JPH03219373A - Method and device for two-dimensional coordinate transformation - Google Patents

Abstract

PURPOSE:To shorten coordinate transformation time by outputting coordinates which satisfy specific transformation equation corresponding to arbitrary input coordinates. CONSTITUTION:Values f(0), f(1), to f(n) are stored in the cells Xx0, Xx1, to Xxn of an (x) related X-coordinate value table 3 in correspondence with integer values of (x) in a prescribed area, and also, values h(0), h(1), to h(n) are stored in the cells Yx0, Yx1, to Yxn of a (x) related Y-coordinate value table 5, and similarly, the respective value of an (y) related X-coordinate value table 4 and a (y) related Y-coordinate value table 6 is stored. Then, f(x) and g(y) are added on (x,y) supplied sequentially with an X-coordinate calculator 13, and is outputted as X, and similarly, the value h(x) of a cell Yxx and the value k(y) of a cell Yyy are read out, respectively, and added with each other, then, it is outputted as Y. In such a way, the coordinate transformation time can be shortened.

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Field of Application] This article relates to a two-dimensional coordinate transformation method and device, which are used in digital image processing devices and the like.

[Prior Art] Two-dimensional digital images are represented by arranging a large number of pixels in rows and columns vertically and horizontally, and giving image information such as density to each pixel.

Therefore, when enlarging, reducing, rotating, moving, transforming, etc. for digital image editing, it is necessary to transfer the density of each pixel of the original image to other pixels, and the coordinates of each pixel must be transferred to other pixels. A two-dimensional coordinate transformation is required to convert the coordinates of the pixels into the coordinates of the pixels.

Conventionally, such conversion has been performed either by hardware or by software (program) using a CPU.

[Problems to be Solved by the Invention] When using hardware, processing time is not required, but the type of transformation is limited to simple calculation types such as affine transformation and those with a small number of calculation circuits, and the size of the image is also limited. , there is a problem that the position is also fixed, and when using software, instead of being able to freely select the type of conversion,
There is a problem in that the calculation time required to convert the entire image is enormous.

This invention was made in view of the above-mentioned circumstances, and includes not only affine transformations such as enlargement, reduction, rotation, translation, or a combination thereof used in normal image editing, but also transformations with a higher degree of freedom. Naturally, when X takes an integer value in a certain range and y takes an integer value in a certain range and changes over time, (however, f(X) and h(X) are arbitrary functions of X, a(y)
, k(y) is an arbitrary function of y) can be outputted at high speed according to arbitrary input coordinates (x, y), which satisfies the transformation formula, reducing the coordinate transformation time. It is an object of the present invention to provide a two-dimensional coordinate conversion method and device that is possible and does not require a large-sized device.

[Means for Solving the Problem] Corresponding to this objective, the two-dimensional coordinate conversion method of the present invention converts coordinates (x, y) in a predetermined area on the x-y coordinate system to the X-Y coordinate system. The conversion formula to the coordinates (X, Y) in the predetermined area above is (where f (x) and h (x) are any functions of X,
Q(y), k(y) are arbitrary functions of y) is a two-dimensional coordinate transformation method that performs coordinate transformation expressed by An X-coordinate X-related value table XX, an x-coordinate y-related value table Prepare a Y-coordinate, (X) and h(X) respectively
q(y) corresponding to the multi-value of y is stored in each cell XXx of x and each cell Yxx of Yx.

The value of k (y) is stored in each cell Xy of Xy and each cell Yy of Yy, and XXx corresponding to X.

Read values f(X) and h(X) from Yx, respectively, and read values 1a(y) from Xy and Y'y corresponding to y, respectively.

Read out k(y), add 1ilf(X) and value g(V), output the obtained value as X, and output value h(X) and value k(
y) and outputs the obtained value as Y, and the two-dimensional coordinate conversion device of the present invention is characterized by adding x-y
The conversion formula from coordinates (x, y) within a predetermined area on the coordinate system to coordinates (X, Y) within a predetermined area on the X-Y coordinate system is (where f (x), h (x) is any function of X, g
(y), k (y) is an arbitrary function of y).
X, y), an X-coordinate 11x relational value table XX that can store the values of f(x) corresponding to the multiple values of X, and g corresponding to each axis of y. An X-coordinate y-related table Xy that can store the value of (y), a Y-coordinate X-related value table YX that can store the value of h(x) that corresponds to multiple values of A Y-coordinate y-related value table Yy that can store the value of k (y) to be stored, and a cell xX of the X-coordinate
an X-coordinate x111I coefficient value readout device for reading out the value of x; a Y-coordinate Cell Xy of the X coordinate y relationship value table corresponding to the value of y.

