JPH03216771A - Method and device for rotating picture at optional angle - Google Patents

Abstract

PURPOSE:To rotate a picture at an optical angle and at a high speed by dividing an original picture into blocks having a size of a prescribed picture element respectively and processing these blocks for each row without processing an optional angle of the picture for each picture element. CONSTITUTION:A reference block generating means 1 is provided together with an X axis directional shift means 2, an X axis directional reduction means 3, a Y axis directional magnification means 4, a rotary block production means 5, and a shift means 6. An original picture is divided into blocks of each prescribed size. Then such operations are carried out on these blocks for each row as the shift, reduction, magnification, replacement of rows, 90-degree rotation, etc. Thus a picture can be quickly rotated at an optional angle with use of a memory of a normal structure.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to an image data rotation method and apparatus for rotating image data such as characters and figures by arbitrary angles.

BACKGROUND OF THE INVENTION Conventionally, many techniques have been disclosed for rotating an image by 90 degrees, but the following method has been used for rotating an image by an arbitrary angle.

SX one pixel of the source image (original image) with X and Y coordinates
Expressed as ISY, the rotation angle is a, and the corresponding X and Y coordinates of the rotated destination image (target image) are Dx and DY, then DxfDY is DX = SXCOS a - Sy S IN aD
It was calculated using the formula: y ``'' Sy S IN a 10 Sy COS a, and was sequentially written bit by bit in the corresponding position of the destination image.

Problems to be Solved by the Invention However, according to the above method, it is necessary to perform four multiplications and two additions per pixel, and to sequentially write bits at corresponding positions in the destination image. Therefore, as the size of the rotated image increases, the amount of calculation increases in proportion to the square of the size, resulting in a problem that the calculation time becomes longer.

The present invention was made in view of the above-mentioned problems, and instead of processing arbitrary corners of the image for each pixel, the present invention divides the original image into blocks of a predetermined size and divides the blocks into rows. An object of the present invention is to provide a method and apparatus for rotating an image at an arbitrary angle, which enables high-speed processing.

