Method and apparatus for image rotation

Abstract: An image rotation method and an image rotation processing apparatus in an image processing apparatus are disclosed. The image rotation method obtains the coordinates (x',y') of a second memory (6) where the rotated image will be recorded, by sequentially scanning a first memory (5) where the M× N original image is recorded and adding the increments of x and y corresponding to a rotation angle ϑ repeatedly, and transmits the image element data of the coordinates (x,y) of the first memory (5) to the coordinates (x',y') of the second memory (6) with one-to-one correspondence, thereby obtaining the rotated image through the rotation angle ϑ from the original image. Thus, the present invention can obtain the rotated image using only addition operations and without any multiplication operations, so that high-speed operation is possible and an image can be rotated through a specified angle ϑ through software in common computer graphic systems having no floating point multiplier.

Description: The present invention relates to an image processing method and apparatus, and more particularly to an image rotation method and an image rotation processing apparatus which can do high-speed real-time processing. Recently, introduced image processing system using a computer carries out image processing functions such as reduction or enlargement of an image, rotation, etc. Since the image processing needs to process a great deal information at a high speed, a high-priced, special operation processing circuit is provided pertaining to each field. Accordingly, in a general personal computer which is not provided with the special operation processing circuit, image processing such as reduction, enlargement, rotation, etc. depends on software, so that the processing speed is slow and the real-time processing is difficult. For example, when the image rotation method displays an image on an X-Y plane, and the coordinates of the present position of the image element are denoted (x,y), the coordinates of the resulting position of the image element after rotation through a specified angle  are denoted (x',y'). These post-rotational image element coordinates (x',y') are easily obtained according to image transformation relations including the following matrix relations. The matrix relations are as follows. From the above matrix relations (1), the coordinate of the X-axis (hereon denoted x') and the coordinate of the Y-axis (hereon denoted y') of the image element coordinates (x', y') after rotational transformation are obtained. easily. Here, if the sine value (sin ) and the cosine value (cos ) of the rotational displacement resulting from rotation through the stated specified angle  are denoted as first and second rotational displacement data (m, n) respectively, the relations (2) may be changed to the following relations (3). Therefore, if the X-axis point (hereon x) and the Y-axis point (hereon y) of the coordinates of the image element (x,y) before rotation are known, the coordinates (x',y') of the new position can be obtained by four multiplication operations, based on the relations. Thus, since the conventional method requires the four multiplication operations when the image rotates, a floating point multiplier is needed for the image rotation processing hardware. The image processing system of a general personal computer without such hardware processes the multiplication through software, but requires such a long time to do the four multiplication operations of the rotation, that real-time processing is difficult. A method of image rotation is described in an article "Hardware for image rotation by twice skew transformations" in the IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-35, No. 4, April 1987, at pages 527 to 531. This describes a method of image rotation through an angle  in which the matrix relations described above are used to calculate the rotated x and y coordinates corresponding to a base pixel in the image before rotation and the rotated x and y coordinates of the pixels in the same row of the image before rotation as the base pixel are calculated by adding cos and sin to the rotated x and y coordinates of the base pixel respectively. The rotated x and y coordinates of a base pixel must be separately calculated for each row of the image before rotation. It is an object of the present invention to provide an image rotation method which can do a high-speed, real-time processing, to solve the conventional problem. It is another object of the present invention to provide an image rotation processing apparatus which simplifies circuit constitution and reduces cost. According to a first aspect of the present invention, there is provided an image rotation method for rotating an image, which determines coordinates x',y' for a second memory for recording a rotated image from coordinates x,y of an M X N image in a first memory and transmits the data of the image elements related to the determined coordinates from said first memory to said second memory, to obtain the image rotated from the M X N image stored in the first memory by a specified angle  using the reference point x=0, y=0 as a rotational axis, said method being characterised by comprising the steps of: (a) setting the value x=0 of said first memory , setting nominal values a=0 and b=0 and setting the cosine value of cos = n, the sine value sin =m and the negative sine value -sin =-m; (b) incrementing the value of x of said first memory by one; adding the initial values n,m to accumulated sums a,b respectively; setting the value y=0 of said first memory; and storing the values a,b as coordinates x',y' respectively, related to coordinates x,y of said first memory, in said second memory; (c) incrementing