An X-coordinate y-open reading device for reading out the value of y, and a cell YV of the Y-coordinate yll value table corresponding to the supplied y value.
A Y-coordinate y-related value reader for reading out the value of the cell Xx and the cell Xy.

and a Y-coordinate calculator that outputs as Y the sum of the read value of cell Yxx and the value of cell Yy. It is a feature.

[Action 1] In the two-dimensional coordinate conversion device configured as described above,
In advance, an integer value of X within a predetermined area, e.g. 0.1.2
．． ..., corresponding to n, the X coordinate X relation value Chisol's cell Xx , Xx , -, Xx o 1
n respectively f (0), f (1), −, f (n)
Cell YX of the Y-coordinate and X-related value table
. .

h(0), ? for Yx, ..., Yxo, respectively? 1 (1)
.

... stores the value of h(n), and also stores the integer value of y within a predetermined area, for example 0.1.2... ... Cells Xy, Xy1..., x of the X coordinate y relationship value table corresponding to 1m
y, respectively Q (0), Q (1),...q(m)
cell yy of the Y-coordinate y-related value table,
'l/y,..., YyIm (0), k(1
), ..., k(m), the value f(x) of cell Xxx will be X
The value of cell Xy (J
(V) is read out by the X coordinate y relationship reading device, and the X coordinate calculator adds "(x) and a (y) and outputs it as The values of Yyy x k (y) are read out, added together, and output as Y.

(X, Y) that satisfy the following are sequentially output and the coordinate transformation is completed.

In a two-dimensional coordinate conversion device, the time required to convert one coordinate is the time required for one addition, which is extremely short.

However, if X, Y) are, for example, the coordinates of pixels in an image and are obtained as a set of integers as a result of conversion, they can be used as is, but if they are not a set of integers and at least one of them has a fraction less than an integer. is (X', Y') = ([X],
[Y]) may be used.

[Example] Hereinafter, details of the present invention will be explained with reference to drawings showing an example.

In FIG. 1, 1 is a two-dimensional coordinate conversion device.

The two-dimensional coordinate conversion device 1 is connected to a two-dimensional coordinate supply device 2, and the two-dimensional coordinate supply device 2 is expressed by, for example, O≦X≦n, Q≦y≦m on the x-y coordinate system. Integer coordinates (x,y) within the region may be generated.

Here, m is, for example, the coordinates of a pixel in a digital image (
It is possible to assume that the maximum value of

The two-dimensional coordinate transformation device 1 also converts the multi-value f(0) of f(x) corresponding to the multi-value of the integer X in the area.

Cell Xxo storing f (1) , ・, f(n)
.

Xxl , ..., Xx, , X-coordinate and
1).

..., cells Yx, Yxl, . . . which store h(n)
... YX, and the Y coordinate X relational value table 5 consisting of
), Q (1), ..., Q (m) are stored in the x coordinate y relationship value table 4 consisting of cells Xy, Xyl, ..., ).

Cell Yy storing k (1) , ., k (m)
o.

A Y-coordinate y-related value table 6 consisting of Yyl, . . . , yy is provided.

The multivalues stored in these X coordinate X relationship table 3, Y coordinate X relationship table 5, The value obtained by calculating is stored before conversion.

The two-dimensional coordinate conversion device 1 also includes an X coordinate X relationship value reader 7 that reads out the value of cell XX of the A Y-coordinate X-related value reading device 11 that reads out the value of the cell YXx of the corresponding Y-coordinate X-related value table;
an X-coordinate y-related value reading device 8 for reading out the value of cell Xy of the X-coordinate y-related value table corresponding to the value of y;
The Y-coordinate y-related value reader 12 reads the value of cell Yy of the Y-coordinate y-related table corresponding to the value of , and calculates the sum of the read value of cell XX and the value of cell Xy. It includes an X coordinate calculation number 13 that outputs as X, and a Y coordinate calculator 14 that outputs as Y the sum of the read value of cell YXx and the value of cell Yy.

