JP2636225B2 - Image rotation device - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image rotation device that controls a rotation process of image information by a computer.

2. Description of the Related Art In recent years, with an increase in storage capacity, processing for handling image information that is not coded has been increasing. In addition, development of an image processing system with improved resolution of a scanner, a copying machine, and the like, which is fast and has little deterioration is desired. Hereinafter, the conventional image rotation processing will be described with reference to FIG. For simplicity of description, first, the processing is limited to rotation processing of a one-dimensional image.

FIG. 6 is for explaining a method of rotating a one-dimensional image. As shown in FIG. 6, the interval between grid lines defining the x-axis and the y-axis is "1" in both the xy directions. The image exists only on the grid, and the coordinates of the grid points are represented by integers. The straight line L is a straight line that passes through the center of rotation 402 and has an inclination θ. Image _{(A) {a 0, a} 1, ... a 6} is parallel the original image to the _{x-axis, (B) {b 0,} b 1, ..., b 6} is the center of rotation 601, the image When (A) is rotated by the angle θ, the converted positions of the elements (a ₀ , a ₁ ,... A ₇ ) of the image (A) are shown. Also, image (C) {c ₀ , c ₁ ,... C, ₅ }
Is obtained by arranging the position (B) on a lattice point (hereinafter referred to as quantization). The image rotation process is a process of converting the image (A) into the image (C). (The above process of converting the image (A) into the image (C) is a process of performing movement and rotation. Hereinafter, this will be referred to as rotation).

Since the grid spacing is “1”, Holds. If the coordinates of bo are (x _bo , y _bo ) and the coordinates of bi are (x _bi , y _bi ), Becomes Therefore, given the coordinates of bo, the coordinates of the remaining points can be obtained by sequentially adding △ x and △ y. Furthermore, bi (hereinafter referred to as true position)
Let Cj (Cxj, Cyi) be the grid point closest to
By transferring the image to Cj, an image (C) that is the result of rotating the image (A) is obtained. That is, Is performed. (However, [d] represents the largest integer that does not exceed d. The addition of 0.5 in Equations 5 and 6 means that the true position is quantized to the nearest lattice point. As described above, in the rotation processing, the true position is calculated and quantized.

Next, the case where the two-dimensional image is rotated will be described below. FIG. 7 is for explaining the rotation of the two-dimensional image. FIG. 7 (a) is the original image, and FIG. 7 (b) is the image of FIG. 7 (a) rotated by an angle θ. The result image at the time is shown. The true position when rotating the one-dimensional image (11) {A ₀ , A ₁ , A ₂ , A ₃ } constituting the first row of FIG. 7A is (21) {a ₀ , a _1, the a _2, a _3} resulting image, (2
1 ′) {A ₀ ′, A ₁ ′, A ₂ ′, A ₃ ′}. Similarly, images (12) {B ₀ , B ₁ , B ₂ , B ₃ }, (22) {b ₀ , b ₁ , b ₂ ,
b _3}, image _{(22 ') {B 0'} , B 1 ', B 2', B 3 '}, image _{(13) {C 0, C} 1, C 2, C 3}, (23) {c _0, c _1, c _2,
c ₃ ｝ and the image (23 ′) {C ₀ ′, C ₁ ′, C ₂ ′, C ₃ ′} are defined.

The rotation processing of the two-dimensional image can be performed by performing the rotation processing of the one-dimensional image a plurality of times. Hereinafter, the processing procedure will be described.

First, the image (11) is rotated based on the above-described one-dimensional image rotation processing procedure. Next, the image (12) is rotated. In this case, first, the elements in the second row and first column in FIG. 7A are used. And it calculates the true position of the B _0. The procedure is shown below. That is, It is. When the coordinates of ao are (x _ao , _yao ) and the coordinates of _bo ( _xbo , _ybo ) are obtained, Becomes Therefore, given the coordinates of ao, the coordinates of the true position in the first column element of the remaining rows can be obtained by sequentially adding △ x 'and △ y'.
After calculating the true position of bo, the bo is sequentially processed in accordance with the one-dimensional image rotation processing procedure. This flow is shown in FIG.

FIG. 8 is a diagram showing a flow when performing a rotation process of a two-dimensional image.

At 801, initial settings are made.