the value of y of said first memory; adding the values -m, n to the previously stored coordinates x',y' respectively; and storing data of the image elements related to coordinates x,y of said first memory, in said second memory at the new coordinates x', y'; (d) repeating said step c a further N-1 times; and (e) repeating said steps b, c and d a further M-1 times. According to a second aspect of the present invention, there is provided an image rotation processing apparatus which rotates an image of the magnitude M X N recorded in a first memory according to the given rotation angle  and the image magnitude M X N, by generating the coordinates x',y' of said second memory corresponding to the coordinates x,y of said first memory in order to record the image in the second memory, said apparatus comprising: an address generator for generating the coordinates x,y of said first memory corresponding to said given image magnitude M X N by the linear sequential scanning method wherein said address generator scans each line of said given image such that each line has a single x coordinate and a sequentially increasing y coordinate and such that each subsequently scanned line has a sequentially increasing x coordinate; and an address converting circuit, for generating the coordinates x',y' of the second memory corresponding to the coordinates x,y of the first memory, characterised in that said address converting circuit comprises: means for setting first, second, third and fourth accumulator means to zero; a first accumulator means, for cumulatively adding the cosine value cos=n, each time that said value x has been incremented by one, for determining a first sum a and for transmitting the value of said first sum a each time that said value x has been incremented by one, a second accumulator means, for cumulatively adding the sine value sin=m, each time that said x value has been incremented by one, for determining a second sum b and for transmitting the value of said second sum b each time that said value x has been incremented by one, a third accumulator means, operable to be initialised to the value of said first sum a from said first accumulator means whenever it is transmitted, for cumulatively adding the negative sine value -sin=-m, each time that said value y has been incremented by one, to said received value of said first sum a for determining the value of the coordinate x' and a fourth accumulator means, operable to be initialised to the value of said second sum b from said second accumulator means whenever it is transmitted, for cumulatively adding the cosine value cos=n, each time that said value y has been incremented by one, to said received value of said second sum b for determining the value of the coordinate y', and means for transmitting the image data stored in said first memory at coordinates x, y to coordinates x', y', generated by said third and fourth accumulator means, of said second memory each time that said value y has been incremented. In the context of the present invention, the x,y notation and the principle of rows and columns of the array are purely arbitrary and in each case may be transposed. Similarly, any reference to incrementing from 1 to M and/or 1 to N may equally be regarded as decreasing from M to 1 and/or N to 1. In such case(s) the relevant accumulator function by sequential subtraction rather than by incrementing. The above objects and other advantages of the present invention will become more apparent by describing the preferred embodiment of the present invention with reference to the attached drawings, in which: FIG. 1 is a block diagram schematically showing the constitution of the image processing system using a computer; FIG.2 is a flowchart showing the conventional rotation method; FIG.3 is a view for visualizing the image rotation method according to the present invention; FIG.4 is a flowchart showing a preferred embodiment of the image rotation method according to the present invention; and FIG.5 is a block diagram of a preferred embodiment of the image rotation processing apparatus according to the present invention. The present invention will be described in more detail with reference to the accompanying drawings. Referring to FIG.1, the image processing system comprises a keyboard 1, an image input device 2, a processor 3, an address circuit 4, a first memory 5, a second memory 6, data I/O registers 7 and 8, a display controlling circuit 9, and a monitor 10. The keyboard 1 supplies data such as the image processing mode designation, the rotation angle  in an image rotation mode, the image magnitude M× N, etc., to the processor 3. The image input device 2 which receives the original image comprises an image scanner 2a and an interface circuit 2b. The processor 3 controls the system and processes the image data according to the given image processing program. The address circuit 4 comprises an address generator 4a and an address converting circuit 4b. The first memory 5 records an original image received from the image input device 2, and the second memory 6 records an image processed from the original image in the first memory 5. The data I/O registers 7 and 8 latch the data when the data, which is recorded or read in the first and second memories 5 and 6, is input or output. The display controlling circuit 9 receives the image data supplied from the processor 3, the first and second memories 5 and 6 and control the display on the monitor 10. In such an image processing system, the conventional image rotation method is described with reference to FIG.2 as follows. An image is composed of M image element rows and N image element columns, thus forming an entire image of M× N image elements. In the first portion of the procedure steps 101 