Image magnification

Abstract: A magnified version of an image, is produced by determining values of new pixels which are to be interpolated between original pixels of the image. The interpolation is carried out in each unit area which is surrounded by original pixels centers. The magnification process includes a first step for detecting an angle of an original line image in a predetermined vicinity of the unit area by comparing values of a combination of original pixels in the predetermined vicinity of the unit area with each of a plurality of predetermined patterns of an arrangement of pixel values; a second step for selecting one of a plurality of predetermined modes of division of the unit area so that an angle of a dividing line which divides the unit area in the selected mode of division conforms substantially to the angle detected in the first step; and a third step for determining a value of each of the new pixels by assigning a value which is determined based on the values of the original pixels in the vicinity, to all of the new pixels the centers of which are in each section of the unit area which section is generated by the mode of division selected in the second step. Such a process is applicable, for example, to conversion between different facsimile transmission types, and can improve the reproduction of magnified oblique lines.

Description: The present invention relates to image magnification, for example image magnification of the type in which the magnified image is formed by determining values of new pixels which are to be interpolated between original pixel centers constituting an original image. A process and apparatus for such image magnification is applicable both to a simple image magnification with a constant pixel density carried out in image display and image printing, and to an increase in pixel density, for example, in the conversion from a Group 3 (G3) type to a Group 4 (G4) type in facsimile transmission systems. One example of an image conversion process suitable for magnifying an image is a high speed projection method as proposed in Japanese Unexamined Patent Publication A58-97958 and the Journal of the Institute of Image Electronics Engineers of Japan vol. 11, NO. 2, 1982, pp 72 ∼ pp 83. Such an image conversion process employs a first set of pixel values representing an original image to be converted, which pixel values relate respectively to the points of a first two-dimensional array of points on the original image, to derive a second set of pixel values representing a converted version of the original image, which pixel values are greater in number than the pixel values of the first set and relate respectively to the points of a second two-dimensional array of points on the converted version of the original image. The process may be considered to comprise the following steps for each pixel value in turn of the said second set, the said second array being considered as projected onto the first array so that the projected second array occupies the same area as the first array and so that rows and columns of the projected second array are parallel respectively to rows and columns of the first array: (a) calculating the location, on the first array, of the second-array point to which the second-set pixel value concerned relates, and identifying a corresponding unit area of the first array that contains the calculated location, which unit area has at its periphery the four first-array points that are nearest to the said calculated location; (b) determining which one of a predetermined plurality of different sections, into which the said corresponding unit area is sub-divided, contains the said calculated location; and (c) employing predetermined logical calculations, in dependence upon the determined section, to derive the second-set pixel value concerned from the first-set pixel value relating to the first-array point that is located closest to the said calculated location or from the first-set pixel values relating to respective predetermined points of the first array. Such a process employing the high speed projection method can provide high speed processing in the determination of the concentration (pixel values) of the converted pixels by carrying out logic calculations instead of arithmetic calculations during the image conversion (magnification) process. Figure 1 shows an example of a process according to such a high speed projection method in which, as a first step, a unit area of the first array, surrounded by four adjacent original pixel centers (first-array points) A to D, is divided into four regions corresponding respectively to the four adjacent original pixel centers, in such a way that all points in a particular region are nearer to the associated one of the four adjacent original pixel centers than they are to the other three centers. As a second step, the area of a converted pixel of the magnified image, whose pixel center (second-array point) lies within the unit area of the original image when the magnified image is considered as projected onto the original image, is projected onto that unit area, as shown in Fig. 1. When the magnification factors in the lateral (horizontal) direction and in the longitudinal (vertical) direction are p and q respectively, the length of a lateral side of the area of the converted pixel is 1/p of the length of a lateral side of the area of an original pixel, and the length of a longitudinal side of the area of the converted pixel is 1/q of the length of a longitudinal side of the area of the original pixel. When the concentrations (first-set pixel values) of the above four adjacent first-array pixels are denoted by I A , I B , I C , and I D , respectively, and the respective proportions of the area of the converted pixel projected onto the above sections are denoted by W A , W B , W C , and W D , the concentration (second-set pixel value) of the converted pixel (second-array point) is expressed as I R = Σ I i * W i (i = A, B, C, and D), and the calculated value I R is quantized to a binary value, I.e., I R is set to one (black) when the calculated I R value is greater than or equal to 0.5, and I R is set to zero (white) when the calculated I R value is smaller than 0.5. In the high speed projection method, the above multiplication and summation for obtaining I R is replaced by a logic calculation as explained in the following, to enable high speed processing. First, when the calculated location of the center of a converted pixel (second-array point) is within a predetermined short range of one of the four adjacent original pixel centers, the above calculated value of the concentration I R is made equal to the concentration value of that (nearest) original pixel regardless of the concentrations of the other three original pixels. The boundary for defining such a range is generally given as a hyperbolic curve for each of the original pixels. However, as the magnification rate becomes large, the boundary comes close to the center of the unit area, i.e., the boundaries for the four original pixels come close to the lines which divide the unit area into the above four regions, i.e, the x and y axes in Figure 1. Therefore, a smooth oblique line in an original image becomes a step-like, angular shape when magnified by a large magnification factor. Generally, a hyperbolic boundary additionally causes computational complexity. Thus, the boundary lines x±y=±1/2, were adopted in the high speed projection method as shown in Figure 2, to avoid the reproduction of step-like, angular shapes when oblique lines are magnified and to reduce the computational complexity. This results in sub-division of the unit area into eight different sections G1 to G8. Nevertheless, the high speed projection method as mentioned above is only effective for providing smoothness in magnified oblique lines at the angle of 45 degrees. Magnified oblique lines at angles other than 45 degrees exhibit distortion. Figures 3A, 3B, and 3C show the results of the magnification of an oblique line in an original image by the above-mentioned high speed projection method, wherein the angle of the oblique line is 45 degrees in Fig. 3A, an intermediate angle between 45 degrees and 90 degrees in Fig. 3B, and an intermediate angle between 0 degrees and 45 degrees in Fig. 3C. As shown in Figs. 3A, 3B, and 3C, a satisfactorily smooth magnification is not assured for oblique lines at an angle other than 45 degree. In particular, when the magnification factor becomes large, the step-like shape becomes prominent. It is desirable to provide a process and apparatus for image magnification whereby smooth magnification of oblique line images at angles other than 45 degrees is possible. An image conversion process embodying the present invention is characterised by the step of determining, between steps (a) and (b), whether the first-set pixel values relating to a group of first-array points in the vicinity of the calculated location match any one of a plurality of predetermined image patterns that are consistent with original image line portions extending at a predetermined angle to a predetermined reference direction of the first array, and, if such a match is found, the mode of sub-division used to define the said predetermined plurality of different sections for the purposes of step (b) is selected from a predetermined set of different possible modes of sub-division, so that a dividing line employed in the selected mode and separating the section containing the calculated location from an adjacent section of the said corresponding unit area extends at substantially the said predetermined angle to the said predetermined reference direction. According to another aspect of the present invention, there is provided image conversion apparatus for employing a first set of pixel values representing an original image to be converted, which pixel values relate respectively to