Claims
- 1. An interpolating operation method for an image signal, wherein an interpolated image signal component corresponding to an interpolation point is calculated from original image signal components of an original image signal representing an original image, which represent a plurality of sampling points arrayed at predetermined intervals and in a lattice-like form, the method comprising the steps of:i) making a judgement as to whether the interpolation point belongs to an image edge portion, at which a change in the original image signal is sharp, or belongs to a flat portion, at which the change in the original image signal is unsharp, and ii) changing interpolating operation processes, one of which is to be employed for the interpolation point, over to each other in accordance with the results of the judgment; and wherein the interpolating operation process, which is employed in cases where, as a result of said judgment, it has been judged that the interpolation point belongs to a flat portion, is an interpolating operation process, with which the sharpness of the same flat portion is manually rendered variable.
- 2. A method as defined in claim 1, wherein said interpolating operation process, with which the sharpness of the flat portion is rendered variable, is a spline interpolating operation process.
- 3. A method as defined in claim 2, wherein said spline interpolating operation process is an interpolating operation process for obtaining an interpolated image signal component with Formula (1):Yp=ak−1Yk−1+akYk+ak+1Yk+1ak+2Yk+2 (1) in which Yk−1, Yk, Yk+1, and Yk+2 represent the original image signal components representing sampling points serving as picture elements Xk−1, Xk, Xk+1, and Xk+2 in the original image, Yp, represents the interpolated image signal component corresponding to an interpolation point Xp, located between the picture elements Xk and Xk+1and ak+1, ak, ak+1, and ak+2 represent the interpolation coefficients,the process comprising the steps of: a) calculating the interpolation coefficients ak−1, ak, ak+1, and respectively corresponding to the original image signal components Yk−1, Yk, Yk+1, and Yk+2 such that, in cases where the original image signal components representing the two picture elements Xk−1 and Xk located before the interpolation point Xp, which is located between the picture elements Xk and Xk+1 in the original image, are represented by Yk−1 and Yk, the original image signal components representing the two picture elements Xk+1 and Xk+2 located after the interpolation point Xp are represented by Yk+1 and Yk+2, a third-order spline interpolating function between the picture elements Xk and Xk+1 is represented by fk, a third-order spline interpolating function between the picture elements Xk−1 and Xk is represented by fk−1, and a third-order spline interpolating function between the picture elements Xk+1 and Xk+2 is represented by fk+1: {circle around (1)} the spline interpolating function fk at the picture elements Xk+1 and Xk+2 may satisfy the original image signal components Yk and Yk+1, as represented by Formulas (2) and (3): fk(Xk)=Yk (2) fk(Xk+1)=Yk+1 (3) {circle around (2)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the first-order differential coefficient of the spline interpolating function fk−1 at the picture element Xk, as represented by Formula (4): fk′(Xk)=fk−1′(Xkk) (4) {circle around (3)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the first-order differential coefficient of the spline interpolating function fk+1 at the picture element Xk+1, as represented by Formula (5): fk′(Xk+1)=fk+1′(Xk+1) (5) {circle around (4)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may have an inclination of an arbitrary parameter α with respect to the gradient of the original image signal components Yk−1 and Yk+1 representing the picture elements Xk−1 and Xk+1, which are located before and after the picture element Xk, as represented by Formula (6), the arbitrary parameter α being selected previously and determining the sharpness of a secondary image represented by the interpolation image signal obtained from the interpolating operation, fk′(Xk)=α(Yk+1−Yk−1)/(Xk+1−Xk−1) (6) and{circle around (5)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may have an inclination of said parameter α with respect to the gradient of the original image signal components Yk and Yk+2 representing the picture elements Xk and Xk+2, which are located before and after the picture element Xk+1, as represented by Formula (7): fk′(Xk+1)=α(Yk+2Yk)/(Xk+2Xk) (7) andb) calculating the interpolated image signal component Yp corresponding to the interpolation point Xp in accordance with the calculated interpolation coefficients ak−1, ak, ak+1, and ak+2, and the original image signal components Yk−1, Yk, Yk+1, and Yk+2.
- 4. A method as defined in claim 3 wherein the calculated interpolation coefficients ak−1, ak, and ak+2 are represented respectively by Formulas (8), (9), (10), and (11):ak−1=−(α/2)t−(t−1)2 (8) ak=(2−α/2)t3−(3−α/2)t2+1 (9) ak+1=(α/2−2)t3+(3−α)t2+(α2)t (10) ak+2=(α/2)t2(t−1) (11)in which t, where 0≦t<1, represents the position of the interpolation point Xk, the position being taken with respect to the picture element Xk+1, that serves as a reference position, and in the direction heading toward the picture element Xk+1, the lattice interval of the original image signal components being set to be equal to 1.