to 103, the x value is initialized at zero and incremented by one, and when x becomes greater than the above number of horizontal image element rows M, the above rotational transformation ends. Conversely, until the above x value is not greater, the procedure proceeds to the next step 104. In the second portion of the following steps 104 to 106, the y value is cleared to zero and incremented by one, and when y becomes greater than the above number of vertical image element columns N, the procedure loops back to the above step 102 where the x value is incremented by one. Conversely, until the above y value is not greater, the procedure proceeds to the next step 107. Next, in step 107, the image element coordinates x' and y' of the new position are computed based on the above relations (3), and in step 108, the pre-rotational image element coordinates (x,y) are stored in post-rotational image element coordinates (x',y'). Subsequently, the procedure loops back to the above step 105 where the y value is incremented by one. Therefore, the pre-rotational image element coordinates (x,y) are transformed into post-rotational image element coordinates (x',y') through a specified angle . Here, the arithmetic process in the above step 107 requires four multiplication operations as shown in the above relations (3) for every increment of the x and y values. Accordingly, the above computer graphic system requires 4× M× N multiplication operations to rotate an image composed of M× N image elements, so that if M=2500 and N=2500, 25 million multiplication operations are carried out. If, for example, 10µs are required for one multiplication process in the above computer graphic system, approximately 250 seconds are required to rotate the image composed of M× N image elements, creating the disadvantage of a greatly decreased processing speed for the rotational transformation of images. Also, in a computer graphic system in which the geometric transformation mechanism which includes a rotational transformation means is realized through hardware, the system is designed so as to only rotate through certain angles such as 90° or 180° , so there exists the disadvantage of having to alter the hardware itself in order to rotate images through specific angles desired by the user. Furthermore, in the above computer graphic system for realizing rotational transformation method, special processors suited to such graphic processing are required, and there is the disadvantage that geometric transformations cannot be executed on widely used PCs (personal computers). The image rotation method of the present invention to improve the conventional image rotation method is described with reference to FIG.3. Referring to FIG.3, if the coordinates (x,y) of the first memory 5 are rotated through the relation angle  , the coordinates are rotated to the coordinates (X,Y). The x-axis coordinate values, (1,0), (2,0), (3,0) and (4,0), correspond to (cos ,sin ), (2cos ,2sin ), (3cos , 3sin ) and (4cos ,4sin ) of the X-axis. Similarly, the y-axis coordinate values, (0,1), (0,2), (0,3), and (0,4) correspond to (-sin , cos ), (-2sin , 2cos ), (-3sin , 3cos ), (-4sin ,4cos ) of the Y-axis. That is, if sin is m and cos is n, the coordinate values on the X-axis (n,m), (n+n,m+m), (n+2n,m+2m) and (n+3n,m+3m) and the coordinate values on the Y-axis are denoted as (-m,n), (-m-m,n+n), (-m-2m,n+2n), (-m-3m,n+3n). Accordingly, if X sequentially varies from 1 to M, all of the X-Y coordinates can be obtained by accumulating the initial value to the initial value (n,m) and if Y sequentially varies from 1 to N, all of points on the X-Y plane can be obtained by accumulating the initial value to the initial value (-m,n). With this principle, the M× N image is sequentially scanned, and the increments of X and Y corresponding to the rotation angle  are sequentially summed, so that the coordinates (x',y') of the rotated image can be obtained using only addition operations and without any multiplication. Accordingly, in an image transformation method and the apparatus thereof according to this invention, new relations which incorporate addition and not multiplication operations, and which form the rotational transformation relations on which the process for computing the new rotationally transformed coordinates (x',y') is based, are obtained as follows. The aforesaid relations (2) and (3) are derived from the relation (1) where the values of x and y are incremented from 1 through M and from 1 through N, respectively, and if, from relations (3), nx is said to equal ax and mx is said to equal bx, when x is at its initial value "1", then the following is true. a 1 = n b 1 = m When x is incremented to its next value "2", then a 2 = n(1+1) = n + n = a 1 + n b 2 = m(1+1) = m + m = b 1 + m Therefore, considering the case where the value of x is incremented by ones, the following relation (4) may be obtained from the above derivations. Also, considering the case where the value of y is incremented while the value of x remains constant, if the values of coordinates (x',y') of a rotational transformation through a specified angle  of an image element in an arbitrary position with coordinates (x,y) prior to the rotation have been computed, the rotated coordinates (x',y') of the original coordinates (x,y) with an incremented value of y which is adjacent to the above pre-rotational coordinates (x,y) may be obtained from the following relations (5). Therefore, rotation variables a and b are computed when x is incremented by one, and the values of x' and y' of the rotated coordinates (x',y') are obtained through addition operations as y is incremented by one. A flowchart of a preferred embodiment of an image rotation method according to this invention including a process of addition