JPS62296280A - Restoration and generation system for compressed data - Google Patents

Abstract

PURPOSE:To efficiently obtain a high quality linear conversion pattern by linearly approximating the horizontal, vertical and decoration parts of character and graphic patterns, using compressed data approximate to a curve obtained by n-degree spline function for an oblique line and a curved stroke, linearly converting them, then restoring and generating a pattern. CONSTITUTION:The titled system is composed of a part 12 enlarging and reducing critical point coordinate data from the compressed data 10 on character and graphic patterns, a part 14 restoring a profile through a DDA, a part 16 which takes out a polynomial data and linearly converts it, a part 18 restoring a border point, a part 20 for restoring a profile 20, a part 22 connecting a linear approximate part and a curve approximate part, and a part 22 which paints out an inner area enclosed by border points and generates linearly converted character and graphic patterns. The horizontal, vertical and decoration parts of the border lines of a character and graphic are linearly approximated. The compressed data 10 obtained by approximating with a curve through the use of the n-degree spline function is used for the oblique line and the curved stroke. As a result the linearly converted character and graphic patterns are restored and generated efficiently and beautifully.

Description

[Detailed Description of the Invention] 3. Detailed Description of the Invention [Summary] Characters and graphic patterns are approximated by straight lines for their horizontal, vertical, and decorative parts, and diagonal lines and curved strokes are approximated by zero-order splines. Using compressed data approximated by a curve using a function, it is linearly transformed, then restored and pattern generated to efficiently obtain a beautiful, high-quality linear transformation pattern.

[Industrial application field]

The present invention relates to a method for restoring the bending points of the contours of characters and graphics using compressed data of characters and graphics to generate patterns.

Storing character and graphic data as full dots requires a large capacity memory, and enlarging or reducing a full dot pattern without leaving it as full dots results in a beautiful pattern. Therefore, there is a need for a pattern data compression, restoration, and pattern generation method that can store character and graphic data with a small memory capacity and generate high-quality enlarged and reduced patterns. The present invention relates to a pattern data restoration and pattern generation method.

Pattern enlargement or reduction is necessary when transferring to a facsimile machine with a different pixel density, or when converting the pixel density of character and graphic data read by a scanner with a certain pixel density and using it, for example, when recording it on a printer and displaying it on a display. It is essential.

[Conventional technology]

Linear approximation is one method of enlarging and reducing conversion.

This approximates the contours of characters and figures using a group of straight lines, and uses the coordinates of the end points of each straight line (vector) as a pattern enlargement mark for the characters and figures. Compared to the method using dot patterns, the memory capacity can be significantly reduced. , It is also easy to enlarge or reduce the pattern. For example, to enlarge characters or figures by 2 times or reduce them by 1/2, the coordinates of the end points of each straight line should be enlarged by 2 times or reduced by 1/2.
It can be reduced to 2. However, this linear approximation method has a high degree of approximation for horizontal and vertical lines, and can generate beautiful patterns even when enlarged or reduced. However, for diagonal lines or curved strokes, unevenness becomes noticeable and a beautiful pattern is generated. I can't. In other words, diagonal lines trace lattice points on the display, so quantization errors occur and they become step-like.Also, when a curved stroke is approximated by a straight line, the degree of approximation is generally low (if this is increased, many straight lines are created). If you enlarge or reduce these, you will not get a beautiful pattern. Therefore, a pattern data compression, restoration, and pattern generation method that can generate smooth diagonal lines and curved strokes is desired.

There is also a method of approximating the contours of characters and figures using curved lines instead of straight lines. An example is shown in FIG. In this example, the hiragana “
The outline of `` is approximated by a group of lines marked with ○, △, and O.

When approximating the contour with a curve, the function representing that curve is
It must be a monovalent function for one axis, for example the X axis, so that these lines tracing the character contour are partitioned into one y value for one x value. The ○ marks indicate the start and end points of one divided line (one block). The Δ marks are sample points obtained by linear approximation, i.e., two points on the contour are connected by a straight line, and the distance between the two points is to make the straight line as long as possible within the range where the deviation between the straight line and the contour is within the allowable value. This is the end point of the straight line when the distance is increased. Further, the mark e is a curve dividing point. In other words, the outline of the character is divided into 1 (i
There are some strokes that include two strokes intersecting each other (an inflection point where the slope changes suddenly), but the boundary between a curve and a straight line and an inflection point (marked with a *) ) divides the line into multiple blocks to facilitate functional expression.