Next, a method of converting two-dimensional coordinates (x, y) into two-dimensional coordinates (X, Y) using such two-dimensional coordinate converting device 1 will be explained with reference to FIG.

First, the functions f (x), Q (y), h (x>).

Determine k (y) and set each table 3, 4, 5.6. For example, Xx, Xx, Xx, ., Xx.

o 1 2 , the values f (0), f (1), ' f (2>, ・,
f (store n>, Xy, Xy, Xy2..., xy.

1, respectively the values 0, (0), a (1), Cl (2), ..., g
Store (m), YX , YX , YX ,...I' Y X
no 1 2, respectively the values h (0), h (1), h (2), -, h (
n), YV , Y'j , Yy2 , -, X"T"
111, respectively, the values k (0), k (1), k (2), ・, k
(m) is stored.

Then, the two-dimensional coordinate supply device 2 supplies integer coordinates (x, y) within the area expressed by the x-y coordinate system ◯≦X≦n, Q≦y≦m.

This supply can be done, for example, by first setting y=O and then setting X to x=0.
1.2. ...change it to n, then increase the value of y by 1 y
=1, x=0.1.2. -n, and then increase the value of y by 1 to X-0°1.2. ..., n and the coordinates (0,0).

(0,1), ... (m, n) are supplied.

Of the supplied (x, y), if X is input to the X coordinate X relationship readout device 7 and the Y coordinate X relationship readout type 11, as a result, If (x) stored in h
(x) is read, so f(x) is an X coordinate calculation type 1
3, and h(x) is input into the Y coordinate calculation type 14.

On the other hand, y is input to the X-coordinate y-related direct reading device 8 and the Y-coordinate y-related reading device 12, and as a result, In (y) and k (y) stored in Xy and Yy, respectively, are read out. Therefore, q
(y) is input to the X coordinate calculation type 13, and k(y) is input to the Y coordinate calculation type 14.

X coordinate calculation type 13 adds f(x) and Q (V),
Output the value f(x)+g(y) as X.

Further, the Y coordinate calculation type 14 adds h(x) and k(y) and outputs the value h(x)+k(y) as Y.

As a result, the coordinate transformation from (x, y) to (X, Y) is completed.

The image conversion device 20 shown in FIG. 2 utilizes the coordinate conversion method and device of the present invention. The coordinates (x, y) generated by the device 2 are also supplied to the image memory 15 for writing converted images,
The two-dimensional addresses (x, y) are generated sequentially.

On the other hand, coordinates (x, y) are converted into coordinates (X
, Y), and the output (X, Y) is supplied to the image memory 16 for recording the original image, and its two-dimensional address (
The image information (gradation values, etc.) recorded in the area (X, Y) is read out and written to the address (x, y) of the image memory 15 for writing the image after the first two conversions.

An example of image conversion is shown below.

n=36. Assuming that m=32, the following function is selected in which f(x) and the value of each X are made to correspond to each other.

f (0)=O, f (1)=1. f, (2) = 1°f
(3)=2. f (4)=3. f (5)=2゜f
(6)=1. f (7)-1, f (8) = 4゜f
9)=O, f(10)=O, f(11)=4°f
12 = O, f 13) = O.

f 14 = O, f 15) = O.

f 16 = O, f 17) = 5°f
18 = 6. f 19) = 5° f 20
=O,f, 21>=O.

f 22 = 0. f　　　23)-〇.

f (24 = ○, f 25 = 4・f 26
-0. f 27 =O.

f 28 =4. f 29 = 1f(
30=1. f 31 =2°f (32=3.
f 33 = 2°f (34 = 1. f
35 = 1°f (36=O.

