interpolation image signal is obtained with Formula (6), said interpolation image signal being made up of a series of image signal components, which occur at intervals different from those of the original image signal components, Y p =a k-1 Y k-1 +a k Y k +a k+1 Y k+1 +a k+2 Y k+2 in which Y k-1 , Y k , Y k+1 , and Y k+2 represent the original image signal components representing picture elements X k-1 , X k , X k+1 , and X k+2 in the original image, Y p represents the interpolated image signal component corresponding to an interpolation point X p located between the picture elements X k and X k+1 , and a k-1 , a k , a k+1 , and a k+2 represent the interpolation coefficients, the apparatus comprising: 1) a storage means for storing information representing the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , which respectively correspond to the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 representing the picture elements X k-1 , X k , X k+1 , and X k+2 in the original image, and which are set to be respectively represented by Formulas (25), (26), (27), and (28): (25) a k-1 =-{(α+2β+1)/4}t 3 +{(2α+3β+2)/4}t 2 -{(α+1)/4}t-β/4 (26) a k ={(-α+6β+7)/4}t 3 +{(α-9β-11)/4}t 2 +β/2+1 (27) a k+1 ={(α-6β-7)/4}t 3 +{(-2α+9β+10)/4}t 2 +{(α+1)/4}t-β/4 (28) a k+2 ={(α+2β+1)/4}t 3 -{(α+3β+1)/4}t 2 in which α and β represent the parameters determining the sharpness of a secondary image represented by the interpolation image signal, and t, where 0≦t<1, represents the position of the interpolation point X p , the position being taken with respect to the picture element X k , that serves as a reference position, and in the direction heading toward the picture element X k+1 , the lattice interval of the original image signal components being set to be equal to 1, 2) an input means for inputting the arbitrary parameters α and β, which determine the sharpness of the secondary image reproduced from the interpolation image signal, 3) an interpolation coefficient operation means for calculating the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 in accordance with the parameters α and β, the calculation being carried out from the interpolation coefficients, which are stored in said storage means, and the parameters α and β inputted from said input means, and 4) an interpolating operation means for storing Formula (6) as the operation formula, and calculating the value of the interpolated image signal component Y p , which corresponds to the interpolation point X p , with Formula (6) in accordance with the interpolation coefficients a k-1 , a k , a k+1 , and a k+2 , which have been calculated by said interpolation coefficient operation means, and the original image signal components Y k-1 , Y k , Y k+1 , and Y k+2 .

Claim 46

A spline interpolating operation apparatus for an image signal as defined in Claim 45 wherein the original image is a radiation image.

Claim 47

A spline interpolating operation apparatus for an image signal as defined in Claim 46 wherein the radiation image has been stored on a stimulable phosphor sheet.

Claim 48

A spline interpolating operation apparatus for an image signal as defined in Claim 47 wherein the original image signal representing the radiation image is obtained by exposing the stimulable phosphor sheet to stimulating rays, which cause the stimulable phosphor sheet to emit light in proportion to the amount of energy stored thereon during its exposure to the radiation, and photoelectrically detecting the emitted light.

Claim 49

A spline interpolating operation apparatus for an image signal as defined in Claim 45 wherein the original image has been recorded on photographic film.