Means for solving the problem In order to achieve the above objective, the original image is divided into blocks of a predetermined size of pixels, and operations such as shift, reduction, enlargement, 90 degree rotation, rotation, etc. are performed on the blocks. The image rotation method of the present invention may be performed in units of rows of the constituent matrices, and the image rotation method of the present invention rotates the original image by an arbitrary angle θ with respect to the reference point on the reference coordinate axis to create the target image. Representing the image as a collection of reference blocks consisting of N×N pixels and consisting of squares with one side parallel to an axis rotated by −θ with respect to the reference coordinate axis, and one of the vertices of each reference block being a rotation apex, A rotation block is created by rotating each of the reference blocks by θ around this point, and the amount of movement in the reference coordinate axis direction that occurs when the rotation apex of this rotation block is rotated by θ around the reference point is △
The target image is obtained by moving the rotating block in parallel in the direction of the reference coordinate axes by ΔY and in the direction perpendicular to the reference coordinate axes, respectively, with the amount of movement in the direction perpendicular to the reference coordinate axes being ΔY. It is something. Also,
When creating the rotation block from the reference block, an axis passing through the rotation apex and parallel to the reference coordinate axis is defined as Y.
The coordinates of the X-axis and Y-axis of the elements constituting the reference block are (
x, y), shift the X coordinate of the element in the X-axis direction so that it becomes x - y * tan θ, further multiply it by cos θ in the X-axis direction to make x cos θ - y * sin θ, and then change the y-coordinate to the Y-axis. Multiply 1/cosθ in the direction y/c+
)sθ as (x cosθ−y * sinθe y/co
sθ) coordinate so that the reference block is the same as the length of the rotating block in the X-axis and Y-axis directions, and
It is formed into a parallelogram with one side protruding from the rotating block in the axial direction in a triangular shape and the other concave, and in the part that protrudes from the triangular shape, reading is performed for each row bit row parallel to the X axis, and the protruding triangular part The readout row pit arrangement and the corresponding row bit arrangement of the recessed triangular part are logically ORed so that the row bit arrangement overlaps the recessed triangular part, and N rows by N columns that match the shape of the rotating block are obtained. Find the transposed matrix of this N-row by N-column matrix, and for each row of this transposed matrix, if the bits of the part protruding from the triangle are arranged from the left end of the row to the right end, calculate the arrangement. It is preferable that a rotated image is obtained by performing left rotation by the number of protruding bits, a transposed matrix of this rotated image is calculated, and this transposed matrix is used as the rotation block. To obtain the transposed matrix, the target matrix is N rows x N columns, and the number of conversion modes M for this matrix is M = (1og2 N) (where [ ] is when the internal value is an integer) is the integer,
(If it contains a value below the decimal point, round it up to an integer), number the N rows from 0 to N-1, and set the conversion mode L.
For each (=1 to M), find the A and B rows by A=k*2 to k$2 +2 -1 B=A+2L-1 k=0 to (N/2L) -1, and The row pit arrangement of No. row and B row is A(j
), B(j), −1A′(j), B′(j
) to -1A'(j)=A(j) j=k*2L=kne2L+ 2L-" - 1-1A'
(j) 1B (j-2) j=kne2L+2L-1~k$2L+2L-1B'(
j) = B (j) j=kne2L+2L-"~k$2L+2L-1B'
(j)-4 (j + 2L-1)? =k*2 ~k
! 2 +2 -1k=0~(N/2)-1, and convert A(j) to -1A'(j) by B (j)
It is preferable that a matrix of N rows and N columns is obtained by converting B' (j) into B' (j) and changing L from 1 to M, and this matrix is used as the transposed matrix. Further, when creating the rotation block from the reference block, the reference block is constructed by setting an axis passing through the rotation apex and parallel to the reference coordinate axis as the Y axis, and an axis perpendicular to this and passing through the rotation apex as the X axis. Assuming that the X-axis and Y-axis coordinates of the element are (x, y), shift the X-coordinate of the element in the X-axis direction so that it becomes x-3'*tanθ, and further multiply it by cosθ in the X-axis direction to obtain x cosθ- Let y*sioθ be 1. Next, multiply the y coordinate by 1/c■sθ in the Y-axis direction and calculate y/co.
By moving the reference block to the (X cOsθ-y*sinθ, y/COSθ) coordinate as sθ, the reference block is moved to the same length as the rotating block in the X-axis and Y-axis directions, and below the rotating block in a triangular shape on the Y-axis. When a parallelogram is formed that protrudes out and is concave at the top, and this triangle is formed by n rows of row bits arranged parallel to the X axis, each row of the parallelogram formed by n+N rows is defined as 0 to n + Numbered N-1, n
The triangularly concave range of +1 rows and N columns is 0,
To create a mask matrix where the others are 1, and to find the 0th row, first create the 0'th row to n'th row by ANDing the 0th row to the nth row and the mask matrix, and then ' line, 0th
Mask the part where the bit in the ' row is not O, make this masked part a θ pit, take the logical OR of this masked row and the 0' row, create the 0' modified row, and change the 2' row to the 0' row. Mask the part of the 0' correction line where the bits are not 0, make this masked part 0 bits, perform the logical OR of this masked line and the 0' correction line, create the 1' correction line, and create the 3' correction line. row first
Mask the part of the corrected line where the bit is not O, and make this masked part a 0 pit, and create the 2nd corrected line by ORing this masked line with the 1st corrected line, and do the same. The part where the bit of the (n-2)'th corrected line is not 0 is masked in the n'th line, the masked part is used as a θ pit, and the logic between this masked line and the (n-2)'th corrected line is The sum is taken to create the (n-1)'th modified row, and this (n-1)th
1) It is preferable that the correction row is the 0th row, and the subsequent rows up to N-1 are obtained in the same manner to obtain a matrix of N rows and N columns, and this matrix is used as the rotation block. In addition, the image arbitrary angle rotation device of the present invention generates a reference block that represents the original image as a collection of reference blocks each consisting of a square of N×N pixels, one side of which is parallel to the axis rotated by −θ with respect to the reference coordinate axis. When creating a rotating block by rotating the reference block by θ, one of the vertices of the Moeki reference block serving as the center of rotation is set as the rotation apex, and the axis parallel to the reference coordinate axis is set as Y. The axis that is perpendicular to this axis and passes through the apex is the X axis, and the X axis of the elements constituting the reference block. The coordinates of the Y axis are x, y, and the X coordinate of the element is X - y * tanθ
An X-axis direction shift means for shifting in the X-axis direction so that
X-axis direction reduction means for multiplying the y-coordinate by l/cosθ;
rotational pronk creation means for creating a rotational block by shifting in the Y-axis direction each column of a matrix forming a parallelogram having two sides parallel to the Y-axis direction formed by the output of the axial expansion means; The amount of movement in the direction of the reference coordinate axis and the amount of movement in the direction perpendicular to the reference coordinate axis when the rotation apex of the rotation block is rotated by θ around a reference point on the reference coordinate axis that is a rotation center for rotating the original image. Calculate,
The present invention is characterized by comprising a moving means for moving the rotating block. Further, the rotating block creating means reads triangular portions of the parallelogram that protrude from the rotating block for each row bit arrangement parallel to the X axis, and the protruding triangular portions correspond to the rotating blocks. Matrix generation for generating a matrix that matches the shape of the rotating block by ORing the read row bit arrangement so as to overlap the more concave triangular part and the corresponding row bit arrangement of the concave triangular part. means, a rotation means for performing row rotation for each row of the matrix, and a transposed matrix creation means for creating a transposed matrix of the matrix, the output of the matrix creation means being input to the transposed matrix creation means to create the transposed matrix. output this matrix, and perform left rotation of this matrix by the rotating means for each row in which the bits of the triangularly protruding portion are arranged from the left end to the right end of the row by the number of the arranged protruding bits; It is preferable that the matrix thus created is input to the transposed matrix creating means to output a transposed matrix, and this matrix is used as the value of the rotation block. Furthermore, the transposed matrix creation means is an image data storage means for storing image data, and the number M of conversion modes for image data of N rows by N columns is M=(log2N) (wherein [ ] is an integer value). When, the integer is
a conversion mode calculation means for calculating the conversion mode L (=1 to M) by rounding up the integer when it includes a value below the decimal point; and numbering the N rows as 1 to N-1, According to L, from the N row to the A and B rows A=k 2 ~k$2 +2 -1B=A+2L
-1 k=0~(N/2L) -1 Calculate the row bisotto arrangement of the A and B rows A(
j), B(j);
j), B(j), -1A'(j), B'(
j) as A' (j) = A (j) J=kne2 ~
kne2+2-1-1A'(j)=B(j-2L-")j=k*
2 +2 ~k$2 +2 -1n'(j)-B(j
) J2k2+2 ~kne2 +2 -1B'(j)1A
(j+2L) j=k*2 ~k pieces 2+2 -1k=0~(N/
2L) −1, and A(j), B(j
) into -1A'(j) and B'(j), respectively,
It is preferable to perform this operation by changing L from 1 to M to obtain a matrix of N rows by N columns. In addition, as the rotating block creating means, the parallelogram protrudes below the rotating block in a triangular shape on the Y axis, and is a parallelogram with a concave upper part υ, and this triangle is arranged in n rows of bits parallel to the X axis. If formed by
Each row of the parallelogram formed by n+N rows is 0-n+
A mask matrix numbered N1 and consisting of n1,11 rows and N columns, with the triangular concave range set to 0 and the rest set to 1, and a mask matrix numbered from k rows to k + n rows, consisting of n + 1 rows and N columns. and a masking means for creating the k'th to (k+n)'th rows by ANDing with The mask part is set to 0 bits and the masked line is ORed with the (k-1)'th modified line to create the k'th modified line. Then, the masking means calculates the k'th line to the (k+n)'th line, and the corrected line creating means sequentially calculates the (k+n-1)'th corrected line from the k'th corrected line. )' It is preferable to set the correction row as the k-th row, to obtain the N-1 rows from the θ row, to obtain a matrix of N rows and N columns, and to use this matrix as a rotation block.

