JP2645373B2 - How to vectorize shapes - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a vectorization method for a graphic, and more particularly to a vectorization method effective for vectorizing a contour of a pixel.

[Background of the invention and its problems]

When recording a figure, dot data and vector data can be considered as data formats.Generally, vector data, especially contour vector data, has a smaller capacity than raster data and enlarges a figure while maintaining the quality of the figure. It is easy to display in reduced or deformed form,
It is valid data. Conventionally, this vector data is generally given as a part of the boundary pixels of the figure arranged as a series of data, and the quality of the reproduced figure depends on which boundary pixel is selected. In particular, when a character such as a kanji is recorded and reproduced as a vectorized graphic, the quality of the reproduced graphic (character) greatly affects the commercial value.
In addition, as far as the inventor knows, it seems that in the past, the angle calculation of the boundary pixel was performed at the time of vectorization, and it seems that the detection of the right-angled portion itself required a great deal of processing time. That is, conventionally, vector data that can reproduce high-quality figures
It was not possible to produce in a practical processing time.

[Purpose of the Invention] The present invention was devised in order to solve such a conventional problem, and a vectorization method of a graphic which can generate vector data capable of reproducing a high quality graphic in a practical processing time. The purpose is to provide.

[Summary of the Invention]

The vectorization method for a graphic according to the present invention focuses on the fact that the Freeman chain code or a code equivalent thereto reflects the features of the outline of the graphic, especially the bent state, and in the order of tracing the boundary pixels of the graphic. , A series of code strings of such codes are generated, and a vector point is selected from a boundary pixel or a pixel in the vicinity thereof based on a continuous state in each part of the code string.

As shown in FIG. 1, the Freeman chain code is such that the right side of the target pixel is set to “0” and the numbers 1 to 7 are sequentially provided in 45-degree increments in a counterclockwise direction. When sequentially following the direction, the direction of the next boundary pixel is given to each boundary pixel as a chain code. However, it is of course possible to perform the same processing using a code equivalent to the chain code.

(Example of the invention)

Next, an embodiment of a method for vectorizing a figure according to the present invention will be described with reference to the drawings.

In FIG. 2, there is a figure F in the image, and when this is viewed by ordinary left-to-right and top-to-bottom scanning, the upper left pixel a is found first. Normally, a chain code string is generated by following the boundary pixel counterclockwise starting from the pixel a. The chain code is a code indicating in which direction a pixel existing next to the target pixel (when attention is paid to a, that a is the target pixel), and in FIG. Is displayed on the boundary pixel. When the operation of generating a chain code from the pixel a in FIG. 2 is started, a chain code indicating the direction of a is given to the pixel b on the right side of the last pixel a. (Note that a chain code is often unnecessary for the last pixel in the outer boundary pixels.) In FIG. 3, when a straight line 1 having a width of one pixel protrudes, the pixels a, With respect to b and c, after tracing once toward the end point, tracing in the opposite direction, two chain codes correspond to one boundary pixel. Therefore, the boundary pixel and the chain code are not always one-to-one.

As is apparent from FIG. 2, the chain code of this figure is given by “66000766002222244444”, for example, “6
A straight line pointing downward in a series of 6's, a straight line pointing right horizontally in a series of '00', a straight line pointing up in a series of '22', and
And a straight line pointing left horizontally.

When vectorizing the figure of FIG. 2, ideally the pixel a
→ Pixel c _{1 at} the lower right corner of pixel a → Pixel c _{2 at} the right concave corner at the right concave → Pixel c _{3 at the} lower right corner → Pixel c _{4 at} the right right corner thereof → pixel c ₅ of square corners of the upper be sequentially may be the vector point is clear. And the corner (convex) of these vector points
Of pixels c ₁ , c ₃ , c ₄ , c ₅ , and a are consecutive chain codes “6
"6", "66", "00", "22", and "44" are present at positions where they are increased by "2" (6 → 0 can also be regarded as increased by modulo 8). Thus, it can be seen that the chain code reflects the state of bending of the outline of the figure. Similarly, the convex right-angled pixel b formed by the diagonal straight line shown in FIG. 4 has a chain code obtained by increasing the chain code of the previous boundary pixel by “2”. Although the concave corner c2 in FIG. ₂ should be extracted as a vector point as described above, it is not a boundary pixel, and thus no chain code is attached. Here, there is a difficulty in processing a concave right angle, which will be described later. As is apparent from FIG. 2, the continuation of the same chain code means a straight line.