At 802, the i-th row is rotated.

At 803, it is determined whether all lines have been completed.

At 804, 1 is added to i.

At 805, the true position of the starting point of the next line is calculated.

(This processing is described in Patent Publications 59-229669 and 60-110
No. 080 and the like. FIG. 9 is a diagram showing the result of performing a rotation process using this method. The center of rotation is 0, and the rotation angle is θ. Indicates a true position, and ○ indicates a result of quantization of the true position, that is, a result pixel. (The figure specifically shows four pixels horizontally and five pixels vertically.
The rotation of the original image composed of pixels is shown. However, according to the conventional method, as shown in FIG. 9, two original pixels correspond to one result pixel, or there is no original pixel in the area of the result image. However, there is a problem of image quality deterioration such as that there are lattice points that do not correspond.

Means for Solving the Problems The present invention provides an original image comprising M rows and N columns of pixels located on a grid point which is the intersection of M horizontal grid lines at 1 interval and N vertical grid lines at 1 interval. The image A is divided into M ′ rows and N ′ columns (M ′ = [M / cos θ + 0.5], N ′ = [N cos θ +
0.5], 0 ≦ θ <45 ° (where [α] is the maximum integer not exceeding α), and a pixel number conversion means for converting into an image B composed of pixels, and an image B obtained by the pixel number conversion means Transfer address calculating means for calculating a transfer destination of each pixel to be transferred, and pixel transfer means for transferring each pixel constituting the image B to a position obtained by the transfer address calculating means, wherein the transfer address calculating means Grid point that is the center of rotation included in image A
grid points gi (i) existing at the interval 1 on the same vertical grid line as g1
= 1 to M '), the intersection ej (j = 1 to N') of the straight line li of the slope θ passing through gi and the vertical grid line is defined as the slope-(π / 2-θ) passing through the center g1 of rotation. From the vertical grid line closest to the intersection fi of the straight line F and li on the N ′ vertical grid lines existing at an interval of 1 including the vertical grid line, and the grid point cj closest to ej
Is calculated as the transfer destination of the pixel in the i-th row and the j-th column of the image B, thereby achieving the above object.

Operation According to the present invention, with the above-described configuration, it is possible to eliminate a pixel that is redundantly transferred to one pixel from within the transfer area and a pixel that does not cause transfer, and obtain a rotated image with less deterioration.

Embodiment First, the basic principle of the present invention will be described.

The image rotation processing of the present invention includes a pixel number conversion processing for calculating a vertically enlarged horizontal reduced image corresponding to a rotation angle θ from an original image, and a tilt θ
The pixel transfer process calculates the coordinates of the grid point of the transfer destination along the straight line, and transfers the pixel number converted image to the grid point.

Before beginning the description, [α], which defines some words and symbols, is a symbol representing the largest integer not exceeding α. Elements constituting an image are referred to as pixels, and are represented by ○.
It is assumed that the pixel exists only on the grid point, and the coordinates of the grid point are represented by integers.

The principle of the present invention will be described with reference to FIG. For the sake of simplicity, only a one-dimensional image will be described first. (Hereinafter, the rotation center 0 is on the lattice point, and the rotation angle θ is 0 ≦ θ <45.
゜ shall be satisfied. First, the interval between grid lines is “1” in both the horizontal and vertical directions. The original image is defined as {A} (a ₀ , a ₁ ,..., A ₈ ), and the center of rotation is set to 0.
The result image when rotated only by {C} (c ₀ , c ₁ ,...,
c ₇ ), a straight line passing through the center of rotation 0 and having an inclination of L is denoted by L, and the intersection of the L and the vertical grid line is sequentially determined from the left, e ₀ , e ₁ ,.
and e _7, referred to as vertical intersection _{{E} (e 0, e} 1, ..., e 7) expressed as. (From the above conditions, the coordinates of 0 and e ₀ coincide.) The rotation processing of the present invention is performed as follows.

And Step 1 linear L, the intersection ei (x _i, y _i) of the vertical grid lines are calculated. That is, if eo (x _eo , y _eo ), xi = i + x _eo (11) yi = i tan θ + y _eo (12) (where 0 ≦ i, i is an integer).

Step 2 A process for calculating a grid point Ci ( _xci , _yci ) closest to ei is performed.