Operation First, the basic concept of the present invention will be explained using FIG.

It is assumed that the original image 100 is rotated by an arbitrary angle θ around the reference point 102 on the reference coordinate axis 101 to obtain the target image 103 shown by the broken line.

First, the original image 100 is represented as a collection of reference blocks 104 each having a square shape with one side parallel to an axis obtained by rotating the reference coordinate axis 101 by -θ and consisting of N×N pixels.

Next, each reference block 104 is rotated by θ around one of its vertices as the rotation apex 106, and the rotation block 1
Create 05.

Next, the reference coordinate axis 10 generated when the rotation apex 106 of this rotation block 105 is rotated by θ around the reference point 102
The amount of movement △Y in one direction and the amount of movement △X perpendicular to the reference coordinate axis 101 are calculated, and the rotating block 105 is moved to the reference coordinate axis 1.
△Y in the 01 direction, △X1 in the direction perpendicular to the reference coordinate axis 101
Each moves in parallel.

In this way, the rotation apex 106 moves to the point 107. The aggregate of each of the reference blocks 104 moved in this way constitutes the target image 103 shown by the broken line, so the original image 100
can be rotated by any angle θ. Next, reference block 1
04 to create the rotating block 105 will be explained using FIGS. 2 to 7.

In FIG. 2, all points in the square reference block 104 are
Move (shift) parallel to the axis and move onto the straight line 0+K2.

The rotation angle is θ, and the coordinates of any point in the reference block 104 are
+ If the coordinates after moving yy are X, Y, then X, Y = x-y
*TANθ,y After performing the above transformation, the reference block 104 becomes a parallelogram A shown in FIG.

Next, in FIG. 3, each point in the parallelogram A is compressed in the X-axis direction so that one side m1 of the parallelogram A overlaps one side m2 of the rotating block 105. As a result, the coordinates of each point
Y is X, Y= (x y*'rANθ>COSθ,yx*
cosθ−y−SINθ,y When the above transformation is performed, parallelogram A is transformed into parallelogram B shown in FIG.

Next, in FIG. 4, the parallelogram is enlarged in the Bt-Y axis direction so that the parallelogram BoP point overlaps the Q point. As a result, the coordinates X, Y of each point are: X, Y=x*COSθ−y*SINθ,3'/COSθ
When the above conversion is executed, parallelogram B is transformed into parallelogram C shown in FIG.

In FIG. 5, when all points within the parallelogram C are moved (shifted) in the Y-axis direction so that point b overlaps point C and point f overlaps point g, rotation is completed to the position of rotation block 105.

The coordinates X and Y of each point are:
*TANθ=x*SINθ+y*cosθ, which agrees with the formula explained in the prior art section.