The chain code generally takes the outer periphery of the figure counterclockwise, but can also take the clockwise. However, it is necessary to take a chain cord in the inner circumference of the hole in a direction opposite to the outer circumference. Here, the description will proceed with an example of a chain cord with the outer circumference taken counterclockwise.

When a chain code k is given to a pixel,
The chain code k ′ that can be taken by the next pixel is k−2, k−3 when k is an even number since the next pixel is a boundary pixel.
Cannot be taken, and if k is an odd number, the value of k-3 cannot be taken (however, k is modulo "8"). For example, the first
In the figure, when k = 4, k ′ cannot be “1” or “2”. When k = 5, k 'cannot be "2". As described above, the range in the direction of the next boundary pixel is specified only by the chain code of one boundary pixel. And k '
When = k + 2, the pixel of "k '" is a convex right-angled corner. Whether or not this is displayed as a right angle depends on the application of the vector data.
Are adopted as vector points (pixels a, b, c and pixels d, e, f in FIG. 5). In this case, no processing is performed for the concave right angle. Alternatively, only when both sides of the right angle have a certain length or more (for example, three or more pixels), the image may be displayed as a right angle (pixels a ₁ a _{2 in} FIG. 6).
_{a 3 bc 1 c 2 c 3} ). In this case, abc, d of the figure shown in FIG.
Since all combinations of ef are not displayed as right angles, for example, pixels a, c, d, f are not set as vector points, only pixels b, e at corners are used, and the whole is displayed as a relatively smooth broken line (Broken line 1 in FIG. 6).

Next, the processing of the above-described concave right-angled portion will be described. The pattern of the concave right-angled portion is composed of vertical and horizontal straight lines. FIGS. 7 (a), 8 (a), 9 (a), 10 Only (a) exists.

FIG. 7 (a) shows a concave right-angled portion which opens to the lower left, and the chain code advances to "... 007" in the horizontal portion to reach the pixel a at the corner, and then moves to the vertical portion to "66".
… ” The pixels defining the right angle in this figure are the last two pixels b and c of the horizontal part and the first pixel d of the vertical part
It is. These chain codes are “076”, and when this combination occurs in the chain code row, it is immediately found that the chain codes are concave right-angled portions that open to the lower left. Here, a change is made to the chain code so that the pixel a at the corner is included. FIG. 7 (b) shows the result of the change to the chain code. 7 "
To “6”, and a chain code “6” is given to the pixel a at the corner. This is the chain code set "07
This corresponds to an operation of changing “6” to “0066”.

Due to these changes in the chain code, the last pixel c of the horizontal portion points to the corner pixel a, and the corner pixel a
Indicates the first pixel d of the vertical portion.

FIG. 8 (a) shows a concave right-angled portion which opens to the lower right, and the chain code advances to "... 221" in the vertical portion to reach the pixel a at the corner, and then moves to the horizontal portion to " 00
… ” The pixels defining the right angle in this figure are the last two pixels b and c of the vertical part and the first pixel d of the horizontal part
It is. These chain codes are "210", and when this combination occurs in the chain code string, it immediately turns out that they are concave right-angle portions that open to the lower right. Here, a change is made to the chain code so that the pixel a at the corner is included. FIG. 8 (b) shows the result of the change to the chain code. 1 "
To “2”, and a chain code “0” is given to the pixel a at the corner. This is the chain code set "21
This corresponds to an operation of changing “0” to “2200”.

Due to these chain code changes, the last pixel c of the vertical portion points to the corner pixel a, and the corner pixel a
Indicates the first pixel d in the horizontal part.

FIG. 9 (a) shows a concave right-angled portion which opens to the upper left, and the chain code advances to "..665" in the vertical portion to reach the pixel a at the corner, and then moves to the horizontal portion to "44".
… ” The pixels defining the right angle in this figure are the last two pixels b and c of the vertical part and the first pixel d of the horizontal part
It is. These chain cords are "654", and when this combination occurs in the chain of cords, it immediately turns out that they are concave right angles that open to the upper left. Here, a change is made to the chain code so that the pixel a at the corner is included. FIG. 9 (b) shows the result of the change to the chain code. 5 "
To “6”, and a chain code “4” is given to the pixel a at the corner. This is the chain code set "65
Corresponds to the operation of changing "4" to "6644".

