JPS6297072A - Picture display device - Google Patents

Abstract

PURPOSE:To produce a picture pattern at a high speed with conversion given to an original picture pattern just with addition, by adding the converted relative position vector to the picture elements on the picture pattern produced finally to obtain the next picture element. CONSTITUTION:An original picture pattern 101 is shown in the form of a train of adjacent picture elements starting at a certain picture element by an adjacent picture element detecting means 102. Then the conversion defined by the 2-dimensional affine transformation is applied only to some reference vectors showing the relative position relation between the adjacent picture elements. Then a picture pattern 109 to be produced is obtained in the form of a train of picture elements having the reference rector converted from the picture element corresponding to the start point after conversion at the relative position. An increment producing means 103 and an addition means 104 add the relative position displacement corresponding to the converted reference vector to the genuine coordinate value. A coordinate value replacement means 106 detects the over- digit of an error and changes the coordinates of the picture elements drawn in response to the detection of the over-digit. Then a drawing means 108 produces picture elements.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to an image display device that generates an image pattern by performing transformations such as enlargement, reduction, and two rotations on an image pattern.

2. Description of the Related Art In general, a two-dimensional affine transformation is often used as a transformation applied to an image pattern. The two-dimensional affine transformation is defined by the following equation (1).

x'abx (a,) = (.d) (a) ・・・・・・・・・
...(1) (ad-be lol 0) It's a sign.

For example, rotation by angle θ around the origin is defined by the following equation (2).

X'CO3θ−5inθI ()−(,)() ・・・・・・・・・・・・
- (2) 7' SiH6 cos θ y Further, double expansion (or reduction) in the I-axis direction and the y-axis direction centering on the origin is defined by the following equation (3).

〆 ko x (1) = (.k) (a) ・・・・・・・・・
...(3) Conventional image conversion methods (e.g. Computer, P24-P25,
(IEEE, Tune 1983, etc.), formula (1) is used for all pixels of the original image pattern to be converted.
Performed matrix operations such as

Problems to be Solved by the Invention However, calculations such as equation (1) require four multiplications per pixel, making it difficult to speed up the processing. Furthermore, since pixels are points on a square grid having discrete coordinate values, pixels may be dropped in image patterns generated during enlargement conversion, resulting in problems in image quality.

In view of this, the present invention has been developed to convert an image pattern into which an original image pattern is transformed by simple addition without using calculations such as equation (1) for each pixel, at high speed while avoiding deterioration of image quality. The purpose of the present invention is to provide an image display device that generates images.

Means for Solving the Problems In order to solve the above-mentioned problems, the present invention provides an adjacent pixel detection means for detecting rows of mutually adjacent pixels from an original image pattern and outputting relative position information between two adjacent pixels. , a coordinate value storage means for holding the coordinate value of the last generated pixel of the generated image pattern, an error storage means for holding the rounding error of the coordinate value, and relative position information outputted by the adjacent pixel detection means. an increment generating means for generating a corresponding increment value; an addition means for adding the increment value to the error held by the error storage means; and an addition means for evaluating the addition result in the addition to calculate the coordinate value held by the coordinate value storage means. The image display device includes a coordinate value updating means for updating, and a drawing means for generating pixels of a generated image pattern at the position of the coordinate values updated by the coordinate value updating means.

According to the above configuration, the present invention expresses the original image pattern as a row of adjacent pixels starting from a certain pixel using the adjacent pixel detection means, and expresses the original image pattern as a row of adjacent pixels starting from a certain pixel, and expresses the original image pattern with respect to some reference vectors indicating the relative positional relationship between the adjacent pixels. By performing the transformation defined by Equation (1), an image pattern is generated as a string of pixels whose positions are relative to the transformed reference vector from the pixel corresponding to the transformed starting point. The coordinate value storage means holds the coordinate values of the currently drawn pixels of the converted pixel string, and the error storage means stores the true coordinate values of the converted pixel string and the rounded coordinates actually drawn. The increment generating means and addition means are means for holding the error between the values and adding the relative positional displacement according to the converted reference vector to the true coordinate value. The coordinate value updating means detects the digit deviation of the error and updates the coordinates of the pixel to be drawn accordingly, and the drawing means actually generates the pixel.