the points of a first two-dimensional array of points on the original image, to derive a second set of pixel values representing a converted version of the original image, which pixel values are greater in number than the pixel values of the first set and relate respectively to the points of a second two-dimensional array of points on the converted version of the original image; which apparatus comprises: co-ordinate calculation means operable, for each pixel value in turn of the said second set, to calculate the location, on the first array, of the second-array point to which the second-set pixel value concerned relates, the said second array being considered as projected onto the first array so that the projected second array occupies the same area as the first array and so that rows and columns of the projected second array are parallel respectively to rows and columns of the first array; means for identifying a corresponding unit area of the first array that contains the calculated location, which unit area has at its periphery the four first-array points that are nearest to the said calculated location; section determining means for determining which one of a predetermined plurality of different sections, into which the said corresponding unit area is subdivided, contains the said calculated location; and pixel value determining means for employing predetermined logical calculations, in dependence upon the determined section, to derive the second-set pixel value concerned from the first-set pixel value relating to the first-array point that is located closest to the said calculated location or from the first-set pixel values relating to respective predetermined points of the first array; characterised by: pattern detecting means for determining, prior to the section determination performed by the said section determining means, whether the first-set pixel values relating to a group of first-array points in the vicinity of the calculated location match any one of a plurality of predetermined image patterns that are consistent with original image line portions extending at a predetermined angle to a predetermined reference direction of the first array; and selector means operable, if such a match is found, to select the mode of sub-division, used to define the said predetermined plurality of different sections for the purposes of the said section determination, from a predetermined set of different possible modes of sub-division, so that a dividing line employed in the selected mode and separating the section containing the calculated location from an adjacent section of the said corresponding unit area extends at substantially the said predetermined angle to the said predetermined reference direction. Reference will now be made, by way of example, to the accompanying drawings, in which: Figure 1 shows an example of a high speed projection method; Figure 2 is illustrative of the high speed projection method of Fig. 1; Figures 3A, 3B and 3C show results when an oblique line image in an original image is magnified by the high speed projection method of Fig. 2; Figure 4 shows original pixel centers used in a step of a process for magnifying an image embodying the present invention; Figure 5 shows examples of predetermined patterns used in the process of Fig. 4; Figures 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8C, 8D, illustrate a feature of a second step of the process of Fig. 4; Figure 9 shows a table illustrating a basis of a third step of the process of Fig.4; Figure 10 shows an example of a process involving a first embodiment of the present invention; Figures 11A, 11B and 11C show various results when oblique line images are magnified by the process of Figure 10; Figures 12A, 12B, 12C, 12D, and 12E, and 13A, 13B, 13C, 13D, and 13E illustrate a modification to the process of Figure 10; Figure 14 shows additional initial steps in a process according to a second embodiment of the present invention; Figure 15 illustrates a step in the process of Figure 14; Figures 16A and 16B illustrate a feature of the process of Figure 14; Figure 17 shows a table illustrating a basis for a step in the process of Figure 14; Figure 18 shows an arrangement of original pixel centers used in a process according to a third embodiment of the present invention; Figures 19A and 19B show the combinations and the patterns which are predetermined for each of the sub-areas R1, R2, R3, and R4; Figures 20A and 20B show two examples of the magnification of the above sharp angle changes between 90 degrees to 45 degrees and between 0 degrees to 45 degrees; Figure 21 shows a detail of the magnification process of the image shown in Fig. 20B; Figure 22 shows a block diagram of an apparatus for image magnification according to an embodiment of the present invention; Figure 23A shows an example of the construction of the x-coordinate calculating portion 1 and the original pixel data input portion 2 in Fig. 22; Figure 23B shows an example of the construction of the pattern detecting portion 4 in Fig. 22; Figure 23C shows an example of the construction of the section detecting portion 5 in Fig. 22; Figure 23D shows an example of the construction of the converted pixel value calculating portion 6 in Fig. 22; and Figure 24 shows the x-coordinates X(M1), X(M2), X(M3), X(M4), X(M5), and X(M6) of the dividing lines in all modes of division M1, M2, M3, M4, M5, and M6 (Fig. 16A), at the y-coordinate Y 1 of the converted pixel, when the center of the converted pixel exists in the sub-area R1. In a process embodying the present invention, the angle of an original line image (original image line portion) in a predetermined vicinity of the unit area is determined by comparing values of a group of original pixels in that predetermined vicinity of the unit area with a set of predetermined image patterns. Figure 4 shows the original pixel centers used in a step for comparing values of such a group of the original pixels in that predetermined vicinity of the unit area with each pattern in the set of predetermined patterns. The area surrounded by the four original pixel centers A, B, C, and D, is a unit area wherein new (converted) pixels are to be interpolated, and the other twelve original pixel centers denoted by M, L, K, P , E, J, F, I, N, G, H, and O, together with the above A, B, C, and D, are included in a sub-array in the above predetermined vicinity of the unit area, i.e. in the pattern matching step of the process, the group members are selected from amongst the sub-array of these sixteen original pixels, and the pixel values of the group members are compared with each of the predetermined patterns. An example of the above set of predetermined image patterns is shown in Figure 5. The patterns are sorted into eight types denoted by P1, P2, P3, P4, P5, P6, P7, and P8, according to the combination of the original pixel centers as shown in Fig. 5. In the types P1 to P4, the patterns Nos. 1 and 5 correspond to an oblique line image at the angle 45 degrees, I.e.,  = tan -1 1, Nos. 2 and 6 correspond to  = tan -1 2, Nos. 3 and 7 correspond to  = tan -1 1/2, and Nos. 4 and 8 each correspond to a pattern showing a right-angled corner. In the types P5 and P6, each pattern corresponds to a portion of an oblique line image at the angle  = tan -1 2 in one unit area continuing to another unit area in which one of the above Nos. 2 and 6 patterns in the types P1 to P4 (corresponding to a line image at the angle  = tan -1 2) is detected by means of the above comparison, i.e., one unit area in which one of the patterns in the types P5 and P6 is detected by means of the above comparison, belongs to a first portion of the line image at the angle  = tan -1 2 which portion continues to a further portion in another unit area wherein one of the above Nos. 2 and 6 patterns in the types P1 to P4 is detected. Similarly, in the types P7 and P8, each pattern corresponds to a portion of an oblique line image at the angle  = tan -1 1/2 in a unit area continuing to another unit area in. which one of the above Nos. 3 and 7 patterns in the types P1 to P4 (corresponding to a line image at the angle  = tan -1 1/2) is detected by means of the above comparison, ie., a unit area in which one of the patterns in the types P7 and P8 is detected by means of the above comparison, belongs to a first portion of the line image at the angle  = tan -1 1/2 continuing to a further portion in another unit area wherein one of the above Nos. 3 and 7 patterns in the types P1 to P4 is detected. The above continuation will be explicitly shown in the example of Figure 10. As the next step (mode selection step) in the process, a selection of one of a plurality of predetermined modes of division of the unit area, is made according to the line image detected in the pattern matching step, the predetermined modes of division of the plurality having been provided in advance corresponding to the predetermined patterns, so that each of the new pixels in a section which is generated by one of the modes of division, has the same value determined by values of the original pixels in the predetermined vicinity. The predetermined modes of division of the unit area are shown in Figures 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8C, 8D, and 8E. The mode of division shown in Fig. 6 corresponds to the patterns of Nos. 1, 4, 5, and 8 in the types P1 to P4 in Fig. 5. This mode of division is identical to the division shown in the conventional division of the unit area as shown in Fig. 2. (The previously-proposed high speed projection method provides only this one mode of division). The mode of division shown in Fig. 7A corresponds to Nos. 2 and 6 in the types P1 to P4. The mode of division shown in Fig. 7B corresponds to Nos. 1 and 2 in the type P5. The mode of division shown in Fig. 7C corresponds to Nos. 1 and 2 in the type P6. The mode of division shown in Fig. 7D corresponds to Nos. 3 