- 5. A method as defined in claim 2 said spline interpolating operation process is an interpolating operation process for obtaining an interpolated image signal component with Formula (1):Yp=ak−1Yk−1+akYk+ak+1Yk+1ak+2Yk +2 (1) in which Yk−1, Yk, Yk+1, and Yk+2 represent the original image signal components representing sampling points serving as picture elements Xk−1 , Xk, Xk+1, and Xk+2 in the original image, Yp represents the interpolated image signal component corresponding to an interpolation point Xp located between the picture elements Xk and Xk+1, and ak−1, ak, ak+1, and ak+2 represent the interpolation coefficients,the process comprising the steps of: a) calculating the interpolation coefficients ak−1, ak, ak+1, and ak+2 respectively corresponding to the original image signal components Yk−1, Yk, Yk+1, and Yk+2 such that, in cases where the original image signal components representing the two picture elements Xk−1 and Xk located before the interpolation point Xp, which is located between the picture elements Xk and Xk+1 in the original image, are represented by Yk−1 and Yk, the original image signal components representing the two picture elements Xk+1 and Xk+2 located after the interpolation point Xp, are represented by Yk+1 and YK+2, a third-order spline interpolating function between the picture elements Xk and Xk+1 is represented by fk, a third-order spline interpolating function between the picture elements Xk−1 and Xk is represented by fk−1, and a third-order spline interpolating function between the picture elements Xk+1 and Xk+2 is represented by fk+1: {circle around (1)} the spline interpolating function fk at the picture elements Xk and Xk+1 may slightly deviate from the original image signal components Yk and Yk+1 in accordance with an arbitrary parameter β, as represented by Formulas (12) and (13), the arbitrary parameter β being selected previously and determining the sharpness of a secondary image represented by the interpolation image signal obtained from the interpolating operation, fk(Xk)=−0.5βYk−1+(1+β)Yk−0.5βYk+1 (12) fk(Xk+1)=−0.5βYk+(1β)Yk+10.5βYk+2 (13) {circle around (2)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the first-order differential coefficient of the spline interpolating function fk−at the picture element Xk, as represented by Formula (4): fk′(Xk)=fk−1′(Xk) (4) {circle around (3)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the first-order differential coefficient of the spline interpolating function fk+1 at the picture element Xk+1, as represented by Formula (5): fk′(Xk+1)=fk+1′(Xk+1) (5) {circle around (4)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the gradient of the original image signal components Yk−1 and Yk+1 representing the picture elements Xk−1 and Xk+1, which are located before and after the picture element Xk, as represented by Formula (14): fk′(Xk)=(Yk+1−Yk−1)/(Xk+1−Xk−1) (14) and{circle around (5)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk−1 may coincide with the gradient of the original image signal components Yk and Yk+2 representing the picture elements Xk and Xk+2, which are located before and after the picture element Xk+1, as represented by Formula (15): fk′(Xk+1)=(Yk+2−Yk)/(Xk+2−Xk) (15) andb) calculating the interpolated image signal component Yp corresponding to the interpolation point Xp in accordance with the calculated interpolation coefficients ak−1, ak, ak+1, and ak+2, and the original image signal components Yk−1, Yk, Yk+1, and Yk+2.
- 6. A method as defined in claim 5 wherein the calculated interpolation coefficients ak−1, ak, ak+1, and ak+2 are represented respectively by Formulas (16), (17), (18), and (19):ak−1=−(β+1/2)t3+(3β/2+1)t2−(1/2)t−β/2 (16) ak=3(β30 1/2)t3−(9β/2+5/2)t2+β+1 (17) ak+1=−3(β+1/2)t3+(9β/2+2)t2+(1/2)t−β/2 (18)ak+2=(β+1/2)t3−(3β/2+1/2)t2 (19) in which t, where 0≦t<1, represents the position of the interpolation point Xp, the position being taken with respect to the picture element Xk, that serves as a reference position, and in the direction heading toward the picture element Xk+1, the lattice interval of the original image signal components being set to be equal to 1.