Embodiments First, the principle according to the present invention will be explained. The current original image pattern is pixel row P = (PQ + ” 1
r P2+ """r" n-11Pn)...
・・・・・・・・・・・・(4) shall be given. A vector indicating the relative positional relationship between two adjacent pixels Pk-1 and Pk in a pixel column is expressed as vk=PkPk-1(k-1, 2,...-...,n)
・・・・・・・・・・・・・・・(6) When expressed as, the pixel Pi on the original image pattern P is Pt=
Pi-1+vt (i=1.2. ・=”, n)・
It can be expressed as ・・・・・・・・・・・・・・・(6). The two-dimensional affine transformation matrix applied to the original image pattern is T
Then, the generated image pattern P' after conversion is expressed by equation (4)
is multiplied by T, P/=T(Po, P, , P2.-・
-...,, Pn-1, Pn) = ('rp0. TP
l, TP2. ,=・-・,, TPn-1, TPn
)・・・・・・・・・・・・・・・(7) is given. On the other hand, using equation (6), P' becomes P'-T(To, P
O+v1. P1+v2゜”' ”・+Pn-2+v
n −1+”n −1+vn )=(TP() , T
P() +Tv1, TPl +Tv2.

..., TPn-20Tvn-1, TPn-10Tvn) ...... (8). Now, P = TP, (t = 1.2.-・-・, n )・
・・・・・・・・・・・・・・・ (9) Then, the formula (8
) from Pi' = T P i -1+ T v i=P,'
+Tv, ・・・・・・・・・・・・・・・
・It becomes (10).

Here, equation (9) represents the above-mentioned conventional method of performing affine transformation on all pixels of the original image pattern and finding corresponding pixels in the generated image pattern. On the other hand, equation (10) is a recurrence equation that expresses the principle on which the present invention is based, and the next pixel is calculated by adding the converted relative position vector to the pixel on the last generated image pattern. It represents the method.

In general, if there are no constraints on the pixel sequence P given by equation (4), the relative position vector Vk can also take any vector, so the multiplication process of the relative position vector by T in equation (10) This method requires a position vector, and is not superior to the conventional method in terms of calculation amount. However, two adjacent pixels Pk-1 in the pixel row P
By setting a constraint on the relative positional relationship between PkO and PkO, "they are adjacent to each other in the sense of 8-connection (that is, one pixel is in the 8-neighborhood of the other pixel)",
The relative position vector is U shown in FIG. It is limited to 8 ways from u7. Furthermore, since any two vectors selected from these eight vectors are linearly independent of each other, the relative position vector that actually needs to be multiplied by the two-dimensional affine transformation matrix is U. Only two of u7 are required. Now, select vectors u0 and u2 in Figure 2, and write b T-() (ad-bc key 0)...
・(11) Let ad be the vector obtained by multiplying each of the eight vectors by T.

′ to u7′, the following relationship holds true, and similarly below. As is clear from equations (12) and (13), no multiplication is necessary to obtain from uol to u7'.
It simply involves adding and subtracting elements of the two-dimensional affine transformation matrix T. However, the calculation required to determine ' is excluded. 0 From the above, by setting a constraint that the pixel strings that make up the original image pattern are 8 connected pixel strings, two-dimensional affine is applied to the original image pattern. It can be seen that the pixel string on the transformed image pattern is obtained by the recurrence formula (10), and that only addition and subtraction are required.

Embodiments of the present invention will be described below, taking as an example a case where an image pattern obtained by rotating an original image pattern is generated. FIG. 1 is a block diagram showing an embodiment of an image display device of the present invention. 101 is an original image pattern, 102 is an adjacent pixel detection means, 103 is an incremental generation means, 104 is an addition means, 106 is an error storage means, 106 is a coordinate value updating means 107 is a coordinate value storage means, 108 is a drawing means, 109 is a The generated image is a turn. Adding means 104 and error storage means 10
5 and the coordinate value storage means 107 are each configured as a pair for I coordinate and y coordinate.

An outline of a method for generating a converted image pattern realized by the image display device according to the embodiment of the present invention configured as described above will be explained.

Now consider the image pattern shown in FIG. 3 301 as an example of the original image pattern 101. Consider the case where this original image pattern is rotated 600 times counterclockwise around the origin. The adjacent pixel detection means 102 uses the 8-connected pixel array P P = (P P . . . , Pll) under the above-mentioned constraints.
(14) ()l 11 is detected, and information regarding the relative position between two adjacent pixels is output. In this example, relative position vector sequence V=
(vl, v2....., vll) is ■=(uOl
uOl uOl uOl uOl u31 u2 j
u3. u s r u 4. us)...
・・・・・・・・・(15) However, U...
...+u7 is the vector 0ν tor shown in FIG. Next, the incremental generation means 103 uses uO′ according to the two-dimensional affine transformation to be applied to the original image pattern 101.
,..., u7' is calculated and made into a table. In this example, U7', . . . , U7' are as shown in FIG. The increment generation means 103 selects the corresponding vector component from u0' to u7' according to the relative position information inputted from the adjacent pixel detection means 102, and stores it in the error storage means 105. It is output as an increment and added in the adding means 104.