(* X _eo and y _eo are both integers). (However, [α] represents the largest integer not exceeding α.) Step 3 A process of converting the number N of pixels of the original image {A} to [N cos θ + 0.5] is performed.

Step 4 The value of the image (hereinafter referred to as a reduced horizontal image) {D} (d ₀ , d ₁ ,..., D ₇ ) converted in the process of Step 3 is calculated by the grid point group {C} (c ₀ , c ₁ ,..., C ₇ ).

 Hereinafter, a specific calculation process will be described.

Between ei (x _ei , y _ei ) and ei + ₁ (x _{e.i + 1} , y _{e.i + 1} ), since the grid line spacing is 1, There is a relationship.

That is, when eo (x _eo , y _eo ) is given, “1” and y
By adding tan θ to the coordinates, the coordinates of the remaining points can be calculated in order. The transfer destination of the reduced horizontal image can be obtained by performing the processing of equations (12) and (13) on the obtained ei. By performing the above processing, a one-dimensional rotated image is obtained.

Next, rotation of the two-dimensional image will be described with reference to FIG. FIG. 3 is a diagram for explaining two-dimensional image rotation according to the present invention. The interval between the grid lines is 1 in both the x and y directions, and 0 is the center of rotation. The point gi is a grid point existing on the same vertical grid line as the center of rotation 0, and g ₁ ,
g ₂ , ..., g ₆ . (However, g ₁ indicates the center 0 and the same point of rotation.) The vertical li is a straight line of slope θ through the grid points gi. The straight line F passes through the intersection point gi and has a slope of − (π / 2
−θ). The intersection of the straight line li and the straight line F is defined as fi. The rotation processing of the two-dimensional image of the present invention is performed as follows.

Step A A process of converting the number M of vertical pixels of the original image into [M / cos θ + 0.5] is performed.

Step B The above-described processing of steps 1 to 4 is performed on the i-th row of the image converted in the processing of step A (hereinafter, referred to as a vertically enlarged image). However, the center of rotation is defined as gi. Furthermore, the coordinates of the first transfer destination grid point (hereinafter, referred to as a transfer start grid point) when performing the processing of step 4 are described.
Is a value obtained by converting the vertical intersection point hi closest to the point fi by the expressions (13) and (14).

By repeating the processing of step B described above, 2
Rotation processing of a two-dimensional image can be performed.

Hereinafter, a method of calculating the transfer start grid point will be described with reference to FIG. FIG. 4 is a diagram for explaining a method of calculating a transfer start grid point.

FIG. 4 is a partially enlarged view of FIG.

Set the transfer start grid point on the i-th row of the vertically enlarged horizontally reduced image to ai (x
_ai , _yai ). The x-coordinate of the point f _i-1 to x _fi-1, the x-coordinate of the point fi and x _fi. Streamed grid line is because it is _{1 x fi -x fi-1 =} cosθ · sinθ ...... (17). When the x-coordinate of the point f ₁ is given, cos [theta] · sin [theta
Are sequentially added, the x coordinate of the point fi can be calculated. That is, x _fi = x ₀ + _(i−1) cos θ · sin θ (18) Next, the x coordinate j of the vertical grid line closest to the point fi
Satisfies j = [x _fi +0.5] (19) From the above, the center of rotation in the i-th row is defined as gi (x _gi , y
_gi ), from formulas (12) and (13), x _ai = j + x _gi ... (20) y _ai = [j tanθ + y _gi ] (21) (where x _gi and y _gi are both integers) There is.)

As described above, the case where the rotation angle θ is 0 ≦ θ <45 ° has been described.
Next, processing in the case of 45 ° ≦ θ <91 ° will be described with reference to FIG. 0 is the center of rotation, the spacing between grid lines is horizontal,
It is 1 both in the vertical direction. A point g _i1 (where i is a positive integer) is a grid point existing on the same horizontal grid line as 0, and is g ₁₁ , g ₂₁ , g ₃₁ , g ₄₁ ,. g ₁₁
Exists on the same grid point as 0. ) The straight line li is a straight line that passes through g _{i1 and} has an inclination θ. Straight F passes through the point g _11,
This is a straight line having a slope θ−π / 2. The score between the straight line li and the straight line F
fi. A point g _1j (where j is an integer) is a straight line l
_At the intersection of ₁ and the horizontal grid point (hereinafter referred to as horizontal intersection),
G ₁₁ , g ₁₂ , g _13, ... From the bottom to the top. The point hi is the point fi
The horizontal intersection closest to is described below.