- 7. A method as defined in claim 2 wherein said spline interpolating operation process is an interpolating operation process for obtaining an interpolated image signal component with Formula (1):Yp32 ak−1Yk−1+akYk+ak+1Yk+1ak+2Yk+2 (1) in which Yk−1, Yk, Yk+1, and Yk+2 represent the original image signal components representing sampling points serving as picture elements Xk+1, Xk, Xk−1, and Xk+2 in the original image, Yp represents the interpolated image signal component corresponding to an interpolation point Xp located between the picture elements Xk and Xk+1, and ak−1, ak, ak+1, and ak+2 represent the interpolation coefficients,the process comprising the steps of: a) calculating the interpolation coefficients ak−1, ak, ak+1, and ak+2 respectively corresponding to the original image signal components Yk−1, Yk, Yk+, and Yk+2 such that, in cases where the original image signal components representing the two picture elements Xk−1 and Xk located before the interpolation point Xp, which is located between the picture elements Xk and Xk+1 in the original image, are represented by Yk−1 and Yk, the original image signal components representing the two picture elements Xk+1 and Xk+2 located after the interpolation point Xp are represented by Yk+1 and Yk+2, a third-order spline interpolating function between the picture elements Xk and Xk+1 is represented by fk, a third-order spline interpolating function between the picture elements Xk−1 and Xk is represented by fk−1, and a third-order spline interpolating function between the picture elements Xk+1 and Xk+2 is represented by fk+1: {circle around (1)} the spline interpolating function fk at the picture elements Xk and Xk+1 may satisfy the original image signal components Yk and Yk+1, as represented by Formulas (2) and (3):fk(Xk)=Yk (2) fk(Xk+1)=Yk+1 (3) {circle around (2)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the first-order differential coefficient of the spline interpolating function fk−1 at the picture element Xk, as represented by Formula (4): fk′(Xk)=fk−1′(Xk) (4) {circle around (3)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1, as represented by Formula (5): fk′(Xk+1)=fk+1′(Xk+1) (5) {circle around (4)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may have an inclination of an arbitrary parameter α with respect to the gradient of the original image signal components Yk−1 and Yk+1 representing the picture elements Xk−1 and Xk+1, which are located before and after the picture element Xk, as represented by Formula (6), the arbitrary parameter α being selected previously and determining the sharpness of a secondary image represented by the interpolation image signal obtained from the interpolating operation, fk′(Xk)=α(Yk+1−Yk−1)/(Xk+1−Xk−1 ) (6) and{circle around (5)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may have an inclination of said parameter α with respect to the gradient of the original image signal components Yk and Yk+2 representing the picture elements Xk and Xk+2, which are located before and after the picture element Xk+1, as represented by Formula (7): fk′(Xk+1)=α(Yk+2−Yk)/(Xk+2−Xk) (7) b) calculating interpolation coefficients bk−1, bk, bk+1 and bk+2 respectively corresponding to the original image signal components Yk−, Yk, Yk+1, and Yk+2 such that: {circle around (6)} the spline interpolating function fk at the picture elements Xk and Xk+1 may slightly deviate from the original image signal components Yk and Yk+1 in accordance with an arbitrary parameter β, as represented by Formulas (12) and (13), the arbitrary parameter β being selected previously and determining the sharpness of the secondary image represented by the interpolation image signal obtained from the interpolating operation, fk(Xk)=−0.5βYk−1+(1+β)Yk−0.5 βYk+1 (12) fk (Xk+1)=−0.5βYk+(1+β)Yk+1−0.5βYk+2 (13){circle around (7)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the first-order differential coefficient of the spline interpolating function fk−1 at the picture element Xk, as represented by Formula (4): fk′(Xk)=fk−1′(Xk) (4) {circle around (8)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the first-order differential coefficient of the spline interpolating function fk+1 at the picture element Xk+1, as represented by Formula (5): fk′(Xk+1)=fk+1′(Xk+1) (5) {circle around (9)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the gradient of the original image signal components Yk−1 and Yk+1 representing the picture elements Xk−1 and Xk+1, which are located before and after the picture element Xk, as represented by Formula (14): fk′(Xk)=(Yk+1−Yk−1)/(Xk+1−Xk−1) (14) and{circle around (10)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the gradient of the original image signal components Yk and Yk +2 representing the picture elements Xk and Xk+2, which are located before and after the picture element Xk+1, as represented by Formula (15): fk′(Xk+1)=(Yk+2−Yk)/(Xk+2−Xk) (15) c) calculating a mean value of the set of the interpolation coefficients ak−1 and bk−1, a mean value of the set of the interpolation coefficients ak and bk, a mean value of the set of the interpolation coefficients ak+1 and bk+1, and a mean value of the set of the interpolation coefficients ak+2 and bk+2, which sets respectively correspond to the original image signal components Yk−1, Yk, Yk+1, and Yk+2, the calculated mean values being taken as the values of new interpolation coefficients ak−1, ak, ak+1, and ak+2, and d) calculating the interpolated image signal component Yp corresponding to the interpolation point Xp in accordance with the calculated new interpolation coefficients ak−1, ak, ak+1, and ak+2, and the original image signal components Yk−1, Yk, Yk+1, and Yk+2.