Generally, the increment output from the increment generating means 103 does not necessarily take an integer value. Therefore, the coordinate value of the pixel after conversion (hereinafter referred to as the true coordinate value) corresponding to the pixel on the original image pattern 1o1 does not necessarily take an integer value, so it is necessary to round the coordinate value. arise. It is assumed that the rounding process is performed so that the true coordinate values (Xo, YO) and the rounded coordinate values (x, y) satisfy the following equation (16).

At this time, rounding errors Rx and RY are defined as the following equation (17).

The rounded coordinate values (x, y) are stored in the coordinate value storage means 1.
07, and the rounding error (Rx, RY) is held in the error storage means 105. The coordinate value updating means 106 calculates the rounding error (RX,
coordinate value storage means 1 so that RY) satisfies equation (17).
The coordinate value held by 07 (x.

Y) and instructs the drawing means 108 to generate a pixel at the position of the updated coordinate values.

The method described above will be confirmed using the original image pattern 301 in FIG. FIG. 6 shows the image pattern generation process in this example. Column 601 contains coordinate values of pixel rows detected by adjacent pixel detection means 10'2 from original image pattern 301, and column 501 contains information regarding relative positions between adjacent pixels output by adjacent pixel detection means 102 (in this example, The column 503 shows the increment value generated by the increment generating means 103 (in this example, the relative position vector r input from the adjacent pixel detecting means 102). Column 504 shows the addition result of the increment value performed in addition means 104 and the error held in error storage means 105, and column 506 and column 505 show the coordinate value updating means based on the addition result 604. 106, the above formula (17
) The coordinate values and errors rounded to satisfy the following are shown. The coordinate values given in column 506 are the generated image.
' indicates the pixel row of the image pattern. Figure 3 302
(The broken line part) shows the generated image pattern.

303 (solid line portion) shows the true converted image pattern.

Here, the processing in the coordinate value updating means 106 will be specifically explained. For example, when calculating P1' from P'
The increment value (column 503, first line) -〇 , 072 0.6 () is added to the error (column SO6, first line) of 0.267 (), and the addition result (column 504, first line of 10.866 0. 768.

row)() or obtained. This value is corrected so that the error is 0.794. Now RX/and RY/Tomo 1
By subtracting, the equation (17) is satisfied. As a result, the corrected Rx
', RY' is the error storage means 1 as the error in P1'.
06, and the amount equivalent to the correction is added to the coordinate values held by the coordinate value storage means 107 (note that the addition and subtraction of the amount equivalent to the correction in the correction of the temporary error and the correction of the coordinate values are reversed). At this time, since the coordinate values have been updated, the drawing means 108 generates a pixel at the position of the updated coordinate values. Following the same process, P2', P3',...1P
11' is sought.

In this example, P3' and P4' and p6/ and P71 overlap, but as described above, pixels are generated only when updating actually occurs in the coordinate value updating means 107 (in this case, P4' and P7 ' is not generated), but it goes without saying that it may be generated repeatedly.

Next, the generated image quality will be explained. Figure 3 302
The pixel rows that make up the image pattern shown in are not necessarily 8.
It is not connected. That is, between P6' and 267, P7
' and 287 and Pl. There is no connectivity between ' and 2117, and from the point of view of image quality, it is considered that pixels are missing. Before explaining how to avoid pixel dropouts, first of all, why do pixels drop out? The following relationship holds true from equation (17). Since the y component can be considered in the same way as the X component, only the X component will be described below. Now, (a) 1Δxi+11×1 and (b)
Let us consider the case of 1ΔXt+IDf separately.

In the case of (a), equation (21) can be rewritten as follows.

-1,5<:RX,' (1,6(22)1+1 The positive absolute value must be less than or equal to 1.) The updated coordinate value xi+1 of Pi+1 is xi+1=xi±n (n=o, 1) ...
(23), and the connectivity of the X components of Pi' and Pi41 is maintained. On the other hand, in the case of (b), equation (21
) can be the % expression %(24). At this time, the correction to be added to Rx, /!
+1 The absolute value becomes larger than 1, and the updated coordinate value xi+1 of Pi+1 is xi+1""xi2n(n=2,3,4...song)...
It can be seen that a condition must be satisfied that the connectivity of the X component of P,' and Pi+4 is maintained because the following equation holds: (25).