Due to these chain code changes, the last pixel c of the vertical portion points to the corner pixel a, and the corner pixel a
Indicates the first pixel d of the vertical portion.

FIG. 10 (a) shows a concave right-angled portion that opens to the upper right, and the chain code advances to “... 443” at the vertical portion to reach the pixel a at the corner, and then moves to the horizontal portion to “22”.
… ” The pixels defining the right angle in this figure are the last two pixels b and c of the vertical part and the first pixel d of the horizontal part
It is. These chain cords are "432", and when this combination occurs in the chain of cords, it is immediately determined that they are concave right-angle portions that open to the upper right. Here, a change is made to the chain code so that the pixel a at the corner is included. FIG. 10 (b) shows the result of the change to the chain code. 3 "
To “4”, and the chain code “2” is given to the pixel a at the corner. This is the chain code set "43
Corresponds to the operation of changing "2" to "4422".

Due to these chain code changes, the last pixel c of the vertical portion points to the corner pixel a, and the corner pixel a
Indicates the first pixel d of the vertical portion.

The above is the processing of the boundary pixel on the outside of the figure. Next, the processing of the boundary pixel on the inside, that is, the hole will be described. No.
FIG. 12 (a) shows a state in which a chain code is attached to the inner boundary pixel, and the chain code is “000766654443222”.
1 ". Here, assuming that the end of the chain code string continues to the beginning of the chain code string, the chain code string at the concave right-angled portion has “076”, “654”, and “432” as in the case of the outer boundary pixel. ”And“ 210 ”. If the same processing is performed on the outer boundary pixels, the chain codes become “0066”, “6644”, “4422”, and “2200” (FIG. 8), and the pixels a ₁ , a ₂ , and a _{3 at the} corners are obtained. , with chains code is given to a _4, immediately preceding pixel _{c 1, c 2, c 3} , c
Chain code of ₄ is "7" → "0", "5" →
“6”, “3” → “4”, “1” → “2” are changed. As a result, a right-angled portion can be clearly expressed even for a hole.

In the above processing, the pixel value of "3 pixels" was used for the determination of the right-angled portion. However, a series of relatively fine right-angled portions, for example, a stepwise boundary in units of two pixels as shown in FIG. In some cases, it is preferable not to express as a continuation but express as a straight line l. In this case, the above-described determination may be performed only when a straight line having a predetermined length or more is continuous before or after at least one of the three pixels to be determined. For example, "076"
Is determined as a right angle portion only when one side of the right angle portion is 3 pixels or more, such as “0 076 6”, and converted to “000666”.

The embodiment in which the counterclockwise chain code is added to the outer boundary pixel and the counterclockwise chain code is added to the inner boundary pixel, but conversely, the clockwise chain code is added to the outer boundary pixel. In this case, a counterclockwise chain code is attached to the inner boundary pixel.

FIG. 13 (a) shows the same figure as FIG. 5 but with a clockwise chain code attached, and the set of chain codes defining the right angle is "234". By changing this to “2244” as shown in FIG. 13 (b), a sharp right angle portion is provided.

FIG. 14 (a) shows the same figure as FIG. 6 with a clockwise chain code attached, and the set of chain codes defining the right angle is "456". By changing this to "4466" as shown in FIG. 14 (b), a sharp right angle portion is provided.

FIG. 15 (a) shows the same figure as FIG. 9 but with a clockwise chain code added, and the set of chain codes defining the right angle is "012". By changing this to “0022” as shown in FIG. 15 (b), a sharp right angle portion is provided.

FIG. 16 (a) shows the same figure as FIG. 8 but with a clockwise chain code attached, and the set of chain codes defining the right angle is "670". By changing this to “6600” as shown in FIG. 16 (b), a sharp right angle portion is provided.

FIG. 17 shows the processing of holes in this embodiment. A chain code is attached to the inner boundary pixel in the opposite direction to the outer boundary pixel, that is, counterclockwise. 17th
As shown in Fig. (A), this chain code is "566670
0012223444 ". Assuming that the end of the chain code string continues to the beginning of the chain code string as in the first embodiment, the outer boundary pixels are similar to those shown in FIGS. Is "234", "4
56 ”,“ 012 ”, and“ 670 ”, which are“ 2244 ”and“ 44 ”.
By changing them to "66", "0022", and "6600", a clear expression of a right angle portion is performed in the same manner as in the first embodiment.

