An improved interpolation method in which a threshold value used for determining a pixel value of a pixel generated by interpolation according to a context which is a state value of adjacent pixels. In the interpolation method, the ambiguity between the interpolation value and the threshold value is removed by using the context, thereby reducing the blocking and smoothing phenomena in the restored binary image.
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0. 9. An apparatus comprising:
(a) means for preparing a threshold table showing various threshold values corresponding to a context cp (state value) of pixels (reference pixels) of the reduced image, around an interpolated pixel;
(b) means for calculating an interpolation value based on the pixel values of pixels (object pixels) adjacent to and/or around the interpolated pixel;
(c) means for calculating the context cp which is the state value of the reference pixels around the interpolated pixel;
(d) means for obtaining a threshold value corresponding to the calculated context from the threshold table; and
(e) means for comparing the interpolation value with the threshold value of the step (d), and setting the pixel value of the interpolated pixel as “1” if the interpolation value is greater than the threshold value, and setting the pixel value of the interpolated pixel as “0” if the interpolation value is equal to or less than the threshold value.
1. A computer usable medium having embodied thereon a computer program for restoring a binary image block reduced through a down sampling into the block with the size of the original binary image block, the computer program being executable by a machine to perform:
(a) preparing a threshold table showing various threshold values corresponding to a context cp (state value) of pixels (reference pixels) of the reduced image, around an interpolated pixel;
(b) calculating an interpolation value based on the pixel values of pixels (object pixels) adjacent to and/or around the interpolated pixel;
(c) calculating the context cp which is the state value of the reference pixels around the interpolated pixel;
(d) obtaining a threshold value corresponding to the calculated context from the threshold table; and
(e) comparing the interpolation value with the threshold value of the step (d), and setting the pixel value of the interpolated pixel as “1” if the interpolation value is greater than the threshold value, and setting the pixel value of the interpolated pixel as “0” if the interpolation value is equal to or less than the threshold value.
2. The computer usable medium of
INP[P1]=r*A+s*(B+c+D)+t*(E+F+G+H+I+J+K+L) INP[P2]=r*B+s*(A+c+D)+t*(E+F+G+H+I+J+K+L) INP[P3]=r*c+s*(A+B+D)+t*(E+F+G+H+I+J+K+L) INP[P4]=r*D+s*(A+B+c)+t*(E+F+G+H+I+J+K+L) where P1, P2, P3 and P4 represent an interpolated pixel, A, B, c and D are the objective pixels adjacent to the interpolated pixel, E, F, G, H, I, J, K and L are the objective pixels around the pixels A, B, c and D, INP[P] represents the interpolation value of the interpolated pixel P, r is the weight of the object pixel which is the closest to the interpolated pixel, s is the weight of three object pixels which are the next closest to the interpolated pixel, and t is the weight of eight object pixels around the next closest pixels, and the condition of r>s>t is satisfied.
3. The computer usable medium of
where P represents the position of the interpolated pixel, O represents the reference pixel, and k is an index of the reference pixels.
4. The computer usable medium of
5. The computer usable medium of
(a1) calculating possible sums of the reference pixels;
(a2) calculating possible interpolation values with respect to the possible sums of the reference pixels;
(a3) setting possible candidate threshold values with respect to the possible sum of the reference pixels; and
(a4) selecting a threshold value from the candidate threshold values with respect to each context corresponding to the possible sum of the reference pixels, resulting in the threshold table.
6. The computer usable medium of
7. The computer usable medium of
8. The computer usable medium of
0. 10. The apparatus of
INP[P1]=r*A+s*(B+c+D)+t*(E+F+G+H+I+J+K+L) INP[P2]=r*B+s*(A+c+D)+t*(E+F+G+H+I+J+K+L) INP[P3]=r*c+s*(A+B+D)+t*(E+F+G+H+I+J+K+L) INP[P4]=r*D+s*(A+B+c)+t*(E+F+G+H+I+J+K+L) where P1, P2, P3 and P4 represent an interpolated pixel, A, B, c and D are the objective pixels adjacent to the interpolated pixel, E, F, G, H, I, J, K and L are the objective pixels around the pixels A, B, c and D, INP[P] represents the interpolation value of the interpolated pixel P, r is the weight of the object pixel which is the closest to the interpolated pixel, s is the weight of three object pixels which are the next closest to the interpolated pixel, and t is the weight of eight object pixels around the next closest pixels, and the condition of r>s>t is satisfied.
0. 11. The apparatus of
where P represents the position of the interpolated pixel, O represents the reference pixel, and k is an index of the reference pixels.
0. 12. The apparatus of
0. 13. The apparatus of
(a1) means for calculating possible sums of the reference pixels;
(a2) means for calculating possible interpolation values with respect to the possible sums of the reference pixels;
(a3) means for setting possible candidate threshold values with respect to the possible sum of the reference pixels; and
(a4) means for selecting a threshold value from the candidate threshold values with respect to each context corresponding to the possible sum of the reference pixels, resulting in the threshold table.
0. 14. The apparatus of
0. 15. The apparatus of
0. 16. The apparatus of
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This is a continuation of U.S. patent application Ser. No. 08/979,107, filed Nov. 26, 1997,
INP[P2]=r*B+s*(A+C+D)+t*(E+F+G+H+I+J+K+L)
INP[P3]=r*C+s*(A+B+D)+t*(E+F+G+H+I+J+K+L)
INP[P4]=r*D+s*(A+B+C)+t*(E+F+G+H+I+J+K+L)
where r, s and t are weights according to the distance from the interpolated pixel, that is, r is the weight of the object pixel which is the closest to the interpolated pixel, s is the weight of object pixels which are the next closest to the interpolated pixel, and t is the weight of object pixels around the next closest pixels. Also, the condition of r>s>t is satisfied.