By the way, in the structure of a normal memory, the bit arrangement in the X-axis direction and the row direction can be read and written together in word units, but the bit arrangement in the Y-axis direction, that is, in the column direction, is one bit. Otherwise, reading and writing cannot be performed. If a special memory structure is adopted, it is possible to perform processing in units of multiple bits in the column direction, but the circuit configuration becomes large and complicated. Considering these characteristics of memory, until the parallelogram C shown in Figure 5 is created, it is possible to perform bit processing on a line-by-line basis with ordinary memory because it is a shift, enlargement, and reduction process. The process of shifting parallel to the Y axis and matching with the rotation block 105 is 1
Due to bit processing, quick processing is not possible. Therefore, in the present invention, two methods are used to shift the parallelogram C in parallel to the Y axis using an ordinary memory, as shown below.

First, one method will be explained using FIG. 6.

In FIG. 6, step 1 is the same as the state in FIG. Move triangle abc of parallelogram C to the upper triangle. The movement is done row by row, moving row O to row 0' and row 2 to row 2', triangle abe moves to the top.Step 2
It becomes a square matrix as shown in . Next, in step 3, the transposed matrix of the step 20 matrix was obtained. In step 3, the triangular part is moved to the position shown. Next, perform a left rotation shift so that all the parts of triangle abc are on the right side, and step 4 is obtained. When the transposed matrix of the matrix in step 4 is taken, the state shown in step 5 is obtained. At this time, the position b of the triangular part has moved to the position C in step I as shown in the figure.

A rotation block 105 is obtained in which all the shapes are translated in parallel in the Y-axis direction.

Another method will be explained using FIG.

This method represents a process of converting a parallelogram C matrix into a square matrix, and shows a method of converting k rows from AXX to ABCD rows.

In step 1, mask 1 determined by the size of the triangular portion is applied from row k to the row determined by the size of mask 1 to obtain the right-most matrix. In step 2, mask 2 is set to (k
+1)' Overlap the line to get the rightmost line. k in step 3
' row and the row obtained in step 2 are logically summed to obtain the rightmost row. In step 4, mask 3 is applied to row (k+2)' to obtain the rightmost row, and in step 5, this row is ORed with the row obtained by step 3 to obtain the rightmost row. In step 6, the rightmost row is obtained by covering the (k+3)' row with mask 4, and in step 7, the logical sum of the lever row and the row obtained in step 5 is taken to obtain the desired row ABCD. By performing such processing for each row, the same result as when the parallelogram C is translated in parallel to the Y axis is obtained, and the rotation block 105 is obtained.

EXAMPLE An example of the present invention will be described below with reference to FIGS. 1 to 16.

FIG. 8 is a block diagram showing the configuration of an embodiment of the present invention.

The reference block generation means 1 rotates the original image 100 by -θ with respect to the reference coordinate axis 101 as explained in FIG. ) This is means for generating reference blocks 104, which are constituent elements, so as to be configured as a set of reference blocks 104 each consisting of N×N pixels with one side parallel to the rotated axis. As explained in FIG.
The axis passing through this rotation apex 106 and parallel to the reference coordinate axis 101 is the Y axis, and the axis perpendicular to this and passing through the rotation apex 106 is the X axis. Let the coordinates be xe'l, and as explained in Fig. 2, move the point on the straight line 01-Kl, which is one side of the reference block 104, parallel to the X-axis and move it to the straight line 01-K2 on the Y-axis. , is means for moving all points within the reference block 104 to create a parallelogram A shown in FIG. At this time, the point X+y in the reference block 104 is represented by X, Y, and X, Y=x*TANθ,y.

The X-axis direction reduction means 3 is a means for reducing the parallelogram A shown in FIG. 3 into the parallelogram B shown in FIG. 4 in the X-axis direction.

As a result, the coordinates X, Y after reduction are X. Y=x*COSθ−y*SINθ,y.

A specific example of this reduction in the X-axis direction is shown in FIG.

In Figure 9, the Saone data is the row data before reduction, and if the reduction rate is 2/3, then as shown in the data after reduction processing, 6 bits are obtained by thinning out 3 bits out of the 9 bits of the source data. This becomes row data.

The Y-axis direction enlarging means 4 is a means for enlarging the parallelogram B shown in FIG. 4 in the Y-axis direction to form a parallelogram C shown in FIG. As a result, the coordinates X, Y after enlargement are X, Y = x * COS
θ-y*SINθ, y/COSθ.

FIG. 10 shows a specific example of enlargement processing in the Y-axis direction.

In Figure 10, the source data shows each row before enlargement, and if the enlargement rate is 1.5 times, 4 rows of source data have 0
By adding this line and 2 lines, we have 6 lines of data as shown in the enlarged data.

The rotation block creating means 5 is a parallelogram C shown in FIG.
The rotation block 105 shown in FIG. 1 is created by shifting each column of the matrix forming the .

The moving means 6 includes a rotating block 105 as shown in FIG.
Calculate the amount of movement ΔY in the direction of the reference coordinate axis 101 and the amount of movement ΔX in the direction perpendicular to the reference coordinate axis 101 when the zero-rotation vertex 106 is rotated by θ around the reference point 102, which is the rotation center for rotating the original image 100, This is means for moving each rotation block 105, whereby the original image 100 is rotated by θ and becomes the target image 103. Next, details of the rotating block generating means 5 will be explained.