The straight line section refers to a section where the distance between the sample points is greater than or equal to a predetermined value. The straight line portion is expressed by a first-order subnomial, and the curved portion is expressed by an nth-order (second-order or third-order) polynomial. The coefficients of the n-th degree polynomial are determined from the coordinates of both ends of the curve-approximating section and its slope. To perform curve approximation, find the slope at each sample point (point obtained by linear approximation), then determine the approximate curve using two contour points on the contour, and calculate the deviation between the approximate curve and the contour. is calculated for each contour point, and if each deviation in the approximation curve section in question is less than the allowable error, move the sample point forward by one and repeat the process to find the maximum deviation within the allowable error. A section (sample section) is determined, and the contour is divided into each sample section.

The contour curve portion is approximated by an n-th degree polynomial representing this sample section. The details are JP-A-60-75975, JP-A-75
976, 75977. 17978 and 75979.

[Problem that the invention seeks to solve]

In this conventional method, a curve is approximated within a block, and if the deviation between the curve and the sample point is less than the tolerance, the sample point is increased by one, and the deviation is checked, and if it is less than the tolerance, the contour points are re-approximated. It is inefficient because it performs sequential processing such as increasing the number by one.

Furthermore, in the conventional method, curve approximation is performed for all curved sections other than straight sections, which is inefficient. When characters are enlarged or reduced, unevenness is noticeable in long curved strokes and diagonal lines such as the left edge and right edge, but it is not noticeable in short parts such as decorations, so it can be simplified.

Furthermore, since the conventional method does not take curve vibration phenomena into consideration, there are cases where appropriate curve approximation cannot be performed. In other words, when dividing the contour line and approximating the curve using the conventional method, (1) polynomial approximation of the curve in which both the enlarged value and the local minimum value exist within the block (there are cases where the curve has both the enlarged value and the local minimum value); When approximating a curve, it is not possible to judge whether the obtained curve is vibrating or not, and it is not always possible to fit an appropriate curve and generate a beautiful pattern. However, it is difficult to accurately calculate the number of local maximums and minimum values from a sequence of contour points.

In addition, in the conventional method, only contour points are used as reference points when performing curve approximation, but if there are few contour points in one bronc, there are fewer reference points for calculating errors, so it is not always possible to obtain an appropriate curve. .

The present inventor has devised a pattern data compression method that improves these points, and the present invention provides a method for linearly transforming the compressed data and restoring the bending points after the linear transformation to generate a pattern. This is what I am trying to do.

[Means for solving problems]

A block diagram of the principle of the restoration and generation method of the present invention is shown in FIG. As shown in the figure, this involves extracting bending point coordinate data for horizontal lines, vertical lines, and decorative parts from the compressed data of characters and graphic patterns (10), and linearly converting it, for example, enlarging and contracting parts (12), linear Part (14) where the contour is restored by DDA using the converted bending point coordinate data
, a part (16) that extracts polynomial data for diagonal lines and curved strokes from the compressed data (10) and linearly transforms it; a part (18) that restores contour points by calculating function values after the transformation; A portion (20) where the contour is restored by filling in the holes using DDA for those where the contours are far apart, a portion (22) connecting the straight line approximation portion and the curve approximation portion generated by these contour restoration portions, and the calculated contour point. It consists of a part (22) that fills in the internal area surrounded by to generate linearly converted character and graphic patterns.

[Effect]

According to this method, the outline of characters and figures can be
For vertical parts and decorative parts, use straight lines (U, Pl).
For lines and curved strokes, compressed data (10) approximated by curves using nth-order spline functions can be used to efficiently restore and generate linearly converted character and graphic patterns as beautiful patterns.

〔Example〕

, First, the creation of the compressed data 10 will be explained in detail, and then the restoration and generation method of the present invention will be explained in detail.

As shown in Fig. 6, the compressed data creation process involves converting input cover patterns (dot patterns of characters and figures) into bending points (points representing bends, which correspond to the start and end points, sample points, and curve division points of the block). ), processing to recognize horizontal and vertical lines from the coordinate values of bending points, extract decorations and memorize the coordinate values of these bending points, processing to extract diagonal lines and curved strokes, and processing to extract bending points. A process of calculating each coefficient of a contour approximation polynomial (n-th order spline function) using only points, and contours of diagonal lines and curved strokes that are arranged in parts with few bending points and subjected to straight line approximation by DDA 19
The original processing, the process of determining whether the obtained polynomial does not oscillate, and the process of storing the coefficients of the obtained polynomial and the coordinate values of both end points of the curve-approximated section (compressed data by curve approximation). , the process of storing compressed data in which horizontal and vertical lines and decorations are linearly approximated.