Step (a) The number of vertical pixels M of the original image is Perform the process of converting to individual.

Step (b) The number of horizontal pixels N of the original image is Perform the process of converting to individual.

Step (c) A horizontal intersection _gij which is an intersection between the straight line li and the horizontal grid line is calculated.

Step (d) The grid point closest to the horizontal intersection calculated in step (c) is calculated.

Step (e) The grid point closest to the point hi calculated in the processing of step (d) is set as the transfer start grid point, and the first grid point of the i-th row of the image is obtained by the processing of steps (a) and (b). Are sequentially transferred to the grid points calculated in step (d).

 Next, a specific calculation process will be described.

Since the grid line interval is 1, the point g _l1 (x _g11 , y _g11 )
When given, other horizontal intersection g _1j on the line l ₁ (x _1j, y
_1j ) is obtained from x _g1j = x _g11 + j cot θ (22) y _g1j = y _g11 + j (23) Further, another point g _i1 (x _gi1 , y _gi1 ) on the same horizontal grid line as the point g ₁₁ is obtained from x _gi1 = x _g11 + i (24) y _gi1 = y _g1l (25) Can be Another horizontal intersection g _ij (x
_gij and y _gij ) are given by x _gij = x _g11 + i + j cot θ (26) y _gijyg11 + j (27) from equations (22) to (25). Next, the coordinate y _fi of y of the point fi is _{y fi = y 11 -i · cosθ} · sinθ ...... (28). Therefore, the y coordinate k of the horizontal grid line closest to point fi
Satisfies k = [y ₁₁ −i · cos θ · sin θ] (29) From the above, the coordinates (x _i1 , y _i1 ) of the transfer start grid point at the time of performing the processing on the i-th row are x _i1 = x _g11 + i + k cot θ (30) y _i1 = y _g11 + k (31) ).

The above method can be easily extended to other rotation angles.

Hereinafter, a specific configuration of the image rotation device according to the embodiment of the present invention will be described with reference to FIG.

In FIG. 1, 101 is an original image storage circuit for storing an original image, 102 is a rotation angle holding circuit that holds rotation angle information for rotating the original image, and 103 is based on information of the rotation angle holding circuit 102. A pixel number conversion circuit for reading the original image information from the original image storage circuit 101 and converting the original image information into the number of vertical and horizontal pixels;
Reference numeral 4 denotes a grid point coordinate calculation circuit that calculates grid point coordinates (addresses) of (X, Y) based on information from the rotation angle holding circuit 102. Reference numerals 105 and 106 denote grid points calculated by the grid point coordinate calculation circuit 104. An X and Y coordinate storage circuit 10 for storing coordinates (X, Y) and transferring the current grid point coordinates when the grid point coordinate calculation circuit 104 calculates the next grid point;
7, a temporary storage circuit for temporarily storing the conversion result of the pixel number conversion circuit 103; 108, a temporary storage circuit 10 based on grid point coordinates (addresses) held by the X and Y coordinate storage circuits 105, 106;
The content of 7 is stored at a fixed position (address) in the result image storage circuit 109.
Is a pixel transfer circuit to be stored.

 The operation of the above configuration will be briefly described below.

First, the pixel number conversion circuit 103 reads the original image stored in the original image storage circuit 101, and performs a process of converting the number of vertical and horizontal pixels based on the value held by the rotation angle holding circuit 102. Is written into the temporary storage circuit 107. The pixel transfer circuit 108 inputs one pixel of the image stored in the temporary storage circuit 107, and stores an X coordinate storage circuit 105 and a Y coordinate storage circuit 106.
Is transferred to the position indicated by the value stored in the result image storage circuit 109. On the other hand, the grid point coordinate calculation circuit 104
Are the rotation angle holding circuit 102, the X and Y coordinate storage circuits 105 and 10,
The grid point coordinates are calculated based on the value of 6, and the pixel transfer circuit 108
X and Y coordinate storage circuits 105 and 106 each time
Update the stored value of.