The present invention discloses two techniques for the rotating block generating means 5. First, the first method is shown in Figures 11 to 13.
This will be explained using figures.

FIG. 11 is a block diagram showing the configuration of the rotation block generation means 5. As shown in FIG. This is means for reading each row bit arrangement and writing the read row bit arrangement in a recessed triangular portion so as to overlap the recessed triangular portion efg from the rotation block 105. Figure 12(a). (b
) represents this specific example, which will be explained below.

(a) The figure shows a matrix representing a parallelogram C. The underlined bits are the bits that make up the protruding triangle.

(a) Perform the following operations on the matrix shown in the figure.

■ Line data of the 8th line with underline added (
Read out the ``Shinichi Mutualtan - 6L Jikuichiwang''. Next, the data row 0 (0001
) and write the logical sum of these two row data in the 0th row.

■ Next, the 9th row data (74 75
The first row data (1o 11 02 03 ) into which this row data should be written is read out, and the logical sum of these two row data is written in the first row.

■ io-th row data (engineering IO
and write the second row data (20 21 12 13 04 05
) is read and the logical sum of these two row data is written in the second row.

The above processing creates the matrix shown in the original figure b).

Next, by the transposed matrix creation means 52, ? When the transposed matrix in figure (b) is created, it becomes as shown in figure (c). Creation of the transposed matrix will be described later using FIG. 13. Next, with respect to the row having the underlined bits in the figure (c), the rotation means 53 performs left rotation until all the underlined bits move to the right side. As a result, the ω diagram is obtained. This process is performed in the following steps.
2 5262). Rotate left by 1 bit, which is the number of underlined bits, and the result is (021
Write 2 22 32 42 52 62ヱυ in the original second line.

■ Third row data (U03 13 23 33 34
4353 63), rotate left by 1 bit, and the result is (03 13 23 33 43 53
63 73) on the original third line.

The same process is repeated from the 4th line to the 6th line.

■ Data on the 7th line (and Heng-77 07 17 27
3747) and left-rotate 3 bits, which is the number of underlined bits, and the result is (07 17 27 37
47 57 67 77) on the 7th line.

Next, when the matrix in figure (d) is again transformed into a transposed matrix by the transposed matrix creation means 52, figure (e) is obtained. The matrix shown in Figure (e) is a matrix obtained by shifting Figure (a) column by column in the Y-axis direction, and represents the rotation block 105.

Next, a method for creating a transposed matrix will be explained using FIG.

Image data storage means 521 stores image data. The conversion mode calculation 1,000 stages 522 calculates the conversion mode number M using the following formula when image data of N rows by N columns is stored in the image data storage 521.

M = (logz N) However, [ ] represents the integer when the internal value is an integer, and represents the integer rounded up when it includes a value below the decimal point. After determining the number of conversion modes M, change the value of conversion mode L from 1 to M.
Output up to.

The row selection means 523 selects the A number from among the N rows, assuming that the row numbers of the N rows×N columns are numbered from 0 to N-1 according to the value of the conversion mode L output from the conversion mode calculation means 522. row and B
The bank line is determined by the following formula.

A=k lines 2 ~k*2 +2 -1B=A+2L -1k=0~(N/2)-1 The bit arrangement of the A-th row and B-th row is A(j), B(j
) (where j=o to N-1).

The image conversion means 524 converts this A(j). Input B(j) and find A'(j) and B'(j) using the following formula.

A'(j) = A (j) L L-1 j=kning2 ~k rate 2+2 -I -1A'(j)=B (j-2) L L
−I L Lj=kne2 +
2 ~k$2 +21 B'(j)=B(j) j=k*2 1,0002 ~k pieces2+2 B'(j)=A (j+2) 1 j=k$2~k$2 +2 -1 k=0 to (N/2)-1 Then, image data A(j) and B(j) are converted to A'(j) and B'(j), respectively. By performing this operation while changing the conversion mode L from 1 to Mt, N
A matrix with rows and N columns is found. This matrix is the transposed matrix.

Note that many techniques for obtaining the transposed matrix have been published, and these methods may also be used.

Next, regarding the second method of the rotating block generating means 5, the fourteenth
This will be explained using FIGS.