According to this method, curve approximation is applied only to diagonal lines and curved strokes, excluding horizontal lines, vertical lines, and decorations, so when a hector character is enlarged or reduced, unevenness is noticeable on the right side, left side, etc. Long curved strokes or diagonal lines can be reproduced in beautiful patterns, and data can be compressed efficiently.

Furthermore, since there are no local maximum values and local minimum values within each segment to which the curve is approximated, it is possible to easily check whether or not there is a vibration phenomenon in the obtained curve, and an appropriate curve can be determined.

Also, each segment has similar tangential directions to the curve,
Each segment is divided to facilitate curve approximation, such as even a quadratic polynomial can be approximated to some extent. Therefore, the segments are not changed depending on the accuracy of curve approximation, which is good in terms of processing efficiency.

Furthermore, since not only inflection points are used as reference points during curve approximation, but contour points are also used in some cases, there is no possibility that an appropriate curve cannot be obtained due to a small number of reference points for calculating errors.

There are two main types of this pattern compression method: one that applies linear approximation to horizontal lines, vertical lines, and decorations, and the other that applies curve approximation to diagonal lines and curved strokes. Previously filed ■ “Pattern information compression method” (patent application 1986-48895) and ■
"Pattern similarity conversion method" (Patent application 6O-2822
71) can be used.

Many of the printed kanji have straight lines, and they have decorations attached to them. An example is shown in FIG. The end point of the straight line becomes the bending point. Inflection points are of course found in decorations, diagonal lines, and curved strokes, and the dark spots in the figure are inflection points.

By extracting each bending point on the contour line, the contour line can be expressed using the coordinate information of these bending points, making it possible to significantly compress data compared to a method that uses dot data as a character pattern.

The inflection point can be determined by the method described in (1) above.

That is, since the character contour line forms a closed loop, two adjacent points of the contour line represented by a group of dots are set as the starting point Ps and the ending point Pe, and the point P is traced on the contour line while detouring from the ending point to the starting point. Different
1Analyzer) to generate a straight line connecting points P and Ps, and examine the deviation between the straight line and the contour line. Assuming that the point Ps is at a corner, when the point P comes to the corner in front of it, the above deviation will not occur (therefore, the position of the point P at that time (denoted as P+) is the bending point. Next, the point If P1 is set to correspond to Ps and similar processing is performed, the bending point one point before P+ can be found, and all bending points on the contour can be found in the same manner.

The above ■ includes the integration of each line segment that approximates the contour with a polygonal line, line groups,
Decoration detection, line width control, etc. are disclosed.

For example, in the polygonal line approximation of the kanji character "dai" as shown in FIG. 11, P+-P24 is a bending point, and L1 to L24 are line segments connecting these points. Line segments are divided into horizontal lines, vertical lines, etc., and those of the same type are merged, and the horizontal lines of the integrated line segments are El, El, etc. The vertical lines are E2. E
Give a contour number such as a, . . . Line segment L2
Contour numbers are not assigned to items that are not in the horizontal/vertical direction (those that do not meet the predetermined rules). Ei (i=
1.2. ...) For the stressed contours, pairs are found from the degree of overlap and distance, and line groups Gl, G2 .・
...to be found. The decoration is determined as being at the end of a group of lines or at the corner of two groups of lines forming a corner. Pl is the decoration on the left of line group G1, P2 is the decoration on the right, and P5 is the decoration on line group G2.
The decoration above, P2O is the decoration below line group G3...
It is.

The diagonal lines are horizontal lines, vertical lines, and line segments outside the decoration 2.

Horizontal and vertical lines can be easily detected using the coordinate values of bending points. For example, the bending points at both ends of the line segment are Pi (Xi
, Yi), Pj (Xj, Yj), then X1
=Xj, Yi+Yj is a vertical line, Yi-YJ,
If X + ; X J, it is a horizontal line.