and 4 in the type P6. The mode of division shown in Fig. 7E corresponds to Nos. 3 and 4 in the type P5. The mode of division shown in Fig. 8A corresponds to Nos. 3 and 7 in the types P1 to P4 in Fig. 5. The mode of division shown in Fig. 8B corresponds to Nos. 1 and 2 in the type P7. The mode of division shown in Fig. 8C corresponds to Nos. 3 and 4 in the type P7. The mode of division shown in Fig. 8D corresponds to Nos. 3 and 4 in the type P8. The mode of division shown in Fig. 8E corresponds to Nos. 1 and 2 in the type P8. The lines dividing the unit area in the mode of Fig. 6, are x=0, y=0, x±y=1/2, and x±y=-1/2. The lines dividing the unit area in the mode of Fig. 7A, are x=0, y=0, x±y/2 =1/2, and x±y/2=-1/2. The lines dividing the unit area in the mode of Fig. 7B are x=0, y=0, and y=+2x≦0, the lines dividing the unit area in the mode of Fig. 7C are x=0, y=0, and y=-2x≧0, the lines dividing the unit area in the mode of Fig. 7D are x=0, y=0, and y=+2x≧0, and the lines dividing the unit area in the mode of Fig. 7E are x=0, y=0, and y=-2x≦0. The lines dividing the unit area in Fig. 8A, are the lines determined by x=0, y=0, x/2±y=1/2, and x/2±y=-1/2. The lines dividing the unit area in the mode of Fig. 8B are x=0, y=0, and y=+(1/2)x≦0, the lines dividing the unit area in the mode of Fig. 8C are x=0, y=0, and y=-(1/2)x≧0, the lines dividing the unit area in the mode of Fig. 8D are x=0, y=0, and y=+(1/2)x≧0, and the lines dividing the unit area in the mode of Fig. 8E are x=0, y=0, and y=-(1/2)x≦0. Through Figs. 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8C, 8D, to 8E, the point (x,y)=(0,0) corresponds to the center of the unit area, the line determined by x=0 corresponds to the horizontal line, the line determined by y=0 corresponds to the vertical line, the lines determined by x=±1/2 and y=±1/2, correspond to the boundaries of the unit area. As mentioned before, in the high speed projection method, all the new (converted) pixels the centers of which are in a section generated by the above dividing operation, have the same (concentration or brightness) value which is determined by values of the original pixels in the predetermined vicinity. Figure 9 shows the value assigned for the pixels the center of which are in each section generated by the above dividing operation shown in Figs. 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8C, 8D, and 8E. The sections are denoted by the common references G1, G2, ... G8, G9, G10, G11, G12, G9′ , G10′ , G11′ , and G12′ in Figs. 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8C, 8D, 8E and 9. In Fig. 9, A, B, C, ... and I, L denote the respective values of the pixels shown in Fig. 4, and + denotes a logical OR, * denotes a logical AND, and A denotes a logical inversion of the value of the pixel A. As shown in Figs. 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8C, 8D, 8E and 9, values of new (converted) pixels in any of the sections G1, G2, G3, or G4 (the sections nearest respectively to the corners A, B, C, or D of the unit area ABCD among a plurality of sections generated by the mode of division selected in the mode selection step of the present invention) are each made equal to the value of the original pixel the center of which is at the corner concerned. Values of the new pixels in the section G9, the boundaries of which include both x=0 and y=+2x (Fig. 7B), are each an inverse of the value of the pixel A the center of which is at the corner of the unit area nearest to the section G9; values of the new pixels in the section G10, the boundaries of which include both x=0 and y=-2x (Fig. 7C), are each an inverse of the value of the pixel B the center of which is at a corner of the unit area which corner is the nearest to the section G10; values of the new pixels in the section G11 the boundaries of which include both x=0 and y=+2x (Fig. 7D), are each an inverse of the value of the pixel C the center of which is at a corner of the unit area which corner is the nearest to the section G11; and values of the new pixels in the section G12 the boundaries of which include both x=0 and y= -2x (Fig. 7E), are each an inverse of the value of the pixel D the center of which is at a corner of the unit area which corner is the nearest to the section G12, in the modes shown in Figs. 7B to 7E. Further, values of the new pixels in the section G9: the boundaries of which include both y=0 and y= + (1/2)x (Fig. 8B), are each an inverse of the value of the pixel A the center of which is at a corner of the unit area which corner is the nearest to the section G9' ; values of the new pixels in the section G10', the boundaries of which include both y=0 and y=-(1/2)x (Fig. 8C), are each an inverse of the value of the pixel B the center of which is at a corner of the unit area which corner is the nearest to the section G10' ; values of the new pixels in the section G11′ the boundaries of which include both y=0 and y=+(1/2)x (Fig. 8D), are each an inverse of the value of the pixel C the center of which is at a corner of the unit area which corner is the nearest to the section G11' ; and values of the new pixels in the section G12' the boundaries of which include both y=0 and y=-(1/2)x (Fig. 8E), are each an inverse of the value of the pixel D the center of which is at a corner of the unit area which corner is the nearest to the section G12' in the modes shown in Figs. 8B to 8E. The meaning of the assignment of the value A*(B+C+D+ F * K )+B*C*D*( F + K ) for the section G5, is as follows. G5 is black: when both A and 8 are black; when both A and C are black; or when both A and D are black (corresponding to A*(B+C+D)). G5 is black if A is black and B, C, D, F, and K are all white (corresponding to A*(B+C+D+ F * K ), and showing a right-angled corner by a white line image). G5 is white when A is white and B, C, D, F, and K are all black (corresponding to B*C*D*( F + K ), and showing a right-angled corner by a black line image). From the symmetry of the divisions shown in Figs. 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8C, 8D, and 8E, and the logical expressions shown in Fig. 9, the meanings of the assignments of the values for the other sections G6, G7, and G8 are understood by the similar consideration. Figure 10 shows an example of the operation of a first embodiment of the present invention. In the example of Fig. 10, the black and white circles positioned in a square-latticed arrangement are each the original pixel centers constituting an original image, a black circle indicates that the concentration value of the pixel is black, and a white circle indicates that the concentration value of the pixel is white. The magnification factor in both the horizontal and the vertical directions is three, and the small points shown arranged at three times the density of the original pixels show the positions on the original image that are to correspond respectively with the pixel centers of the magnified image. To obtain the concentration value of the converted (magnified image) pixel, whose center is labelled α in Fig. 10, the unit area is the area surrounded by the four original pixels 1, 2, 5, and 6, because the pixel is contained in that area, i.e., the pixels 1, 2, 5, and 6, are selected as the aforementioned pixels A, B, C, and D in the present invention. As may be understood from the values of the original pixels shown in Fig. 10, through the operation of the comparison in the pattern matching step of the process described above the accordance with the pattern No. 7 in the type P2 in Fig. 5 is detected. Accordingly the mode of division shown in Fig. 8A is selected in the mode selection step of the process and then it is determined that the coordinate of the converted pixel α is in the section G2, a convention that, when the coordinate of a converted pixel is on a line which divides a unit area, the converted pixel is assigned to the lower side of the sections divided by the line (hereinafter called lower side convention),being applied in this embodiment. Thus, the value of the converted pixel α is equal to the value of the original pixel B. As B is black, the value of the converted pixel α is black. To obtain the concentration value of the converted pixel whose center is labelled β in Fig. 10, the unit area is the area surrounded by the four original pixels 2, 3, 4, and 5, because the pixel is contained in that area, i.e., the pixels 2, 3, 4, and 5, are selected as the aforementioned pixels A, B, C, and D in the present invention. As may be understood from the values of the original pixels shown in Fig. 10, through the operation of the comparison in the pattern matching step of the process, the accordance with the pattern No. 3 in the type P4 in Fig. 5 is detected. Accordingly the mode of division shown in Fig. 8A is selected in the mode selection step of the process and then it is determined that the coordinate of the converted pixel β is in the section G8 using the lower side convention used before. Thus, the value of the converted pixel β is calculated as D*(A+B+C+ I * L ) +A*B*C*( I + L ). As A, B, and C are black, and L is white, the value of the converted pixel β is black. To obtain the concentration value of the converted pixel whose center is labelled γ in Fig. 10, the unit area is the area surrounded by the four original pixels 5, 4, 7, and 8, because the pixel is contained in that area, i.e., the pixels 5, 4, 7, and 8, are selected as the aforementioned pixels A, B, C, and D in the present invention. As may be understood from the values of the original pixels shown in Fig. 10, through the operation of the comparison in the pattern matching step of the process the accordance with the pattern No. 1 in the type P7 in Fig. 5 is detected. The mode of division shown in Fig. 8B is then selected in the mode selection step of the process, and then it is determined that the coordinate of the converted pixel γ is in the section G2. Thus, the value of the converted pixel γ is equal to the value of the original pixel B, i.e., the value of the converted pixel γ is black. In Fig. 10, a thick line shows a boundary of the area where the converted pixels are black. Thus, a converted (magnified) line image at the angle tan -1 1/2, which is smoother than the magnified line image by the conventional high speed projection method, is obtained by the first embodiment of the present invention. Figures 11A, 11B, and 11C show examples of the result of the magnification by the process for image magnification according to an embodiment of the present invention. Figure 11A shows a magnification result of an oblique line image at the angle of 45 degrees. Figure 11B shows a magnification result of an oblique line image at the angle of  = tan -1 2. Figure 11C shows a magnification result of an oblique line image at the angle of  = tan -1 1/2. In each of Figs. 11A, 11B, and 11C, the magnification factors in the horizontal and lateral directions are both three. As can be appreciated by comparing the above results with the results of the conventional method shown in Figs. 3A, 3B, and 3C, in the above-described method the prominent step-like shapes appeared in the conventional result are much smoothed. Although, in the first embodiment of the present invention, only the line images at the angles of  = tan -1 1,  = tan -1 2, and  = tan -1 1/2, are detected, and the modes of division of the unit area are provided as shown in Figs. 