FIG. 14 is a block diagram configuring the rotary prong generation means 5. The mask 54 has a portion abc in which the parallelogram C shown in FIG. 5 protrudes below the Y axis in a triangular shape.
is formed of n rows with row bits arranged parallel to the
- Create a mask matrix numbered 1, consisting of n+1 rows and N columns, with triangle abc as 0 and the rest as 1,
The k'-th to (k+n)'-th rows are created by ANDing the (n+1 rows by N columns) from the parallelogram COk row to the k+n row. This will be explained using a specific example shown in FIG. In step 1 in FIG. 15, the leftmost matrix represents the parallelogram C in FIG. The rotation block 105 is a matrix with 8 rows and 8 columns, and the triangular part abc is a matrix with 3 rows and 8 columns. Therefore, the mask matrix has 4 rows and 8 columns as shown in Mask 1 in the center. Then, this mask 1 is transformed into a parallelogram C
Step 1 was applied to the 3rd to 7th rows of
A matrix of 4 rows and 8 columns is obtained. Edit line creation 1000 steps 5
5 masked the (k+1)'th obtained by the 1,000th mask stage 54 by masking the part where the bit of the (k-1)'th modified row (this is equal to the k'th row) is not 0. The part is set to 0 bits, and this masked line and the 1st-1)'
Calculate the k'-th modified row by calculating the logical sum with the modified row, use this to sequentially find (k+n-1)' modified rows, set this (k+n-1)'-th modified row as k row, Find rows from 0 to N-1 to obtain a matrix of N rows and N columns. This matrix becomes the rotation block 105.

Next, this will be explained in detail with reference to FIGS. 15 and 16.

In the stenop 2 shown in FIG. 15, the mask 2 is
)' correction row, it is a mask in which the bits of the 3'th row of the rightmost matrix of Systemop 1 are set to 0 and the others to 1, and the result of masking this to the 4'th row is the matrix shown at the right end. becomes. In step 3, the logical sum of the (3-1)'th corrected line and the line obtained in step 2 is calculated, and the obtained line is the 3'th corrected line. In step 4, the 3'
The 5'th line is masked with mask 3, which sets the non-0 bits of the corrected line to 01 and the others to 1, and the resulting line is ORed with the 3'th corrected line in step 5 to obtain the 4th corrected line. line is obtained. Then, in step 6, the 6'th line is masked with mask 4, which sets the part where the bit of the 4'th modified line is not 0 to 01, and the other bits are set to 1, and the line obtained by this is logically used as the 4'th modified line in step 7. By adding the sum, the 5'th modified row is obtained.

Let this 5'th modified line be the third line shown in step 1. By performing such operations up to the 0-N-1 rows in step 1, the 8 rows x 8 columns matrix shown in step 8 is obtained.
This matrix is the rotation block 105.

As a criterion for determining whether to use the first method or the second method for the rotation block generation stage 5, if the number of bits rotated at one time is small or the rotation angle θ is small, the second method is used. method can be executed faster, and in other cases the first method
It is faster to use method b.

Effects of the Invention As is clear from the above explanation, the present invention divides an original image into blocks of a predetermined size, and performs operations such as shifting, reducing, enlarging, swapping lines, rotating 90 degrees, rotating, etc. on a line-by-line basis for each block. By performing this operation, it is possible to quickly rotate an image to any angle using a memory with a normal structure.

[Brief explanation of drawings]

FIG. 1 is a diagram showing the principle of the present invention, FIG. 2 is an explanatory diagram of the X-axis direction shifting means, and FIG. 3 is an explanatory diagram of the X-axis direction reduction means,
Fig. 4 is an explanatory diagram of the Y-axis direction enlarging means, Fig. 5 is a diagram showing the results of processing by the means shown in Figs. 2 to 4, and Fig. 6 is a square by shifting the parallelogram in the Y-axis direction. FIG. 7 is a diagram showing the second method of shifting a parallelogram in the Y-axis direction to make it a square. FIG. 8 is a block diagram showing the configuration of an embodiment of the present invention. 9 is a diagram showing a specific example of reduction in the X-axis direction by the X-axis direction reduction means, FIG. 12 is a block diagram showing an example of the operation of the device shown in FIG. 11; FIG. 13 is a block diagram showing details of the transposed matrix creating means in FIG. 11; FIG. 14 is a block diagram showing a second device of the rotating block generating means, and FIGS. 15 and 16 are diagrams showing an example of the operation of the device shown in FIG. 14. DESCRIPTION OF SYMBOLS 1... Reference block generation means, 2... X-axis direction shift means, 3... X-axis direction reduction means, 4... Y-axis direction enlargement means, 5... Rotation block creation means, 51.・・・
Matrix generation means, 52...Transposed matrix generation means, 521.
...Image data storage means, 522.1.Conversion mode calculation means, 523.. Row selection means, 524.. Image conversion means, 553.. Rotating means, 54.. Masking means, 55.. Correction line creation means, 6...Movement means.