- 8. A method as defined in claim 7, wherein the calculated new interpolation coefficients ak−1, ak, ak+1, and ak+2, which represent the mean values, are represented respectively by Formulas (20), (21), (22), and (23):ak−1=−{(α+2β+1)/4}t3+{(2α+3β+2)/4}t2−{(α+1)/4}t−β/4 (20) ak={(α+6β+7)/4}t3+{(α−9β−11)/4}t2+β/2 +1 (21) ak+1={(α−6β−7)/4}t3+{(−2α+9β+10)/4}t2+{(α+1)/4}t−β/4 (22) ak+2={(α+2β+1)/4}t3−{(α+3β+1)/4}t2 (23)in which t, where 0≦t<1, represents the position of the interpolation point Xp, the position being taken with respect to the picture element Xk, that serves as a reference position, and in the direction heading toward the picture element Xk+1, the lattice interval of the original image signal components being set to be equal to 1.
- 9. A method as defined in claim 1 wherein said interpolating operation process, with which the sharpness of the flat portion is rendered variable, is an interpolating operation process, comprising the steps of:linearly combining 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 (24) and (25), said linear combination being carried out with Formula (26) by use of a variable factor α, where α is set to be one of all real numbers, a new interpolation coefficient Aij being obtained from said linear combination, and carrying out an interpolating operation 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 (27): f=ΣBij·Yij (24) g=ΣCij·Yij (25) Aij=(1−α)Bij+αCij (26) h=ΣAij·Yij (27)which i=1, 2, . . . , j=1, 2, . . . , andα represents one of all real numbers.
- 10. A method as defined in claim 9 wherein one of said two different interpolating functions f and g for obtaining two interpolation images having different levels of sharpness is a cubic spline interpolating operation function, and the other is a B spline interpolating operation function.
- 11. The method of claim 1, further comprising the step of selecting a first user defined input parameter and instructing the employed interpolation process for the flat portion to which the interpolation point belongs to vary the sharpness of the flat portion based on the user defined input parameter.
- 12. The method of claim 1 further comprising the step of manually varying the sharpness of the same flat portion by selecting a user defined variable.
- 13. A method as claimed in claim 1 wherein the sharpness is varied by changing a parameter in an equation having a degree of at least two.
- 14. An interpolating operation method for an image signal, wherein an interpolated image signal component corresponding to an interpolation point is calculated from original image signal components of an original image signal representing an original image, which represent a plurality of sampling points arrayed at predetermined intervals and in a lattice-like form, the method comprising the steps of:i) making a judgement as to whether the interpolation point belongs to an image edge portion, at which a change in the original image signal is sharp, or belongs to a flat portion, at which the change in the original image signal is unsharp, and ii) selecting a first interpolating operation process when the judgement is made that the interpolation point belongs to an image edge portion, and selecting a second alternate interpolation operation process when the judgement is made that the interpolation point belongs to a flat portion; and iii) adjusting to a first sharpness the flat portion by inputting a first user defined parameter; iv) readjusting to a second sharpness from the first sharpness the flat portion by inputting a second user defined parameter that is different from the first user defined parameter.
- 15. A method of enhancing a radiation image, the method comprising:reading data representative of picture elements of the radiation image; separating the picture elements into a plurality of equally-sized portions; determining whether a particular portion is an edge portion of the radiation image or a flat portion of the radiation image; enabling a first interpolation operation if it is determined that the particular portion is an edge portion of the radiation image; determining an edge extending direction if it is determined that the particular portion is an edge portion of the radiation image; enabling a second interpolation operation if it is determined that the particular portion is a flat portion of the radiation image; determining a result of a spline operation if it is determined that the particular portion is a flat portion of the radiation image.
- 16. A method as claimed in claim 15, further comprising:determining whether various other portions, other than the particular portion, are edge portions of the radiation image or flat portions of the radiation image, wherein the various other portions overlap the particular portion.
Priority Claims (2)
| Number |
Date |
Country |
Kind |
| 8-074657 |
Mar 1996 |
JP |
|
| 8-166272 |
Jun 1996 |
JP |
|
Parent Case Info
This is a continuation of application Ser. No. 08/829,471 filed Mar. 28, 1997 now U.S. Pat. No. 6,535,651; the disclosure of which is incorporated herein by reference.
US Referenced Citations (18)
Foreign Referenced Citations (1)
| Number |
Date |
Country |
| 0 753 828 |
Jan 1997 |
EP |
Non-Patent Literature Citations (2)
| Entry |
| “Deriving Shape Functions for Triangular miid-edge finite elements through blending-function interpolation”, K. Ho-Lee, 8340 Computer-Aided Design, No. 9, London GB, pp. 55-60. |
| Patent Abstracts of Japan, vol. 018, No. 073 (E-1503) Feb. 7, 1994. |
Continuations (1)
|
Number |
Date |
Country |
| Parent |
08/829471 |
Mar 1997 |
US |
| Child |
10/193094 |
|
US |
Patent Grant
6766068