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8C, 8D, and 8E, the above angles other than  = tan -1 1, may be changed to arbitrary angles . When the above arbitrary angles each differ little from the  = tan -1 2 and  = tan -1 1/2, the patterns shown in Fig. 5 still may be used, and the corresponding modes of division are shown in Figures 12A, 12B, 12C, 12D, 12E, 13A, 13B, 13C, 13D, and 13E. Figures 12A, 12B, 12C, 12D, and 12E show the mode of division corresponding to line images (original image line portions) at the angle  (tan -1 1 <  < tan -1 2), and Figures 13A, 13B, 13C, 13D, and 13E show the mode of division corresponding to line images at the angle  (tan -1 1/2 <  < tan -1 1). The lines dividing the unit area in the mode of Fig. 12A, are x=0, y=0, y=±(tan)(x-1/2), and y=±(tan )(x+1/2). The lines dividing the unit area in the mode of Fig. 12B, are x=0, y=0, and y+1-(1/2) tan=+(tan)x≦0. The lines dividing the unit area in the mode of Fig. 12C, are x=0, y=0, and y-1+(1/2)tan=-(tan)x≧0. The lines dividing the unit area in the mode of Fig. 12D, are x=0, y=0, and y-1+(1/2)tan=+ (tan )x≧0. The lines dividing the unit area in the mode of Fig. 12E, are x=0, y=0, and y+1-(1/2)tan=-(tan)x≦0. The lines dividing the unit area in the mode of Fig. 13A, are x=0, y=0, and y-1/2=±(tan)x, and y+1/2=±(tan)x. The lines dividing the unit area in the mode of Fig. 13B, are x=0, y=0, and x-(1/2)cot+1=+(cot)y≦0. The lines dividing the unit area in the mode of Fig. 13C, are x=0, y=0, and x-(1/2)cot+1=-(cot)y≦0. The lines dividing the unit area in the mode of Fig. 13D, are x=0, y=0, and x+(1/2)cot-1=+(cot)y≧0; and The lines dividing the unit area in the mode of Fig. 13E, are x=0, y=0, and x+(1/2)cot-1=-(cot)y≧0. In Figs. 12A, 12B, 12C, 12D, 12E, 13A, 13B, 13B, 13C, 13D, and 13E, x=0 corresponds to the vertical line, y=0 corresponds to the horizontal line, and x=±1/2 and y=±1/2 determine the boundary of the unit area. The assignment of the values of new pixels in each of the sections G1, G2, ... G8, G9, G10, G11, G12, G9′ , G10′ , G11′ , and G12′ in Figs. 12A, 12B, 12C, 12D, 12E, 13A, 13B, 13B, 13C, 13D, and 13E, is the same as in Figs. 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8C, 8D, and 8E. Since the line which divides the unit area determines the distribution of the values of the converted pixels, if the angle of the dividing line is much different from the angle of the original line image, unevenness having a cycle corresponding to the size of the original unit area, i.e., the original pixel density, necessarily appears in the magnified line image. However, according to the first embodiment of the present invention, information relating to the angle of a line image is derived from the values of a combination of the original pixels in the predetermined vicinity of the unit area by comparing those values with a plurality of predetermined patterns. This is possible because the patterns are predetermined so as to correspond to portions of arrangements of pixel values each of which arrangements constitutes a line image having a definite angle. Then, according to the information concerning the angle, a corresponding one of the predetermined modes of division is selected. The "corresponding" means that in that mode of division, the angle of a line which divides the unit area conforms to the detected angle of the original line image in the vicinity of the unit area. Thus, the unevenness due to the difference of the angles between the line which determines the distribution of the values of the converted pixels, and the angle of the original line image, can be reduced, ie. the quality of the magnified line image can be greatly improved in terms of smoothness of oblique line images, by the process according to this embodiment of the present invention. The process for image magnification according to the second embodiment, further comprises the following two additional steps, preceding the aforementioned pattern matching step of the present invention. Figure 14 shows the additional steps which are carried out before the aforementioned pattern matching step in the second embodiment of the present invention. In the first additional step, the unit area is divided into four sub-areas R1, R2, R3, and R4, corresponding to each of the original pixel centers A, B, C, and D which are surrounding the unit area, so that all points in each sub-area are nearer to the corresponding original pixel center than to other of the original pixel centers, i.e., the unit area is divided by the lines x=0 and y=0. In the second additional step, it is determined in which of the above four sub-areas a new (converted) pixel exists. In the second embodiment, the patterns, and the combination of original pixels, the values of which are compared with the patterns, are predetermined for each of the sub-areas, and the modes of division are defined within each of the sub-areas, as explained in the following. Figure 15 shows the combinations (sub-arrays) and the patterns which are predetermined for each of the sub-areas R1, R2, R3, and R4. The combination (sub-array) predetermined for each of the original pixel centers A, B, C, and D, respectively includes 3×3 original pixels arranged in a square lattice form having the corresponding corner of the unit area (the corresponding original pixel center) in its center. Three types P1, P2, and P3 of patterns are provided for each sub-area in Fig. 15. The type P1 for the sub-area R1 in Fig. 15 is the same as the patterns in the type P1 in Fig. 5 in the first embodiment of the present invention as a total (though the numberings are different in the two embodiments). The type P1 for the sub-area R2 in Fig. 15 is the same as the patterns in the type P2 in Fig. 5 as a total (though the numberings are different in the two embodiments). The type P1 for the sub-area R3 in Fig. 15 is the same as the patterns in the type P3 in Fig. 5 as a total (though the numberings are different in the two embodiments). The type P1 for the sub-area R4 in Fig. 15 is the same as the patterns in the type P4 in Fig. 5 as a total (though the numberings are different in the two embodiments). The type P2 for the sub-area R1 in Fig. 15 is the same as the patterns Nos. 1 and 2 in the type P5 in Fig. 5. The type P2 for the sub-area R2 in Fig. 15 is the same as the patterns Nos. 1 and 2 in the type P6 in Fig. 5. The type P2 for the sub-area R3 in Fig. 15 is the same as the patterns Nos. 3 and 4 in the type P6 in Fig. 5. The type P2 for the sub-area R4 in Fig. 15 is the same as the patterns Nos. 3 and 4 in the type P5 in Fig. 5. The type P3 for the sub-area R1 in Fig. 15 is the same as the patterns Nos. 1 and 2 in the type P7 in Fig. 5. The type P3 for the sub-area R2 in Fig. 15 is the same as the patterns Nos. 3 and 4 in the type P7 in Fig. 5. The type P3 for the sub-area R3 in Fig. 15 is the same as the patterns Nos. 3 and 4 in the type P8 in Fig. 5. The type P3 for the sub-area R4 in Fig. 15 is the same as the patterns Nos. 1 and 2 in the type P8 in Fig. 5. In the second embodiment, comparison of the aforementioned combination of the original pixel values with all patterns of the types P1 to P8, is equivalent to the comparison of the combination for each of the sub-areas R1, R2, R3, and R4 with the corresponding patterns of the types P1 to P3 after the determination of the sub-area. Thus, the number of the operations of comparison is reduced in the second embodiment of the present invention. Figures 16A and 16B show the modes of division in the second embodiment of the present invention. Six types M1, M2, M3, M4, M5, and M6 of the modes of division are defined for each of the sub-areas R1, R2, R3, and R4, and the modes for each sub-area define divisions within the corresponding sub-area only because it is known that the new pixel center exists in that sub-area. The modes of division defined within each sub-area shown in Fig. 16 are each a part of one of the divisions shown in the first embodiment (Fig. 