In the example shown in Fig. 5, the component of the converted relative position vector is used as the increment value, so P6/
, P8', P9', and P11' are calculated using the formula (
26) is not satisfied, and P6' l P8' l P
The absolute value of the correction when determining ll' was 2, and pixels were dropped between these values.

Therefore, in order to avoid pixel dropout, the incremental generation means 10
When generating the increment value in step 3, instead of using the converted components of the relative position vector as the increment value, the relative position vector is changed so that the absolute value of each vector component is 1.
Means 104 divides the sum of several vectors such that the sum does not exceed , and adds the components of the divided vectors as increment values.
It should be supplied to The simplest method for dividing the converted relative position vector is to repeat the division into two until the absolute value of the component of the divided vector becomes 1 or less. Although this method involves division of components, the actual processing involves shifting the data representing the components and there is no need to perform division. For example, in the example shown in FIG. 4, among the eight vectors, u1'+
u31u61u7 may be replaced with the sum of vectors divided into two, respectively, and the components of the divided vectors may be supplied to the addition stage 104 twice. In this way, the incremental generation means 10
Fix 3 to 4.

If correct, there is a pixel (12) between P6' and P6', or P7
12.

Pixel (12) is added between P1 and P8', or pixel (1) is added between P1 and P11'.

Incidentally, as an example for explaining the operation of the image display device of this embodiment, a case has been described in which the original image pattern is rotated 60 degrees counterclockwise around the origin. Enlarging/reducing the original image pattern by changing only the two-dimensional affine transformation matrix used9
It goes without saying that inverted, sheared, and composite image patterns can be generated.

Furthermore, although a closed curve was used as an example of the original image pattern in the explanation of this embodiment, it is also possible to process a general image pattern as a plurality of 8-connected pixel sequences by dividing it into several partial image patterns. Furthermore, if pixel overlap is allowed, it is possible to process any image pattern as one 8-connected pixel string. It should be added that the constraint that "the patterns are adjacent in the sense of 8-connection" does not impose any constraints on the shape of the image pattern to which the present invention can be applied.

Furthermore, although equation (17) was used as an evaluation criterion for the addition result in the coordinate value updating means 106, the error storage means 105
By setting 0.5 each as the initial value,
Equation (17) can be replaced with: Equation (27) can be evaluated by detecting digit errors in addition means 104, and can be easily implemented in hardware.

Effects of the Invention As described above, according to the present invention, it is possible to generate an image pattern by performing two-dimensional affine transformation on an original image pattern without using complicated calculation means such as matrix multiplication. It has greatly contributed to speeding up image pattern conversion processing and implementing it in hardware.

[Brief explanation of drawings]

FIG. 1 is a block diagram of an embodiment of the present invention, FIG. 2 is an explanatory diagram showing relative position vectors, FIG. 3 is an explanatory diagram showing an example of an image pattern for explaining the operation of this embodiment, and FIG. Fig. 4 is an explanatory diagram showing the result of applying the conversion example shown in Fig. 3 to the relative position vector in Fig. 2, and Fig. 6 is an explanatory diagram showing the image pattern generation process in the conversion example shown in Fig. 3. be. 102... Adjacent pixel detection means, 103...
... Increment generating means, 104 ... Adding means, 10
6...Error storage means, 106...Coordinate value updating means, 107...Coordinate value storage means, 10
8...Drawing means. Name of agent: Patent attorney Toshio Nakao and 1 other person 2nd
Figure 3 Figure 4

Claims (1)

[Claims] Detect rows of pixels adjacent to each other from the original image pattern,
Adjacent pixel detection means for outputting relative position information between two adjacent pixels, coordinate value storage means for holding the coordinate values of the last generated pixel of the generated image pattern, and holding rounding errors of the coordinate values. an error storage means; an increment generation means for generating an increment value according to the relative position information outputted by the adjacent pixel detection means; an addition means for adding the increment value to an error held by the error storage means; coordinate value updating means for evaluating the addition result in and updating the coordinate values held by the coordinate value storage means; and drawing for generating pixels of a generated image pattern at the positions of the coordinate values updated by the coordinate value updating means. An image display device comprising: means.