In the separately filed ``Method for Extracting Diagonal Lines and Curved Strokes'' (Japanese Patent Application No. 1988-), the outlines of diagonal lines and curved strokes are identified as follows. That is, there are N groups of bending point sequences representing the contour line, and the number of bending points in the jth group is n3. Let each bending point of the j-th group be Pji(
Here, i-1゜2..., n4 + j=
1. 2.・Old...N), the x and y coordinates of each bending point of the jth group are set as X (Pji) and Y (Pji), and the following steps 1 to 5 are performed to identify the above contour line.

Stepped: Calculate the length Dj' of the contour line of each group.

Dj/ == , Call, C(X(P41+t) X(P
jt))2+(Y(Pji+1) Y(Pji))'
)・・・・・・(1) However, P jnj+1 is Pjnj
represents the next inflection point.

When the jth group and the j+1th group are connected, the following equation holds true.

X (Pjnj+1) =X (Pjt1
1) Y (Pjnj+1) -Y (Pjt11) Step 2...Dj'>Dt with the threshold value Dth
Let us focus on the group (let us call it j) that satisfies h. Attribute AT of group j
A group k whose attribute ATR(k) of the group with respect to the ROI satisfies the correspondence table of Table 1 is set as a matching candidate for the group j.

Table 1 The arrows indicate the direction of the groups, and as shown in Figure 11, the outline of the letter follows one direction, in this case clockwise, so the upper/lower edge of each stroke (cuff), left /The right edge is traced in the opposite direction. Therefore, the group j having the relationship shown in Table 1 satisfies one of the conditions for forming a diagonal picture.

Step 3: Calculate the next discrimination amount for all groups k that are correspondence candidates for group j.

Djk= (Mj-Mk)2+l'Dj'-Dk'l
(2) Here, the first term on the right side of equation (2) represents the distance between the contour lines, and the second term represents the difference in length between the contour lines. The above distance is that at the midpoint of both contours.

Step 4...Group j is matched with the group that minimizes the discrimination 1Djk (these groups are assumed to be both edges of the image)
.

Step 5...Step 2~ for all j
Do step 4.

An example of bending point data from which diagonal lines and curved strokes have been extracted is shown in FIG. Although it is difficult to see in this diagram, the bending points of horizontal or vertical lines are marked, the bending points of decorations are marked with ↑ marks, and the bending points of diagonal lines and curved strokes are marked with convex numbers. In particular, the numbers indicate contour pairs of diagonal lines and curved strokes. The contour pairs extracted by the above logic are monovalent functions in which the tangential directions are similar and there is no maximum value or minimum value.

In the method of this application (2), diagonal lines and curved strokes are approximated by a straight line, but when the linear approximation is enlarged or reduced, unevenness becomes noticeable. Therefore, in the method of the present invention, curve approximation is applied to each contour pair. There are methods for curve approximation as shown in FIG. 9, but the method of the present invention uses a smoothing method using an nth-order spline function, especially B-Spl i which is numerically stable.
Use that by the ne function.

Curve approximation: B-5 pline smoothing method Smoothing unit There are two methods: a fixed node method that provides a point sequence from the outside, and a node addition method or sequential division method that provides a node sequence internally adaptively. Since there are many ways to provide a node sequence, which differ depending on the shape of the curve, the method of the present invention adopts the latter method of adding nodes. B
General formula S (Xl) of the smoothing method (node addition method) using the -Spline function is shown in equation (3).

However, m is the degree, n is the number of nodes, Cj is the coefficient, Nj, n
++1 is the difference quotient of the (m+1) floor, and the coefficient Cj of equation (3) is
It is obtained from the least squares approximation condition. Specifically (4)
Evaluation of the formula (Determine to satisfy the Western style.

However, δ2 is the sum of squared residuals, δ2th is the dark value of the sum of squared residuals,
yl is the y-coordinate value of the i-th reference point, σ12 is the observation error,
n is the total number of reference points, and observation error 61 is a point representing the weight of the reference points, that is, which point is considered important. Here, the order m of the spline function is set to 3, and the observation error σ12 is given as follows so that each reference point is regarded as a statistical quantity and the relative error is constant.

σ+/)'+=constant ・・・・・・(5
) Vibration Judgment 2 As mentioned above, in the method of the present invention, there are no local maximum values or local minimum values within each segment (line segment) that is subject to curve approximation, so by considering these values, it is possible to determine whether vibration is occurring or not. Can be judged. The presence or absence of local maximum values and local minimum values can be determined by dividing the obtained curve into small pieces and checking the sign of the differential coefficient at each point, but in order to save the effort of calculating the differential coefficient, this is done as follows.