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8B, 8C, 8D, and 8E), and the denotations of the sections G1, G2, G3, G4, G5, G6,G7, G8, G9, G10, G11, and G12, are the same as in Fig. 6, 7A, 7B, 7C, 7D, 7E, 8A, 8B, 8B, 8C, 8D, and 8E. As shown in Figs. 16A and 16B, when the patterns No. 1 or 2 in the type P1 are detected for each section, the mode of division M1 is selected for that section; when the patterns No. 3 or 4 in the type P1 are detected for each section, the mode of division M2 is selected for that section; when the patterns No. 5 or 6 in the type P1 are detected for each section, the mode of division M5 is selected for that section; when the patterns No. 7 or 8 in the type P1 are detected for each section, the mode of division M6 is selected for that section; when the patterns in the type P2 are detected for each section, the mode of division M3 is selected for that section; and when the patterns in the type P3 are detected for each section, the mode of division M4 is selected for that section. Further, in the second embodiment, when one of the patterns corresponding to a line image showing a right-angled corner is detected, an unique mode M2 for the right-angled corners only is assigned, i.e., when one of the patterns Nos. 3 and 4 in the type P1 in each sub-area is detected. Figure 17 shows the logical expressions for obtaining values of the new pixels the center of which exists in each of the sections. Corresponding to the above provision of the modes of division including a provision of the mode M2 for the line images showing a right-angled corner, the logical expressions for obtaining values of the new pixels in each of the sections G5, G6, G7, and G8, are simplified as shown in Figure 17. The third embodiment of the present invention is provided for obtaining a further sharpness in the magnified line image, particularly, where the angle of the line image changes. Figure 18 shows the arrangement of original pixel centers in the vicinity of the third embodiment of the present invention. In the third embodiment, eight further original pixels Q, R, S, T, U, V, W, and X, are added into the vicinity. These additional original pixels are added outside of the aforementioned 4×4 square lattice (sub-array), and two of the eight original pixels are abutting on each of the four original pixels which are at the corners of the 4×4 square lattice, in the vertical direction and in the horizontal direction, as shown in Fig. 18. Similar to the second embodiment, as a first additional step, the unit area ABCD is divided into four sub-areas R1, R2, R3, and R4, corresponding to each of the original pixel centers A, B, C, and D which are surrounding the unit area, so that all points in each sub-area are nearer to the corresponding original pixel center than to other of the original pixel centers, i.e., the unit area is divided by the lines x= 0 and y=0. As a second additional step, a determination is carried out regarding in which of the above four sub-areas a new (converted) pixel exists. The patterns and the combination of original pixels from which the group members whose pixel values will be compared with the patterns are selected, are predetermined for each of the sub-areas, and the modes of division are defined within each of the sub-areas. Figures 19A and 19B show the combinations and the patterns which are predetermined for each of the sub-areas R1, R2, R3, and R4. The combination predetermined for the original pixel center A includes 3×3 original pixels arranged in a square lattice form having the corresponding corner A of the unit area (the corresponding original pixel center) in its center, and two additional original pixels Q and X in the far side from the unit area ABCD. The combination predetermined for the original pixel center B includes 3×3 original pixels arranged in a square lattice form having the corrersponding corner B of the unit area (the corresponding original pixel center) in its center, and two additional original pixels R and S in the far side from the unit area ABCD. The combination predetermined for the original pixel center C includes 3×3 original pixels arranged in a square lattice form having the corresponding corner C (the corresponding original pixel center) in its center, and two additional original pixels T and U in the far side from the unit area ABCD. The combination predetermined for the original pixel center D includes 3×3 original pixels arranged in a square lattice form having the corresponding corner D (the corresponding original pixel center) in its center, and two additional original pixels V and W in the far side from the unit area ABCD. Three types P1, P2, and P3 of patterns are provided for each sub-area in Figs. 19A and 19B. The type P1 for each of the sub-areas R1, R2, R3, and R4 shown in Figs. 19A and 19B is the same as the corresponding patterns in the type P1 in Fig. 15 in the second embodiment of the present invention. The patterns of the types of P2 and P3 provides the characteristic features of the third embodiment of the present invention. The patterns Nos. 1 and 2 in the type P2 for each of the sub-areas R1, R2, R3, and R4, correspond to the line images at the angles ±tan -1 2 without a change of the angle, and the patterns Nos. 3 and 4 in the type P2 for each of the sub-areas R1, R2, R3, and R4, correspond to the line images which are changing in slope between ±tan -1 1 (45 degrees) and ±tan -1 2, or between ±tan -1 1 (45 degrees) and 90 degrees. The patterns Nos. 1 and 2 in the type P3 for each of the sub-areas R1, R2, R3, and R4, correspond to the line images at the angles ±tan -1 1/2 without a change of the angle, and the patterns Nos. 3 and 4 in the type P3 for each of the sub-areas R1, R2, R3, and R4, correspond to the line images which are changing their slope between ±tan -1 1 (45 degrees) and ±tan -1 2, or between ±tan -1 1 (45 degrees) and 0 degrees. The detection of these angle changing points in line images is possible due to the above-mentioned additional eight original pixels. The provided modes of division are totally the same as the modes shown in Fig. 16A and 16B. When the above pattern No. 3 or 4 in the types P2 or P3 is detected, generally, there is an option in selecting a mode. However, in this embodiment, if the above pattern No. 3 or 4 in the type P2 or P3 is detected, the mode M1 corresponding to the angle ±45 degrees is selected for each of the sub-areas R1, R2, R3, and R4, to show a sharp angle change in the magnified image. The reason of the selection is as follows. Suppose that a sharp angle change between 90 degrees to 45 degrees occurs at a point in a line shape. Under this condition, if the aforementioned second embodiment of the present invention using the patterns shown in Fig. 15 is applied, it is deemed that a pattern corresponding to tan -1 2 is detected at the above point, and then a mode of division corresponding to tan -1 2 is applied. Therefore, a portion of a line image where actually a sharp angle change occurs is blunted by the magnification. Further, under this condition, when the abovementioned third embodiment of the present invention using the patterns shown in Fig. 19a and 19B is applied, for example, the pattern No. 3 in the type P2 is detected. Then, if it is deemed that the detection of the pattern No. 3 in the type P2 shows a line image which is changing its slope between ±tan -1 1 (45 degrees) and ±tan -1 2, and the mode of division corresponding to the angles ±tan -1 2 is selected, the magnification result at the angle changing portion is the same as the above result by the second embodiment of the present invention, i.e., no effect appears by the addition of the eight original pixels in the third embodiment of the present invention. Therefore, the third embodiment of the present invention is effective only when the mode M1 corresponding to the angle ±45 degrees is selected for the detection of one of the patterns Nos. 3 and 4 in the types P2 and P3, for each of the sub-areas R1, R2, R3, and R4. According to this selection, an image of a sharp angle change between 90 degrees to 45 degrees or between 0 degrees to 45 degrees is maintained even after the magnification. Figures 20A and 20B show two examples of the magnification of the above sharp angle changes between 90 degrees to 45 degrees and between 0 degrees to 45 degrees, and Figure 21 shows a detail of the magnification process of the image shown in Fig. 20B. Figure 22 shows a block diagram of an embodiment of the apparatus for image magnification according to the present invention, and the construction of Fig. 22 carries out the process of the aforementioned second embodiment. In Fig. 22, reference numeral 1 denotes an x-coordinate calculating portion, 2 denotes an original pixel data input portion, 3 denotes a control portion, 4 denotes a pattern detecting portion, 5 denotes a section detecting portion, and 6 denotes a converted pixel value calculating portion. The x-coordinate calculating portion 1 receives an inverse 1/p of the magnification rate p in x direction and the initial x-coordinate of the converted pixel, calculates the x-coordinate of each converted pixel by adding the inverse 1/p to the x-coordinate of the preceding converted pixel, and then outputs the x-coordinate of the new converted pixel. In the construction of Fig. 22, the interval between two adjacent original pixels in both the x direction and the y direction, are each supposed to be one, i.e., the size of the aforementioned unit area is one. When the x-coordinate output of the x-coordinate calculating portion 1 passes over another size of the unit area, the integer portion of the x-coordinate output is applied to the original pixel data input portion 2 as a carry signal. The decimal portion of the above x-coordinate output is applied to the section detecting portion 5, and the most significant bit of the decimal portion of the above x-coordinate output is applied to the pattern detecting portion 4. The most significant bit of the decimal portion of the above x-coordinate output includes information on the sub-areas (quadrants) where the center of the converted pixel exists, i.e., that most significant bit indicates whether the center of the converted pixel exists in R1, R2 side or R3, R4 side in the unit area shown in Fig. 14. The original pixel data input portion 2 receives three lines of the original pixel data for a