Claims (8)

[Claims] (1) When creating a target image by rotating the original image by an arbitrary angle θ with respect to the reference point on the reference coordinate axis, the original image is rotated by -θ with respect to the reference coordinate axis, which is made up of N×N pixels.
It is represented as a collection of reference blocks consisting of squares with parallel sides, one of the vertices of each reference block is set as a rotation apex, each reference block is rotated by θ around this apex to create a rotation block, and this rotation The amount of movement in the direction of the reference coordinate axis that occurs when the rotation apex of the block is rotated by θ around the reference point is ΔY, the amount of movement in the direction perpendicular to the reference coordinate axis is ΔY, and the rotating block is rotated by ΔY in the direction of the reference coordinate axis. , an arbitrary angle rotation method for an image, characterized in that a target image is obtained by performing parallel translation by ΔX in a direction perpendicular to the reference coordinate axis. (2) When creating the rotation block from the reference block, the axis passing through the rotation apex and parallel to the reference coordinate axis is the Y axis, and the axis perpendicular to this and passing through the rotation apex is the X axis, and the reference block is constructed. The coordinates of the X-axis and Y-axis of the element are (x, y), and the x-coordinate of the element is shifted in the X-axis direction so that it becomes x-y*tanθ, and then multiplied by cosθ in the X-axis direction to obtain xcosθ-y. *sin θ, and then multiply the y coordinate by 1/cos θ in the Y-axis direction to y/cos θ and move the reference block to the (xcos θ - y*sin θ, y/cos θ) coordinate, thereby changing the reference block to the X axis of the rotating block, It is formed into a parallelogram with one side protruding from the rotary block and the other side being concave in a triangular shape in the Y-axis direction and having the same length in the Y-axis direction, and the row bits parallel to the X-axis are formed in the triangular protruding part. Each row is read out, and the read row bit array is logically ORed with the row bit array corresponding to the concave triangular part so that the protruding triangular part overlaps the concave triangular part. A matrix of N rows and N columns that matches the shape is obtained, and the transposed matrix of this N rows and N columns is calculated, and for each row of this transposed matrix, the bits protruding from the triangular shape are shifted from the left end of the row to the right end. For rows lined up facing each other, left rotation is performed by the number of protruding bits in the line to obtain a rotated image, a transposed matrix of this rotated image is calculated, and this transposed matrix is used as the rotation block. 2. The method of rotating an image at an arbitrary angle according to claim 1. (3) When calculating the transposed matrix, the target matrix is N rows x N columns, and the number of conversion modes M for this matrix is M = [log_2N] (where [ ] is an integer when the internal value is an integer) is rounded up to an integer when it includes a value below the decimal point), numbered the N rows from 0 to N-1, and set the conversion mode L (
=1~M), row A and row B, A=k*2^L~k*2^L+2^L^-^1-1B=
A+2^L^-^1 k=0~(N/2^L)-1, and the row bit arrangement of the A and B rows is A(j
), B(j), and A′(j), B′(j) as A′(
j)=A(j) j=k*2^L~k*2^L+2^L^-^1-1A'
(j)=B(j-2^L^-^1) j=k*2^L+2^L^-^1~k*2^L+2^L
-1B'(j)=B(j) j=k*2^L+2^L^-^1~k*2^L+2^L
-1B'(j)=A(j+2^L^-^1) j=k*2^L~k*2^L+2^L^-^1-1k=
0~(N/2^L)-1, and convert A(j) to A'(j) and B(j) to B'
(j) and changing L from 1 to M to obtain a matrix of N rows and N columns, and use this matrix as the transposed matrix. Method. (4) When creating the rotation block from the reference block, an axis passing through the rotation apex and parallel to the reference coordinate axis is the Y axis, and an axis perpendicular to this and passing through the rotation apex is the X axis, and the reference block is constructed. The coordinates of the X-axis and Y-axis of the element are (x, y), and the x-coordinate of the element is shifted in the X-axis direction so that it becomes x-y*tanθ, and then multiplied by cosθ in the X-axis direction to obtain xcosθ-y. *sin θ, and then multiply the y coordinate by 1/cos θ in the Y-axis direction to y/cos θ and move the reference block to the (xcos θ - y*sin θ, y/cos θ) coordinate, thereby changing the reference block to the X axis of the rotating block, The length is the same as the length in the Y-axis direction, and it protrudes below the Y-axis in a triangular shape from the rotating block, forming a parallelogram with a concave upper part, and this triangle is formed by n rows of row bits arranged parallel to the X-axis. In this case, each row of the parallelogram formed by n+N rows is numbered 0 to n+N-1, and n+1 rows×
Create a mask matrix consisting of N columns with the triangular concave range set to 0 and the rest set to 1, and to find the 0th row, first calculate the 0th row by logical product of the 0th to nth rows and the mask matrix. Create 0'th line to n'th line, mask the part where the bit of 0'th line is not 0 in the 1'th line, set this masked part to 0 bit, and set this masked line and 0'th line. The 0'th modified row is created by taking the logical OR of the 0'th modified row, the 2'th row is used to mask the part where the bits of the 0'th modified row are not 0, this masked part is set to 0 bits, and this masked row and the 0'th modified row are The 1st corrected line is created by performing a logical OR with the corrected line, and the 3rd line is used to mask the part where the bits of the 1st corrected line are not 0, making this masked part 0 bits, and this masked line and The 2nd correction line is created by performing a logical OR with the 1st correction line, and the nth correction line is created in the same manner.