Each segment divides the vector between the inflection points into 4 vectors every 90'.
Since the directions are classified and determined based on the attributes thereof, by examining the attributes of each divided section, the presence or absence of local maximum values and local minimum values can be determined, and the presence or absence of vibration can be determined. Assuming that the X coordinate of the second divided point is xt and the y coordinate is 5 (xz),
The attribute can be determined by checking the sign of (Xz+I Xt ) and the sign of (S (XL+, ) −5(xz)) in the interval between (I!+1) and l.

Next, processing steps for vibration determination will be described.

Stepsop... Curve, dividing point N s ll1
Divide into (Ns-1) pieces as il.

Step 2...Dividing point! Find the attribute of =1.

The attributes shown in Table 2 are determined by determining whether (X2-XI) and (S (X2) S (XI)) are positive or negative.

Step 3: The attribute of the dividing point z=2 is obtained in a similar manner, and it is checked whether it matches the attribute of the dividing point z=1 or not.

Step 4...If the attributes match, β-
The urinary nature of 3 is also determined, and the match/mismatch of attributes with f=1 is examined. If the attributes do not match, it is determined that there is vibration,
Abort processing.

Step 5: The process of step 4 is performed from z=4 to 1=Ns-1, and if the matching of attributes is confirmed up to f=Nsl, it is determined that there is no vibration.

Table 2 Contour restoration of diagonal lines and curved strokes: This is as described above (
3) Performed by the formula. In addition, if there are few bending points, (4)
It is difficult to obtain a continuous curve because the reliability of the error obtained by the formula is low and vibration phenomena are likely to occur. Therefore, when the number of bending points is small, the bending points are connected by straight lines generated by DDA, and the number of reference points is increased to perform curve approximation. In addition, even if there are many bending points, if the error condition of equation (4) and the vibration judgment condition of the previous section are not satisfied, the distance between the bending points is
Connect at A, increase the number of reference points, and perform curve approximation.

In the present invention, the compressed data of character and graphic patterns obtained in this way is used to restore the bending point after linear transformation and to generate the pattern.

Pattern restoration and generation: As shown in Figure 1, this involves linear transformation of bending points for horizontal, vertical lines, and decorations, contour restoration using DDA, and polynomial % expression % and % for diagonal lines and curved strokes. Processed by connecting and filling the curve approximation parts.

Linear transformation of polynomials is performed as follows. As shown in equation (6), the polynomial S (X) obtained in equation (3) is linearly transformed into polynomial S (x').

This process corresponds to converting the scales of the X axis and SfXl axis into x' and S(x') having the relationship expressed by equation (6) as shown in FIG. For example, when performing enlargement or reduction conversion, the conversion magnification is α, αX=αs=α, βX=β
Set s=0. Also, when restoring from compressed data, αX=αs=1. Set βX=βS−〇. Furthermore, X,
, S (x, ) corresponds to the bending point of the diagonal line and curved stroke before conversion, and X, ', S (x
I') corresponds to that after linear transformation.

Function value calculation is performed as follows. l from X+' to x'n
x1++ 'Xi'i-1'~ where l=1
Each S (x, ') is calculated for X, ' of n'.

This is to ensure that the interval between the bending points after conversion is appropriate. S
(x, ') can be found from 5(xl), so for each sample interval ΔX in the original x, 5(xl) coordinate system, S
(x, ) and α5s(xI)”β of equation (6)
S(x+') is found from S. For example, in the case of expansion and contraction conversion, αX − αS = α, βX = βS = O, so X, ′
/α=x, and 5(xl) is calculated for every sample interval 1/α in the original x, 5(x) coordinate system. For example, when α=2 (when magnifying 2 times), as shown in Figure 3, 5(xl) is calculated at 0.5 intervals, and 2S(xI)
It is possible to calculate the coordinate values of contour points in a more expanded coordinate system.

Contour restoration is performed as follows. Contour points are found by performing linear transformation of the polynomial and calculating the function value 5 (Xl) corresponding to a certain X coordinate. At this time, there may be cases where adjacent contour points are not connected by 4 or 8 connections. , when performing reduction conversion, if the concavity of the curve exceeds 45°, as shown in Figure 4, adjacent contour points will no longer be connected by 4 or 8 connections.In the figure, the ○ marks are contour points found by curve approximation. In such a case, the contour points ○ are connected with a straight line generated by DDA.