predetermined interval. Each line corresponds to a row of the original pixels in the same y-coordinate, and the three adjacent lines are input into the original pixel data input portion 2 at the same time. These three lines correspond to the three lines in the aforementioned 3×3 square lattice form of the combination of the original pixels as shown in Fig. 15, and the original pixel data input portion 2 prepares a set of four bits data consisting of four original pixels adjacent each other in x direction for each of the three lines. The four original pixels in the three lines correspond to the four original pixels in three adjacent lines in the four lines (M, L, K, P), (E, A, D, J), (F, B, C, I), and (N, G, H, O), in 4×4 square lattice form shown in Fig. 14. The output (prepared data) of the original pixel data input portion 2 in each of the above three lines is shifted by one bit in x direction when the abovementioned carry signal is applied to the original pixel data input portion 2, and the output of the original pixel data input portion 2 is applied to both the pattern detecting portion 4 and the converted pixel value calculating portion 6. The pattern detecting portion 4 holds a plurality of predetermined patterns of the pixel data arrangement as shown in Fig. 15, and receives information on the sub-areas (quadrants) where the center of the converted pixel exists, i.e., information showing whether the center of the converted pixel exists in the R1, R2 side or the R3, R4 side in the unit area shown in Fig. 14, from the x-coordinate calculating portion 1, and information showing whether the center of the converted pixel exists in the R2, R3 side or the R1, R4 side, from the control portion 3, and the set of four hit data for each of the three lines from the original pixel data input portion 2. Then, the pattern detecting portion 4 detects a pattern which is equal to the pattern consisting of the values of the aforementioned combination of the original pixels, among the above predetermined patterns, by comparing the pattern consisting of the values of the combination with each of the aforementioned predetermined patterns. The section detecting portion 5 holds a set of the x-coordinates of the dividing lines at the y-coordinite of converted pixels. The dividing lines include lines for all modes of division, and each of which lines devides a unit area (sub-area) into sections according to the corresponding mode of division as shown in Fig. 16A and 16B. The mode of division is selected according to the pattern which is detected in the pattern detecting portion. The section detecting portion 5 compares the x-coordinate of each converted pixel with the x-coordinates of the dividing lines for the selected mode mentioned above, and detects whether or not the x-coordinate of each converted pixel is larger than the x-coordinates of the dividing lines for the selected mode. Thus, the section detecting portion 5 can show the section where the coordinate of the converted pixel exists, when which mode is selected is known. The converted pixel value calculating portion 6 receives the above output of the section detecting portion 5, the pattern which is detected in the pattern detecting portion 4, the information on the sub-areas where the center of the converted pixel exists, and the set of original pixel data which is output from the original pixel data input portion 2, and then carries out the logical calculation as shown in Fig. 17 to obtain the value for the converted pixel. The control portion 3 controls all operation of the construction of Fig. 22, including supplying of the initial x-coordinate, (the inverse of) the magnification rate p, and the information on whether the center of the converted pixel exists in the R2, R3 side or the R1, R4 side in a unit area. Figure 23A shows an example of the construction of the x-coordinate calculating portion 1 and the original pixel data input portion 2 in Fig. 22. The construction shown in the dashed line 2 in Fig. 23A, corresponds to the original pixel data input portion in Fig. 22, and is constructed by registers 201, 202, 203, 204, 205, 206, 207, 209, 210, 211, 213, 214, 215, and 216, and pixel select circuits 208, 212, and 217. The construction shown in the dashed line 1 in Fig. 23A, corresponds to the x-coordinate calculating portion in Fig. 22, and is constructed by a multiplexer 11, registers 12, 14, 15, and 16, and an adder 13. Before start, the initial x-coordinate of the converted pixel is applied to one of the input terminal of the multiplexer 11, and then that input is selected, and therefore, the initial x-coordinate of the converted pixel is input into the register 12. On the other hand, the inverse 1/p of the magnification rate (in x direction) p is input into the register 16 as a pitch of the x-coordinate of the converted pixel. Each of the pixel select circuits 208, 212, and 217 in the construction shown in the dashed line 2 in Fig. 23A, selects a set of four adjacent original pixels in the corresponding line of the original pixels. Each of three adjacent lines of the original pixel data is supplied to the corresponding one of the pixel select circuits 208, 212, and 217. The registers 205, 206, and 207 supplies the original pixel data in the first line to the pixel select circuits 208, the registers 209, 210, and 211 supplies the original pixel data in the second line to the pixel select circuits 212, and the registers 214, 215, and 216 supplies the original pixel data in the third line to the pixel select circuits 217. Each of the registers 205, 209, 214 holds sixteen bits of the original pixel data until the operation of the corresponding one of the pixel select circuits 208, 212, and 217 using the sixteen bits of the original pixel data is completed. At the same time, each of the registers 206, 210, and 215 holds a last one bit of the preceding sixteen bits of the original pixel data, which preceding sixteen bits were held in the corresponding one of the registers 205, 209, and 214 for the preceding cycle of operation, and each of the registers 207, 211, and 216 holds two bits from the top of the next sixteen bits of the original pixel data, which next sixteen bits is to be held in the corresponding one of the registers 205, 209, and 214 for the next cycle of operation. The last one bit in the preceding sixteen bits of data held in each of the registers 206, 210, and 215 and the two bits from the top in the next sixteen bits of data held in each of the registers 207, 211, and 216 are used for realizing a continuous preparation of a set of four bits (data of pixels) data from the input data which are supplied and renewed by sixteen bits (data of pixels). The content of each of the registers 205, 209, and 214 is renewed by the content of the corresponding one of the registers 202, 203, and 204 when the operations of the pixel select circuits 208, 212, and 217 using the corresponding sixteen bits of the original pixel data is completed. After the contents of the registers 202, 203, and 204 are each written into the corresponding one of the registers 205, 209, and 214, the contents of the registers 202, 203, and 204 are each renewed through the register 201 under the control of the control portion 3. The output of each of the pixel select circuits 208, 212, and 217, i.e., each set of four bits data of the adjacent four original pixels are once held in the register 213, and then are output as the aforementioned output of the original pixel data input portion 2. Figure 23B shows an example of the construction of the pattern detecting portion 4 in Fig. 22. The pattern detecting portion shown in Fig. 23B, is constructed by registers 41, 42, 43, and 45, and a pattern detecting circuit 44. Before starting the operation for converted pixels in a new line, i.e., when a y-coordinate of converted pixels in a line is renewed, the most significant hit of the decimal portion of the y-coordinate of the converted pixels in the line is input into the register 41. This value gives information on the sub-area where the center of the converted pixel exists, i.e., the output of the register 41 shows whether the converted pixel is in the side of the sub-areas R1 and R4, or in the side of the sub-areas R2 and R3 in the division of a unit area shown in Fig. 14. The y-coordinate of the converted pixels in each line is calculated in the control portion shown in Fig. 22, and the above most significant bit is input into the register 41 under the control of the control portion 3. The aforementioned decimal portion of the x-coordinate output of the x-coordinate calculating portion 1 is once input into the register 42, and then the most significant bit of the decimal portion of the x-coordinate is applied to the pattern detecting circuit 44, together with the above-mentioned most significant bit of the decimal portion of the y-coordinate of the converted pixels in the line. The most significant bit of the decimal portion of the above x-coordinate output includes the information on the sub-area where the center of the converted pixel exists. The register 43 receives the output of the original pixel data input portion 2, i.e., the three lines of four adjacent original pixel data. The pattern detecting circuit 44 holds a plurality of predetermined patterns of the pixel data arrangement as shown in Fig. 15, and receives the aforementioned information on the sub-area where the center of converted pixel exists, and the set of four bit data for each of the three lines from the original pixel data input portion 2. Then, the pattern detecting circuit 44 detects one pattern which is equal to a pattern consisting of the values of the aforementioned combination of the original pixels, among the abovementioned predetermined patterns, by comparing the pattern consisting of the values of the combination with each of the predetermined patterns. The output of the pattern detecting circuit 