Further, as k (y), the following function is selected in which the value is individually associated with each value of y.

k (0)=O, k (1)=O, k (2)=1゜k
(3)=1. k(4)=2. k (5) = 3゜k
(6)-2,k (7)=1. k(8)=1゜k(9
)=4. k(10)=O, k(11)−〇.

k 12 = 4. k 13)=O.

k14)-〇, k15)=5゜k
16 = 6. k17)=5゜k
18 = O, k 19) = O.

k 20 =4. k 21 =0゜k
22 =0. k 23 = 4゜k
24 =1. k 25 = 1゜k
26 = 2. k 27 = 3゜k
28)=2. k 29 =1k(30)=1.
k 31 =O.

k(32)=0 Then, the X-coordinate X-related value table 3 and the Y-coordinate y-related value table 6 become as shown in FIG.

Also, a (y) = O, h (x) = 0, that is,
CI (y), h (x) are always functions that are 0, and Xy, Xy, Xy2 . ...1 xy and Yx, Yx, Yx, -...,
Yx.

-012 All stores O.

Then, the correspondence between X and X matches the correspondence between X coordinate and X relationship value table 3 and X, and similarly, Y,! 4).

Then, the coordinate transformation from (x, y) to (X, Y) becomes as shown on the left side of the following table.

(x, y) → (X, Y) Image information of pixel (X, Y) 0, O → (0, 0> I 0 O11→(0,0i 0 0.2 → (0,1): 0 0.3 → (0,1), 0 0.4 → (0,2>I 0 O95→(0,3) I O (1, O → (1, 1→ (1, 2→ (1, 3 → (1, 4 → (1, 5 → i,o,.

1.0 0 1, 1 0 1, 1 0 1, 2.

1, 3 0 (1.

(1.

(1.

(1゜ (1゜ → (1.

→ (1.

→ 〈〈　1　.

→ (1゜ → (1.

(2,0) → (1,0> (2,8) → (1,1) <2.9) → (1,4> (2,10) → (1,0) (3,8) → (2,1) (3,9) → (2,4) (3,10) → (2,0) (4゜(4゜(4゜(4゜8) → (3゜9) → (3゜10) → (3゜11) → (3゜(4゜12)→ (3゜4) → (3°18) → (When rotated by 3°, the original image 17, which is a 21ia image with the X-shaped part ON (dark) as shown in FIG. is converted into a divided converted image 18.

That is, as the coordinates (x, y) are sequentially supplied as (,0,0), (0,1), (0,2)...
The address (X, Y) of (0,0), (0,1>, (0
, 1>..., and the haze information shown on the right side of the table is O (bright), ○ (bright), O (bright)... for image writing after conversion. The converted image 18 shown in FIG. 4 is obtained by sequentially writing to addresses (0,0), (0,1), (0,2), . . . in the image memory 15.

FIG. 5 shows f (x), g (y), h ( x)k
The settings of each table in (y) are shown.

Equation (1) is the case where f(x)=ax ON/) -by+ch h(x)=dx k (V)=ey+f, so X coordinate X relation value table 3, X coordinate y relation value table 4
, Y-coordinate,

The point (4, 3) on the x-y coordinate system is the point (4, 3) on the x-y coordinate system
X, Y) (However, X1=4a+3b+c.

1 Y, = 4d - 3e + f), and the original image [image information at address (X, Y, > on recording image memory 16) is converted to address (4, 3) on converter image writing image memory 5. The original image 17 is converted into a converted image 18.

If the affine transformation in equation (1) is a rotation, a.

Since b, c, and d are decimal numbers between -1 and 1, f
(x), Q (y), h (x), k (y)
The table may also be capable of storing decimal values, and may be constructed so that the addition results X and Y are rounded down to an integer X'Y' as described above.

FIG. 6 shows figures after various transformations have been performed by the image transformation device B20, where (a) shows the original figure, and (b) -
(h) shows a deformed figure obtained by converting to (a).

[Effects of the Invention] As is clear from the above description, according to the present invention, not only affine transformations such as enlargement, reduction, rotation, translation, or a combination thereof used in normal image editing, but also transformations with a higher degree of freedom can be performed. is possible in a short time, that is, when X takes an integer value in a certain range and y takes an integer value in a certain range and changes,
, and g(y) and k(y) are arbitrary functions of y). It is possible to obtain a two-dimensional coordinate conversion method and device that can output data in 2-dimensional coordinates, shorten coordinate conversion time, and do not require large-scale equipment. Using this method, image conversion that can convert a large amount of images at high speed can be obtained. The device can be configured.