Mask the non-zero bits of the (n-2)'th modified row in the 'row', set this masked part to 0 bits, and perform the logical sum of this masked row and the (n-2)'th modified row. Create the (n-1)'th corrected line, set this (n-1)'th corrected line as the 0th line, and do the same to find up to the N-1th line to get N
2. The method of rotating an image at an arbitrary angle according to claim 1, wherein a matrix of rows and N columns is determined and this matrix is used as the rotation block. (5) a reference block generating means for representing an original image as a collection of reference blocks consisting of a square of N×N pixels with one side parallel to an axis rotated by -θ with respect to a reference coordinate axis; When creating a rotating block,
The reference block is configured such that one of the apexes of the reference block serving as the center of rotation is a rotation apex, an axis passing through this rotation apex and parallel to the reference coordinate axis is the Y axis, and an axis perpendicular thereto and passing through the apex is the X axis. The coordinates of the X-axis and Y-axis of the element to be x,
y, and an X-axis direction shifting means for shifting the x-coordinate of the element in the X-axis direction so that
X that multiplies the output of the axial shift means by cosθ in the X-axis direction
It has an axial reduction means, a Y-axis enlargement means for multiplying the y-coordinate by 1/cosθ, and two sides parallel to the Y-axis direction formed by the outputs of the x-axis reduction means and the Y-axis enlargement means. rotation block creation means for creating a rotation block by shifting each column of a matrix forming a parallelogram in the Y-axis direction; and the reference, which makes the rotation apex of the rotation block a rotation center for rotating the original image. The rotary block is characterized by comprising a moving unit that calculates the amount of movement in the direction of the reference coordinate axis and the amount of movement in the direction perpendicular to the reference coordinate axis when rotating by θ around a reference point on the coordinate axes, and moves the rotating block. An arbitrary angle rotation device for images. (6) The rotation block creation means reads triangular portions of the parallelogram that protrude from the rotation block for each row bit arrangement parallel to the X axis, and the protruding triangular portions are rotated accordingly. This read row bit arrangement so as to overlap the triangular part concave from the block,
matrix generating means for generating a matrix matching the shape of the rotation block by performing a logical OR with the corresponding row bit arrangement of the concave triangular part; a rotating means for rotating each row of the matrix; and a transposed matrix creating means for creating a transposed matrix, the output of the matrix generating means is input to the transposed matrix creating means to output a transposed matrix, and this matrix is protruded into the triangular shape for each row by the rotating means. For rows in which the bits of the part are arranged from the left end to the right end of the row, left rotation is performed by the number of bits that are arranged outside the row, and the matrix thus created is input to the transposed matrix creation means to generate a transposed matrix. 6. The apparatus for rotating an image at an arbitrary angle according to claim 5, wherein the rotation block is outputted and this matrix is used as the value of the rotation block. (7) The transposed matrix creation means stores the image data, and the number of conversion modes M for image data in N rows and N columns is set to M=[log_2N] (wherein [ ] is an integer) a conversion mode calculating means for calculating the integer by rounding up the integer when it includes a value below the decimal point and outputting the conversion mode L (=1 to M), and converting the N rows to 1 to N-1. A=k*2^L~k*2^L+2^L^-^1-1B=
A+2^L^-^1 k=0~(N/2^L)-1 is calculated, and the row bit arrangement A(
j), a row selection means for selecting B(j), and said A(j)
, B(j), and convert A'(j) and B'(j) to A'(
j)=A(j) j=k*2^L~k*2^L+2^L^-^1-1A'
(j)=B(j-2^L^-^1) j=k*2^L+2^L^-^1~k*2^L+2^L
-1B'(j)=B(j) j=k*2^L+2^L^-^1k*2^L+2^L-
1B'(j)=A(j+2^L^-^1) j=k*2^L~k*2^L+2^L^-^1-1k=
0~(N/2^L)-1, A(j), B(j) of the image data
to A'(j) and B'(j), respectively, and calculates a matrix of N rows by N columns by performing this operation by changing L from 1 to M. An arbitrary angle rotation device for images according to claim 6. (8) As the rotating block creating means, the parallelogram is a parallelogram that protrudes below the Y axis in a triangular shape from the rotating block and has a concave upper part, and this triangle is arranged in n rows of bits parallel to the X axis. When the parallelogram is formed by n+N rows, each row of the parallelogram is numbered 0 to n+N-1, and the triangularly concave range consisting of n+1 rows and N columns is numbered 0, and the others are numbered 1. By ANDing the mask matrix and the n+1 rows by N columns from row k to k+n, the
+n)' line, and (k+1)'th line, masking the part where the bit of the (k-1)'th modified line is not 0, making this masked part 0 bit, and masking the (k+1)'th line with the masked line. a corrected line creating means for creating a k'th corrected line by taking a logical sum with the (k-1)'th corrected line, and in obtaining the kth line, the masking means )
' line is obtained, and the corrected line creating means sequentially calculates the (k+n-1)' corrected line from the k'th corrected line.
-1)' The image according to claim 5, wherein the correction row is the k-th row, and the rows from 0 to N-1 are obtained to obtain a matrix of N rows and N columns, and this matrix is used as a rotation block. Arbitrary angle rotation device.