44 is applied through the register 45 to the multiplexer 507 in Fig. 23C as a control signal, and is also applied through the register 45 to the register 62 in Fig. 23D. Figure 23C shows an example of the construction of the section detecting portion 5 in Fig. 22. The section detecting portion shown in Fig. 23C, is constructed by registers 501, 502, 503, 504, 505, 506, and 509, and a multiplexer 507, and a comparator 510. A set of the x-coordinates of the dividing lines at the y-coordinate of the converted pixel, are each input into the corresponding one of the registers 501, 502, 503, 504, 505, and 506. For example, Figure 24 shows the x-coordinates X(M1), X(M2), X(M3), X(M4), X(M5), and X(M6) of the dividing lines in all modes of division M1, M2, M3, M4, M5, and M6 (Fig. 16A), at the y-coordinate Y 1 of the converted pixel, when the center of the converted pixel exists in the sub-area R1. Then, the above x-coordinates X(M1), X(M2), X(M3), X(M4), X(M5), and X(M6) of the dividing lines in all modes of division M1, M2, M3, M4, M5, and M6 are applied to the multiplexer 507, and the multiplexer 507 selects one x-coordinates X(Mi) for one of the modes of division according to the pattern which is detected in the pattern detecting circuit 44 and is applied to the multiplexer 507 as a control signal. The selected output of the multiplexer 507 is applied to one input terminal of the comparator 510. The decimal portion of the x-coordinate (x-coordinate in a unit area) is applied through the registers 42 and 509 to the other input terminal of the comparator 510. For example, the output of the comparator 510 is "0" before the x-coordinate passes over the corresponding dividing line, and "1" after it passed over. Therefore, the output of the comparator 510 indicates which section between two sections divided by the dividing line in the selected mode, the coordinate of the converted pixel exists. Figure 23D shows an example of the construction of the converted pixel value calculating portion 6 in Fig. 22. The section detecting portion shown in Fig. 23D, is constructed by registers 61, 62, 63, and 66, and a logic arithmetic circuit 64, and a shift register 65. The logic arithmetic circuit 64 receives: the above output of the comparator 510 and the information on the sub-area where the center of the converted pixel exists, through the register 61; the pattern detected in the pattern detecting circuit 44 through the register 62; and four bits A, B, C, and D in the three lines of the four adjacent bits from the original pixel data input portion 2 through the register 63. Then, the logic arithmetic circuit 64 calculates and outputs the value shown in Fig. 17 according to the information on the sub-area, the detected pattern, the section where the converted pixel exists, and the values of the original pixels A, B, C, and D. Thus, the value of each converted pixel can be obytained. Although the apparatus for image magnification explained above carries out the process of the aforementioned second embodiment of the present invention, it is readily understood that apparatuses carrying out the process according to the first and third embodiments of the present invention can be constructed similarly.

Claims: An image conversion process for employing a first set of pixel values representing an original image to be converted, which pixel values relate respectively to the points of a first two-dimensional array of points on the original image, to derive a second set of pixel values representing a converted version of the original image, which pixel values are greater in number than the pixel values of the first set and relate respectively to the points of a second two-dimensional array of points on the converted version of the original image; which process comprises the following steps for each pixel value in turn of the said second set, the said second array being considered as projected onto the first array so that the projected second array occupies the same area as the first array and so that rows and columns of the projected second array are parallel respectively to rows and columns of the first array: (a) calculating the location, on the first array, of the second-array point to which the second-set pixel value concerned relates, and identifying a corresponding unit area of the first array that contains the calculated location, which unit area has at its periphery the four first-array points (A-D) that are nearest to the said calculated location; (b) determining which one of a predetermined plurality of different sections (G1-G8), into which the said corresponding unit area is sub-divided, contains the said calculated location; and (c) employing predetermined logical calculations (Fig. 9), in dependence upon the determined section, to derive the second-set pixel value concerned from the first-set pixel value relating to the first-array point (e.g. A) that is located closest to the said calculated location or from the first-set pixel values relating to respective predetermined points (e.g. A-D, F, K) of the first array; characterised by the step of: (d) determining, between steps (a) and (b), whether the first-set pixel values relating to a group of first-array points (e.g. A-D, F, K) in the vicinity of the calculated location match any one of a plurality of predetermined image patterns (P1-P4 Nos. 1-8, P5-P8 Nos. 1-4) that are consistent with original image line portions extending at a predetermined angle () to a predetermined reference direction (X) of the first array, and, if such a match is found, the mode of sub-division used to define the said predetermined plurality of different sections (G1-G12) for the purposes of step (b) is selected from a predetermined set of different possible modes of sub-division (e.g. G1-G4, G9), so that a dividing line employed in the selected mode and separating the section containing the calculated location from an adjacent section of the said corresponding unit area extends at substantially the said predetermined angle to the said predetermined reference direction (X). A process according to claim 1, wherein the said corresponding unit area is a rectangle having at the four corners thereof the said four first-array points (A-D) that are nearest to the said calculated location, and the members of the said group of first-array points are selected from a sub-array of 16 points (A-L) occupying four consecutive rows and four consecutive columns of the first array and centered on the said corresponding unit area. A process as claimed in claim 1 or 2, wherein the said plurality of predetermined image patterns includes image patterns that are consistent with original image line portions extending at a plurality of different predetermined angles to the said predetermined reference direction (X). A process according to claim 3, wherein the said plurality of predetermined angles includes 0°, 90°, ± 45°, ± , and ± (π/2-), where  is a predetermined angle less than 90°. A process as claimed in claim 4, wherein: in a first mode of sub-division (Fig. 6), employed in step (b) when no such match is found in step (d), the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, x ± y = ½, and x ± y = -½; and the said predetermined set of different possible modes of sub-division, from which the mode of sub-division used for the purposes of step (b) is selected when such a match is found in step (d), includes: a second mode (Fig. 12A) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, y = ±(tan ) (x - ½), and y = ±(tan ) (x + ½) ; a third mode (Fig. 13A) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, y - ½ = ±(tan )x, and y + ½ = ±(tan )x; and a fourth mode (Fig. 12B) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and y + 1 - ½ tan  = +(tan )x ≤ 0; a fifth mode (Fig. 12C) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and y - 1 + ½ tan  = -(tan )x ≥ 0; a sixth mode (Fig. 12D) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and y - 1 + ½ tan  = +(tan )x ≥ 0; a seventh mode (Fig. 12E) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and y + 1 - ½ tan  = -(tan )x ≤ 0; an eighth mode (Fig. 13B) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and x - ½ cot  + 1 = +(cot )y ≤ 0; a ninth mode (Fig. 13C) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and x - ½ cot  + 1 = -(cot )y ≤ 0; a tenth mode (Fig. 13D) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and x + ½ cot  - 1 = +(cot )y ≥ 0; and an eleventh mode (Fig. 13E) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and x + ½ cot  - 1 = -(cot )y ≥ 0; where x = 0 corresponds to a line extending centrally through the said corresponding unit area in the column direction, y = 0 corresponds to a line extending centrally through the said corresponding unit area in the row direction, and x = ±½ and y = ±½ define the boundaries of the said corresponding unit area. A process according to claim 5, whereinthe predetermined logical calculations employed in step (c) are such that in the cases of: the section (G9) of the said fourth mode (Fig. 12B), the boundaries of which section include both x = 0 and y + 1 - ½ tan  = +(tan )x ≤ 0; the section (G10) of the said fifth mode (Fig. 12C), the boundaries of which section include both x = 0 and y - 1 + ½ tan  = -(tan )x ≥ 0; the section (G11) of the said sixth mode (Fig. 12D), the boundaries of which section include both x = 0 and y - 1 + ½ tan  = +(tan )x ≥ 0; the section (G12) of the said seventh mode (Fig. 12E), the boundaries of which section include both x = 0 and y + 1 - ½ tan  = -(tan )x ≤ 0; the section (G9') of the said eighth mode (Fig. 13B), the boundaries of which section include both y = 0, and x - ½ cot  + 1 = +(cot )y ≤ 0; the section (G10') of the said ninth mode (Fig. 13C), the boundaries of which section include both y = 0, and x - ½ cot  + 1 = -(cot )y ≤ 0; the section (Gll') of the said tenth mode (Fig. 13D), the boundaries of which section include both y = 