Next, the obtained interpolation value INP[P]and a threshold value THR are compared. Here, the threshold value THR is set to a value which is half of the largest possible interpolation value. For example, if r, s and t are 4, 2 and 1, respectively, then the threshold value is set to 9. If the interpolation value INP[P] is greater than the threshold value THR, the pixel value of the interpolated pixel becomes “1”. Otherwise, the pixel value of the interpolated pixel becomes “0”.
Here, only one threshold THR is applied while a plurality of interpolation values INP may be applied. Thus, if the interpolation value INP[P] and the threshold value THR are close to each other, it is unclear whether the pixel value of the interpolated pixel is correct or not. Accordingly, serious blocking or smoothing phenomenon can be present in the restored binary image.
To reduce the blocking or smoothing effects, a threshold value to be compared with the interpolation value INP[P] is adaptively determined according to the context (state values of the pixels (reference pixels) around the interpolated pixel), thereby reducing ambiguity in determination of the pixel value of the interpolated pixel.
An improved interpolation method according to a preferred embodiment of the present invention will be described with reference to
First, an interpolation value INP[P] is obtained by the object pixels as follows:
INP[P1]=r*A+s*(B+C+D)+t*(E+F+G+H+I+J+K+L)
INP[P2]=r*B+s*(A+C+D)+t*(E+F+G+H+I+J+K+L)
INP[P3]=r*C+s*(A+B+D)+t*(E+F+G+H+I+J+K+L)
INP[P4]=r*D+s*(A+B+C)+t*(E+F+G+H+I+J+K+L)
where r, s and t are weights according to the distance from the interpolated pixel, that is, r is the weight of the object pixel which is the closest to the interpolated pixel, s is the weight of object pixels which are the next closest to the interpolated pixel, and t is the weight of object pixels around the next closest pixels. Also, the condition of r>s>t is satisfied. Here, r, s and t are 4, 2 and 1, respectively.
Then, the context Cp which is state value of the reference pixels is calculated by the following equation (1):
where P represents the position of the interpolated pixel, O represents the reference pixel, and k is an index of the reference pixels and also a weight. Here, the index k is varied depending on the relative position between the interpolated pixel and the adjacent object pixels.
Next, a threshold value THRc according to the calculated context is determined with reference to the threshold value table shown in FIG. 4. The threshold value of
In the threshold table of
Since the number of the reference pixels for calculating context is 8, the number of potential combinations become 256.
In
In
The interpolation value INP[P] and the threshold value THRc according to the context of the object pixels are a compared to determine a pixel value of the interpolated pixel.
If the interpolation value INP[P] is greater than the threshold value THRc, the pixel value of the interpolated pixel is set to “1”. Otherwise, the pixel value of the interpolated pixel is set to “0”.
The threshold table used in the present invention is effectively determined in consideration of reference pixel values. The procedure for preparing the threshold table in consideration of the reference pixel values will be described with reference to
Here, the sum of the reference pixels represents the sum of pixel values of the reference pixels which contributes to calculate the context. For example, it refers to the sum of the pixel values of the reference pixels indicated by E, F, G, H, I, J, K and L in FIG. 3.
In
For example, if the sum of the reference pixels is equal to “0”, that is, all the pixel values of the reference pixels are “0”, the interpolation value is one of 0, 2, 4, 6, 8 and 10. If all the pixel values of the adjacent object pixels A, B, C and D are “0”, the interpolation value becomes “0”. Also, if all the pixel values of the adjacent object pixels A, B, C and C are 37 1”, the interpolation value becomes “10”.
In the same manner, if the sum of the reference pixels is equal to “8”, that is, if all the pixel values of the reference pixels are “1”, the interpolation value becomes one of 8, 10, 12, 14, 16 and 18.
In
If the context value is equal to “0”, that is, if the sum of the reference pixels is “0” in
If the context value is equal to “1”, that is, if the sum of the reference pixels is “1” in
If the context value is equal to “2”, that is, if the sum of the reference pixels is “2” in
If the context value is equal to “255”, that is, if the sum of the reference pixels is “8” in
Also,
In the interpolation method of the present invention, the ambiguity in the comparison between the interpolation value and the threshold value is removed by using the state value (context) of the reference pixels around the interpolated pixel, thereby reducing the blocking and smoothing phenomena in the restored binary image.
The invention may be embodied in a general purpose digital computer that is running a program or program segments originating from a computer readable or usable medium, such medium including but not limited to magnetic storage media ((e.g., ROM's, floppy disks, hard disks, etc.), optically readable media (e.g., CD-ROMs, DVDs, etc.) and carrier waves (e.g., transmissions over the Internet). A functional program, code and code segments, used to implement the present invention can be derived by a skilled computer programmer from the description of the invention contained herein.
As can be seen from
As described above, in the interpolation method of the present invention, the ambiguity in the comparison between the interpolation value and the threshold value is removed by using the state value (context) of the reference pixels around the interpolated pixel, thereby reducing the blocking and smoothing phenomena in the restored binary image.
In the interpolation method of the present invention, since variable threshold values according to the context combination are quickly obtained from the threshold table, the interpolation can be performed rapidly.
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