The Δ mark is the contour point to be filled with straight line approximation.

Connection of the straight line approximation part and the curve approximation part: To restore the contour of the straight line approximation part, as shown on the left side of Figure 6, read the bending point coordinate values, which are compressed data, and then linearly transform the bending point coordinate values. , the bending points are connected by DDA and the contour is restored.

The order of contour restoration depends on the compressed data. In this example, the order of contour tracing used when extracting bending points from the original pattern is followed. The straight line approximation unit and the curve approximation unit read the attributes indicating them and perform their respective processing. When applying deformation transformation to compressed data to generate a pattern, the end points of the linear approximation section and the end points of the curve approximation section may not match.

For this purpose, processing is performed to connect the end points using DDA to connect the straight line approximation section and the curve approximation section.

Filling: Generates a filling pattern for the internal area surrounded by the axis points for all calculated contour points.

In this case, each contour point is either a point belonging to the interior or a point belonging to the exterior (
Discriminant points) are determined, and the internal area is filled in using the discriminant points.

FIG. 5 is a diagram showing the effects of the present invention, and (a) is an enlarged conversion by linear approximation (the coordinate values of the bending points are multiplied by the conversion magnification to obtain the coordinate values of the bending points of the enlarged size, and the coordinates between the bending points are D.D.A.
(bl is an example of the result of enlargement conversion using the method of the present invention. In both cases, the 104 x 104 size is converted to 180 x 1.
Expanded to 80 size. (Although there is a chip on the heel in the al, this has been removed in the bl.

FIG. 7 is a diagram of the same type as FIG. 6, but the object is limited to characters. The attributes of the bending point include the above-mentioned direction.

FIG. 8 shows a processing procedure for enlarging and reducing the compressed data obtained in FIG. 7, and restoring and displaying the data, and corresponds to FIG. 1.

(Effects of the Invention) As explained above, the present invention approximates the contour lines of characters and figures by linear approximation for their horizontal parts, vertical parts, and decorative parts, and uses an nth-order spline function for diagonal lines and curved strokes. By using the compressed data (10) approximated by a curve using the compressed data (10), linearly converted character and graphic patterns can be efficiently generated in beautiful patterns in one summer.

Also, when restoring, l Xi+l 'X+'
S(x,') is calculated for J' (of i=l' to n' where l=1). In other words, the contour points after restoration are made to have dot spacing in the X direction, so at this time, 5 each (x
Contour points are generated by DDA for parts where the intervals of t') are not connected by 4 or 8 connections.Furthermore, if there is discontinuity between the straight line approximation part and the curve approximation part, they are connected by DDA, so they are continuous. It is possible to generate beautiful characters and shape patterns.

[Brief explanation of drawings]

Figure 1 is a block diagram of the principle of the present invention. Figure 2 is an illustration of linear transformation of polynomials. Figure 3 is an illustration of how to calculate function values. Figure 4 is an illustration of contour restoration procedures. Figure 5 is an explanatory diagram of an enlargement conversion example, Fig. 6 is an explanatory diagram of compressed data creation procedure, Figs. 7 and 8 are explanatory diagrams of specific examples, Fig. 9 is an explanatory diagram of a conventional curve approximation example, and Fig. 10 11 is an explanatory diagram showing an example of diagonal line extraction, and FIG. 11 is an explanatory diagram of polygonal line approximation.

Claims (1)

[Claims] The outlines of characters and figures are approximated by straight lines for horizontal parts, vertical parts, and decorative parts, and by curved lines using an nth-order spline function for diagonal lines and curved strokes. Characters linearly converted using compressed data (10),
In the method for generating a graphic pattern, means (12) for extracting bending point coordinate data for horizontal lines, vertical lines, and decorative parts from the compressed data and linearly converting the data, and using the bending point coordinate data after the linear transformation. means (14) for restoring contours by DDA; and means (16) for extracting polynomial data for diagonal lines and curved strokes from the compressed data and linearly transforming them.
), a means of calculating the converted function value and restoring the contour points (
18), a means (20) for restoring the contour by filling in holes using DDA for those whose contour points are far apart, and connecting the straight line approximation part and the curve approximation part generated by these contour restoring means, and connecting them. If the edges are far apart, there is a means (22) for connecting them using DDA, and a means (22) for filling in the internal area surrounded by the calculated contour points to generate a linearly converted character or graphic pattern (22).
22) Restoration of compressed data characterized by having
Generation method.