By repeating the above, the contents of the original image storage circuit 101 are converted and stored in the result image storage circuit 109 in accordance with the rotation angle held by the rotation angle holding circuit 102.

Effect of the Invention As described above, the present invention provides an original image including M rows and N columns of pixels located on a grid point, which is the intersection of M horizontal grid lines with an interval of 1 and N vertical grid lines with an interval of 1. A is represented by M ′ rows and N ′ columns (M ′ = [M / cos θ + 0.5], N ′ =
[N cos θ + 0.5], 0 ≦ θ <45 °, where [α] is the largest integer not exceeding α). Transfer address calculating means for calculating a transfer destination of each pixel constituting the image B; and pixel transfer means for transferring each pixel constituting the image B to a position obtained by the transfer address calculating means. The calculation means calculates a straight line li of a gradient θ passing through gi for a grid point gi (i = 1 to M ′) existing at the interval 1 on the same vertical grid line as the grid point g1 which is the center of rotation included in the image A. From the vertical grid line closest to the intersection fi between the straight line F and the li of the slope-(π / 2-θ) passing through the center g1 of rotation. A grid point cj closest to ej is determined on N ′ vertical grid lines existing at an interval of 1 including the vertical grid line, and the grid point cj on the i-th row By calculating as the transfer destination of the pixel, the pixel which is transferred to one pixel and the pixel which does not transfer is eliminated from the transfer area, and a rotated image with little deterioration can be obtained. There is great value.

[Brief description of the drawings]

FIG. 1 is a specific block diagram of an image rotation device according to an embodiment of the present invention, FIG. 2 is a conceptual diagram illustrating rotation of a one-dimensional image according to the present invention, and FIG. FIG. 4 is a conceptual diagram illustrating a method of calculating transfer start coordinates, and FIG. 5 is a conceptual diagram illustrating a rotation process of the present invention when the rotation angle is 45 ° to 90 °. FIG. 6 is a conceptual diagram illustrating rotation of a conventional one-dimensional image, and FIG.
FIG. 8 is a conceptual diagram illustrating rotation of a conventional two-dimensional image, FIG. 8 is a flowchart illustrating a conventional rotation method, and FIG. 9 is a conceptual diagram illustrating a result of rotating a two-dimensional image by a conventional method. 101: Original image storage circuit, 102: Rotation angle holding circuit, 103:
... Pixel number conversion circuit, 104 ... Grid point coordinate calculation circuit, 105 ...
.. X coordinate storage circuit, 106 Y coordinate storage circuit, 107 temporary storage circuit, 108 pixel transfer circuit, 109 image storage circuit.

 ──────────────────────────────────────────────────続 き Continuation of the front page (72) Inventor Katsura Kawakami 3-10-1, Higashi-Mita, Tama-ku, Kawasaki Matsushita Giken Co., Ltd. (56) References JP-A-63-24370 (JP, A)

Claims (1)

(57) [Claims] 1. An original image A consisting of M rows and N columns of pixels located on a grid point which is an intersection of M horizontal grid lines at an interval of 1 and N vertical grid lines at an interval of 1 is represented by a rotation angle θ. M ′ rows and N ′ columns (M ′ = [M / cos θ + 0.5], N ′ = [N cos θ +
0.5], 0 ≦ θ <45 °, where [α] is the largest integer not exceeding α). Pixel number exchange means for converting into an image B composed of pixels, and image B obtained by the pixel number conversion means. Transfer address calculation means for calculating a transfer destination of each pixel to be transferred, and pixel transfer means for transferring each pixel constituting the image B to a position obtained by the transfer address calculation means, wherein the transfer address calculation means comprises: For a grid point gi (i = 1 to M ′) existing at the interval 1 on the same vertical grid line as the grid point g1 which is the center of rotation included in the image A, the inclination θ passing through gi
The intersection ej (j = 1 to N ′) between the straight line li and the vertical grid line of
From the vertical grid line closest to the intersection fi of the straight line F of inclination-(π / 2-θ) passing through the center g1 of rotation and li, on the N ′ vertical grid lines existing at an interval of 1 including the vertical grid line An image rotation device, wherein a grid point cj closest to ej is calculated as a transfer destination of a pixel in the i-th row and the j-th column of the image B.