0, and x + ½ cot  - 1 = +(cot )y ≥ 0; and the section (G12') of the said eleventh mode (Fig. 13E), the boundaries of which section include both y = 0, and x + ½ cot  - 1 = -(cot )y ≥ 0; the second-set pixel value concerned is made equal to the inverse of the first-set pixel value relating to the first-array point which is at the corner of said corresponding unit area nearest to the section concerned. A process as claimed in claim 5 or 6, wherein in the case of each of the sections (G5-G8), the boundaries of which include both x = 0 and y = 0, of the said first, second and third modes (Figs. 6, 12A, 13A), the said respective points of the first array from which the second-set pixel value concerned is derived in step (c) are: the point A at the corner of the said corresponding unit area that is nearest to the section concerned; the point B at the opposite corner of the said corresponding unit area; the points C and D at the other two corners respectively of the said corresponding unit area; and the points F and K in the vicinity of the said calculated location and at opposite ends respectively of the hypotenuse of a right-angled isosceles triangle, which hypotenuse has the said point A mid-way therealong, and the two equal sides of which triangle meet in a right-angle at the point C and pass respectively through the points B and D; the said predetermined logical calculations being such that the second-set pixel value concerned is made equal to: V A * (V B + V C + V D + V F * V K ) + V B * V C * V D * ( V F + V K ) where V A , V B , V C , V D , V F and V K are the respective first-set pixel values relating to the points A, B, C, D, F and K. A process as claimed in claim 3, wherein the said plurality of predetermined angles includes 0°, 90°, ± 45°, ±  1 , and ±  2 , where tan  1 = ½, tan  2 = 2, and 0° <  1 ,  2 < 90°. A process as claimed in claim 8, wherein: in a first mode of sub-division (Fig. 6), employed in step (b) when no such match is found in step (d), the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, x ± y = ½, and x ± y = -½; and the said predetermined set of different possible modes of sub-division, from which the mode of sub-division for the purposes of step (b) is selected when such a match is found in step (d), includes: a second mode (Fig. 7A) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, x ± y/2 = ½, and x ± y/2 = -½; a third mode (Fig. 8A) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, x/2 ± y = ½, and x/2 ± y = -½; a fourth mode (Fig. 7B) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and y = +2x ≤ 0; a fifth mode (Fig. 7C) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and y = -2x ≥ 0; a sixth mode (Fig. 7D) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and y = +2x ≥ 0; a seventh mode (Fig. 7E) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and y = -2x ≤ 0; an eighth mode (Fig. 8B) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and x = +2y ≤ 0; a ninth mode (Fig. 8C) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and x = -2y ≤ 0; a tenth mode (Fig. 8D) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and x = +2y ≥ 0; and an eleventh mode (Fig. 8E) wherein the lines used to sub-divide the said corresponding unit area include the lines determined by x = 0, y = 0, and x = -2y ≥ 0; where x = 0 corresponds to a line extending centrally through the said corresponding unit area in the column direction, y = 0 corresponds to a line extending centrally through the said corresponding unit area in the row direction, and x = ±½ and y = ±½ determine the boundaries of the said corresponding unit area. A process as claimed in claim 1, further comprising, before step (b), the steps of: dividing the said corresponding unit area into sub-areas (R1-R4) corresponding respectively to the said four first-array points (A-D) that are nearest to the said calculated location, the sub-areas being such that all positions in each sub-area (e.g. R1) are nearer to the first-array point (A) to which the sub-area corresponds than to any other (B, C, D) of those four first-array points; and determining which one of the said sub-areas contains the said calculated location; the said predetermined image patterns (Fig. 15) and the members of the said group of first-array points used for the purposes of step (d) being selected according to the determined sub-area, and the said predetermined modes of sub-division of the said predetermined set (Fig. 16A, B) being used to define sections only within each of the said sub-areas. A process as claimed in claim 10, wherein the said corresponding unit area is a rectangle having at the four corners thereof the said four first-array points (A-D) that are nearest to the said calculated location, and the members of the said group of first-array points are selected from a sub-array of nine points (e.g. M, L, K, E, A, D, F, B, C) occupying three consecutive rows and three consecutive columns of the first array and centred on the first-array point (e.g. A) to which the determined sub-area (e.g. R1) corresponds. A process as claimed in claim 1, wherein the said plurality of predetermined image patterns (P2-P3 Nos. 3-4) includes image patterns that are consistent with original image line portions having one part which extends at an angle to the said predetermined reference direction (X) that is different from that of another part of the line portion concerned. A process as claimed in claim 12, wherein the said corresponding unit area is a rectangle having at its four corners the said four first-array points (A-D) that are nearest to the said calculated location; and the members of the said group of first-array points are selected from a sub-array of sixteen points (A-L) occupying four consecutive rows and four consecutive columns of the first-array and centred on the said corresponding unit area, and are also selected from eight further first-array points (Q, X, W, V, R, S, T, U) outside the said sub-array (A-L), there being two of the eight further first-array points adjacent to each of the four first-array points (M, P, O, N) constituting the corners of the said sub-array, which two further first-array points (e.g. Q, X) are the first-array points which immediately precede, or follow as the case may be, the corner point (e.g. M) concerned in the row direction and in the column direction respectively. Image conversion apparatus for employing a first set of pixel values representing an original image to be converted, which pixel values relate respectively to the points of a first two-dimensional array of points on the original image, to derive a second set of pixel values representing a converted version of the original image, which pixel values are greater in number than the pixel values of the first set and relate respectively to the points of a second two-dimensional array of points on the converted version of the original image; which apparatus comprises: co-ordinate calculation means (1) operable, for each pixel value in turn of the said second set, to calculate the location, on the first array, of the second-array point to which the second-set pixel value concerned relates, the said second array being considered as projected onto the first array so that the projected second array occupies the same area as the first array and so that rows and columns of the projected second array are parallel respectively to rows and columns of the first array; means (1) for identifying a corresponding unit area of the first array that contains the calculated location, which unit area has at its periphery the four first-array points (A-D) that are nearest to the said calculated location; section determining means (5) for determining which one of a predetermined plurality of different sections (G1-G8), into which the said corresponding unit area is sub-divided, contains the said calculated location; and pixel value determining means (6) for employing predetermined logical calculations (Fig. 9), in dependence upon the determined section, to derive the second-set pixel value concerned from the first-set pixel value relating to the first-array point (e.g. A) that is located closest to the said calculated location or from the first-set pixel values relating to respective predetermined points (e.g. A-D, F, K) of the first array; characterised by: pattern detecting means (4) for determining, prior to the section determination performed by the said section determining means (5), whether the first-set pixel values relating to a group of first-array points (e.g. A-D, F, K) in the vicinity of the calculated location match any one of a plurality of predetermined image patterns (P1-P4 Nos. 1-8, P5-P8 Nos. 1-4) that are consistent with original image line portions extending at a predetermined angle () to a predetermined reference direction (X) of the first array; and selector means (507) operable, if such a match is found, to select the mode of sub-division, used to define the said predetermined plurality of different sections (G1-G12) for the purposes of the said section determination, from a predetermined set of different possible modes of sub-division (e.g. G1-G4, G9), so that a dividing line employed in the selected mode and separating the section containing the calculated location from an adjacent section of the said corresponding unit area extends at substantially the said predetermined angle to the said predetermined reference direction (X). Apparatus as claimed in claim 14, further including means (41, 42, 44) for determining which first-array point (e.g. A) is the nearest to the said calculated location, the said predetermined image patterns and the said members of the said group of first-array points (Fig. 15) being selected in accordance with the determined nearest first-array point.

Inventors: OKADA YOSHIYUKI, OKADA, YOSHIYUKI
Applicants: FUJITSU LTD, FUJITSU LIMITED
Application year: 1989
Main classification: H04N1
IPC codes: H04N1, G06T3