[Brief explanation of drawings]

Figure 1 is an explanatory diagram of the configuration of a two-dimensional coordinate conversion device, and Figure 2 is a 2-dimensional coordinate conversion device.
An explanatory diagram of the configuration of an image conversion device incorporating a dimensional coordinate conversion device, FIG. 3 is a diagram showing an original image, FIG. 4 is a diagram showing a converted image obtained by converting the original image shown in FIG. 3, and FIG. An explanatory diagram showing how to set each table and the relationship between coordinates in the original image and the transformed image when the two-dimensional coordinate transformation is an affine transformation,
and FIG. 6 are diagrams showing an example of a figure transformed by the two-dimensional coordinate transformation device. DESCRIPTION OF SYMBOLS 1... Two-dimensional coordinate conversion device, 2... Two-dimensional coordinate supply device, 3... X-coordinate X relationship value table, 4... X-coordinate y-related value table, 5... Y-coordinate X relationship Value table, 6... Y coordinate y relationship value table, 7... × coordinate X relationship 1iII reader, 8... X coordinate y relationship li1 reader, 10... Arithmetic device, 11... Y Coordinate X-related value reader, 12... Y-coordinate y-related value reader, 13... X-coordinate calculator, 14... Y-coordinate calculator, 15... Image memory for writing converter image. 16・
...Image memory for recording the original image, 17...Original image,
18... Converted image 20... Image conversion device

Claims (2)

[Claims] (1) Coordinates (x, y) within a predetermined area on the x-y coordinate system
The conversion formula from to coordinates (X, Y) within a predetermined area on the X-Y coordinate system is ▲ There are mathematical formulas, chemical formulas, tables, etc. function, g(y)
, k(y) is an arbitrary function of y) A two-dimensional coordinate transformation method that performs coordinate transformation expressed as A value table Xx and an X coordinate y relationship value table X that can store the value of g(y) corresponding to each value of y.
Y that can store y and the value of h(x) corresponding to each value of x
Coordinate x relationship value table Yx and k(
y) is prepared, and the values of f(x) and h(x) corresponding to each value of x are stored in advance in each of the buildings Xx_x and Yx of Xx. Cell Yx_
g(y), k(y) stored in x and corresponding to each value of y
The value of each cell Xy_y of Xy and each cell Yy_y of Yy
The values f(x) and h(x) are read out from Xx_x and Yx_x corresponding to x, and Xy_x corresponding to y.
Read the values g(y) and k(y) from y and Yy_y, add the value f(x) and the value g(y), output the obtained value as X, and output the value h(x) and the value k( y) and outputs the obtained value as Y. (2) Coordinates (x, y) within a predetermined area on the x-y coordinate system
The conversion formula from to coordinates (X, Y) within a predetermined area on the X-Y coordinate system is ▲ There are mathematical formulas, chemical formulas, tables, etc. function, g(y)
, k(y) is an arbitrary function of y) A two-dimensional coordinate transformation device that performs coordinate transformation expressed as X can store the value of f(x) corresponding to
A coordinate x-related value table Xx and an X-coordinate y-related value table Xy that can store the values of g(y) corresponding to each value of y.
, a Y coordinate x relationship value table Yx that can store the value of h(x) corresponding to each value of x, and k(y
); an X-coordinate x-related value reader that reads the value of the cell Xx_x of the X-coordinate x-related value table corresponding to the supplied x value;
a Y-coordinate x-related value reader for reading out the value of cell Yx_x of the Y-coordinate x-related value table corresponding to the supplied x value; an X-coordinate y-related value reader that reads the value of the cell Xy_y; a Y-coordinate y-related value reader that reads the value of the cell Yy_y of the Y-coordinate y-related value table corresponding to the supplied y value; The read value of cell Xx_x and cell Xy_y
an X coordinate calculator that outputs as X the sum of the sum of the values of
A two-dimensional coordinate conversion device characterized by comprising a Y-coordinate calculator that outputs as Y the sum of the values of