operations based on the above relations (4) and (5) is described in detail with reference to FIG.4. In the first procedure from step 201 to step 203, the value of x and the rotation variables a and b are cleared to zero, and the value of x is incremented by one, and in the comparison of this incremented value of x with the number of horizontal image element rows M, if the value of x is larger, the image transformation ends. Conversely, if the value of x is not greater than M, the procedure proceeds to step 204 which performs the arithmetic operations of the above relations (4). In step 205, the value of y is cleared to zero and the rotation variables a and b computed in the above step 204 are stored in x' and y' of the rotated coordinates (x', y'), respectively. In step 206, the y value is incremented by one, and in step 207, the above incremented y value is compared with the number of vertical image element column N, and if the value of y is larger, the procedure loops back to the above step 202 where the value of x is incremented by one. Conversely, if the value of y is not greater than N, the procedure proceeds to the next step 208, thus ending the second procedure. In step 208, the values x' and y' of the rotated coordinates (x', y') are computed by carrying out the addition operations corresponding to the above relations (5), and in step 209, the values of the coordinates (x, y) are stored in the coordinates (x', y') after being rotationally transformed, and the procedure loops back to the above step 206, thus ending the third procedure. By carrying out the above procedures, an image composed of M× N image elements is rotationally transformed through a specified angle . An image transformation method and the apparatus thereof according to this invention employs a process including addition operations instead of conventional multiplication operations, and thus 2× M× N addition operations are required in rotating an image composed of M× N image elements through a specified angle , and for example, if M=2500 and N=2500, approximately 12,500,000 addition operations are required. Therefore, since a computer system's addition operations require less time relative to multiplication operations, and supposing 50ns are required for one addition operation, rotating the entire image by a specified angle  would require approximately 1 second. Thus, an image rotation according to this invention requires only one second, compared to 250 seconds for conventional image rotations, and because the speed of image rotation is increased dramatically, the process can be executed on widely used processors. The above is a description of an image rotational transformation realized through software and may be applied to an image processing system having the constitution such as the one shown in FIG.1. FIG.5 is a block diagram showing an embodiment of the image rotation processing apparatus according to the present invention. This image rotation processing apparatus corresponds to the address converting circuit 4b of the address circuit shown in FIG.1 and comprises first to fourth accumulators A1 to A4 . The first accumulator circuit A1 accumulates the cosine value (cos =n) corresponding to the rotation angle  of the unit value (1,0) of the value x of the first memory 5 whenever the value x is incremented by one. The second accumulator circuit A2 accumulates the sine value (sin =m) corresponding to the rotation angle  of the unit value (1,0) of the value x of the first memory 5 whenever the value x is incremented by one. The third accumulator circuit A3 adds the negative sine value (-sin =-m) corresponding to the rotation angle  of the unit value (0,1) of the value y of the first memory 5 into the output value of the first accumulator circuit A1, and accumulates the negative sine value (-m) into the added value whenever the value y is incremented by one, thus determining the accumulated value as the x' coordinate value of the second memory 6. The fourth accumulator circuit A4 receives the output value of the second accumulator circuit A2 and determines the y' coordinate value of the second memory 6 by the identical operation of the third accumulator circuit A3. Each of first and second accumulator circuits A1 and A2 respectively comprises adders 40 and 41 for summing the cosine value n or the sine value m and the accumulated value, registers 42 and 43 for recording the added results of the adders 40 and 41 and looping back the accumulated result to the adders 40 and 41 in response to control signals S1 and S2, whenever the value x is incremented by one, and transmitting gates 44 and 45 for transmitting the added results of the adders 40 and 41 to the output value in response to control signals S3 and S4, whenever the value x is incremented by one. Each of third and fourth accumulator circuits A3 and A4 respectively comprises adders 46 and 47 for adding the negative sine value (-m) or the sine value (n) into the accumulated value, registers 48 and 49 for being initialized to the output value supplied from the first or second accumulator circuit A1 or A2 whenever the value y is incremented by one, looping back the accumulated value to the adders 46 and 47 in response to control signals S5 and S6, whenever the value y is incremented by one, and recording the added results of the adders 46 and 47, and transmitting gates 50 and 51 for transmitting the added results of the adders 46 and 47 to the x' or y' coordinate value of the second memory in response to control signals S7 and S8, whenever the value y is incremented by one. Thus, without a floating point multiplier, this image rotation processing apparatus can be made using only adders. Accordingly, the constitution of the circuit is simplified and the cost reduced.

Claims: An image rotation method for rotating an image, which determines coordinates x',y' for a second memory (6) for recording a rotated image from coordinates x,y of an M X N image in a first memory (5) and transmits the data of the image elements related to the determined coordinates from said first memory (5) to said second memory (6), to obtain the image rotated from the M X N image stored in the first memory (5) by a specified angle  using the reference point x=0, y=0 as a rotational axis, said method being characterised by comprising the steps of: (a) setting the value x=0 of said first memory (5), setting nominal values a=0 and b=0 and setting the cosine value of cos = n, the sine value sin =m and the negative sine value -sin =-m; (b) incrementing the value of x of said first memory (5) by one; adding the initial values n,m to accumulated sums a,b respectively; setting the value y=0 of said first memory (5); and storing the values a,b as coordinates x',y' respectively, related to coordinates x,y of said first memory (5), in said second memory (6); (c) incrementing the value of y of said first memory (5); adding the values -m, n to the previously stored coordinates x',y' respectively; and storing data of the image elements related to coordinates x,y of said first memory (5), in said second memory (6) at the new coordinates x', y'; (d) repeating said step (c) a further N-1 times; and (e) repeating said steps (b), (c) and (d) a further M-1 times. An image rotation processing apparatus which rotates an image of the magnitude M X N recorded in a first memory (5) according to the given rotation angle  and the image magnitude M X N, by generating the coordinates x',y' of said second memory (6) corresponding to the coordinates x,y of said first memory (5) in order to record the image in the second memory (6), said apparatus comprising: an address generator (4a) for generating the coordinates x,y of said first memory (5) corresponding to said given image magnitude M X N by the linear sequential scanning method wherein said address generator scans each line of said given image such that each line has a single x coordinate and a sequentially increasing y coordinate and such that each subsequently scanned line has a sequentially increasing x coordinate; and an address converting circuit (4b), for generating the coordinates x',y' of the second memory corresponding to the coordinates x,y of the first memory, characterised in that said address converting circuit comprises: means for setting first, second, third and fourth accumulator means to zero; a first accumulator means (A1), for cumulatively adding the cosine value cos=n, each time that said value x has been incremented by one, for determining a first sum a and for transmitting the value of said first sum a each time that said value x has been incremented by one, a second accumulator means (A2), for cumulatively adding the sine value sin =m, each time that said x value has been incremented by one, for determining a second sum b and for transmitting the value of said second sum b each time that said value x has been incremented by one, a third accumulator means (A3), operable to be initialised to the value of said first sum a from said first accumulator means (A1) whenever it is transmitted, for cumulatively adding the negative sine value -sin=-m, each time that said value y has been incremented by one, to said received value of said first sum a for determining the value of the coordinate x', and a fourth accumulator means (A4), operable to be initialised to the value of said second sum b from said second accumulator means (A2) whenever it is transmitted, for cumulatively adding the cosine value cos=n, each time that said value y has been incremented by one, to said received value of said second sum b for determining the value of the coordinate y', and means for transmitting the image data stored in said first memory at coordinates x, y to coordinates x', y', generated by said third and fourth accumulator means, of said second memory each time that said value y has been incremented. An image rotation processing apparatus as claimed in claim 2, wherein each of said first and second accumulator means (A1, A2) comprises: an adder (40 or 41) for adding said cosine value n or said sine value m into the accumulated result value; a register (42 or 43) for recording the added result of said adder (40 or 41) and looping back the accumulated result value of said adder (40 or 41) whenever the value of x is incremented by one; and a transmitting gate (44 or 45) for transmitting the added result of said adder (40 or 41) to the output value thereof whenever the value of x is incremented by one. An image rotation processing apparatus as claimed in claim 2, wherein each of said third and fourth accumulator means (A3, A4) comprises: an adder (46 or 47) for adding said negative sine value -m or cosine value n into the accumulated result value; a register (48 or 49) for being initialized to the output value supplied from said first or second accumulator means (A3 or A4) whenever the value x is incremented by one, recording the added result of said adder whenever the value y is incremented by one, and looping back the accumulated result value into said adder; and a transmitting gate (50 or 51) for transmitting the added result of said adder to the value of the coordinate x' or y' of the second memory (6) whenever the value y is incremented by one.

Inventors: PARK YOU-KEUN, PARK, YOU-KEUN
Applicants: SAMSUNG ELECTRONICS CO LTD, SAMSUNG ELECTRONICS CO. LTD.
Application year: 1991
Main classification: G06T3
IPC codes: G09G5, G06T3, H04N5, G06F3