In this embodiment, as in the previous embodiment, the right angle is processed as a right angle only when the length of one side of the right angle is equal to or more than a certain value,
Conversely, it is needless to say that the processing as the right angle portion may not be performed when the value is equal to or less than the predetermined value.

Here, an example of a method of generating a chain code string will be described. When generating a chain code string, the first boundary pixel must first be found, but if the scanning direction is limited, the outer and inner first boundary pixels can be identified depending on the situation of surrounding pixels.

When the scanning direction is a normal scanning direction from left to right and from top to bottom, as shown in FIG. 19, a boundary pixel a having no pixels on the upper and left sides can be adopted as an outer first boundary pixel, As shown in FIG. 20, a boundary pixel a having a pixel at the lower left and having no pixel at the bottom can be adopted as the first boundary pixel.

If the first boundary pixel is found, as described above, the value of the chain code that can be taken by the next boundary pixel is limited to a certain range, so that the boundary pixel is searched in the counterclockwise or clockwise order. I do. Here, when a counterclockwise chain code is given to the outer boundary pixel, the search direction is also counterclockwise, and if the clock code is a clockwise chain code, the search direction is also clockwise. The generation of the chain code of the inner boundary pixel can be processed by the same algorithm as the outer boundary pixel. That is, if the chain code of the immediately preceding boundary pixel is k, and if k is an even number, the next boundary pixel is searched counterclockwise sequentially from the direction of k−1, and the direction in which the boundary pixel is first found is determined. If a chain code of the boundary pixel is used, a chain code in which the outer boundary pixel is counterclockwise is generated. When k is an odd number, the next boundary pixel is sequentially searched counterclockwise from the direction of k-2. In this algorithm, all chain codes can be generated by scanning the entire screen only once, and the efficiency is high.In addition, since it is possible to identify whether the boundary pixel is outside or inside, a figure is reproduced from the vectorized data, It is possible to obtain powerful information when painting a figure. Next, a case where a vector point is selected from a more general chain code string will be described.

When different chain codes are given one after another as shown in FIG. 21, complicated irregularities are generated graphically. To express this, all boundary pixels should be adopted as vector points. However, similarly, even when the chain code changes one after another, as shown in FIG. 22, when the chain code decreases by “1” to “5” and “4” (pixels a and b), That is, the chain code
When it changes to k, k-1, it may be better not to use the pixel of k-1. That is, the chain code sequence of k, k−1,... Means a figure in which a straight line of two or more pixels is displaced by one pixel, and the pixel c next to the pixel of k−1 (chain code “6”) If you adopt, erase the subtle recesses,
Vectorization can be performed while minimizing vector points. When this method is adopted, when a chain code k 'is k' ≠ k and k '≠ k-1 next to a certain chain code k, the pixel of k' is adopted as a vector point. This algorithm has a wide range of applications including the above-described algorithm in which a right angle of a convex is set as a vector point.

If k ′ = k−1 and k−1 follows (FIG. 23), the pixel b (5, 4, 4, 4, 4, Pixels changed to 4, 6 ) are defined as vector points. That is, in the chain code sequence of k, k−1, k−1,..., K−1, k ′, when k ′ ≠ k−1, the pixel of k ′ is adopted as a vector point.

Here, the continuation of a constant chain code graphically means a straight line, but it is clear that a graphic can be accurately reproduced by adopting pixels at both ends of the straight line as vector points. Fig. 24 shows the chain code "… 5,5,5,
A boundary pixel group in which a straight line of a chain code “6, 6...” Follows a straight line of a “5”, and the start point of the straight line of the chain code “5” is a pixel a, and the end point is a chain code of “6”
The pixel b has changed to. Here, the pixel a may not be adopted as a vector point depending on the situation of the previous pixel, but the pixel b is the end point of the straight line of the chain code “5” and the straight line of the chain code “6”. It is obvious that it should be adopted because it is the starting point. That is, when a continuous chain code is again followed by a continuous chain code, the pixel b in which the chain code has changed should be adopted as a vector point. FIG. 25 shows a case where a one-pixel concave portion exists after the straight line of the chain code "5". Similarly, the pixel a in which the chain code has changed becomes the bottom of the concave portion and can be adopted as a vector point.

However, as shown in FIG. 26, the chain code "5"
When only one “4” exists after the straight line of, that is, when k ′ ≠ k−1 in the chain code sequence of k, k, k,..., K−1, k ′, FIG. 23, the pixel a of k-1 is not adopted as a vector point and the pixel b of k '
Can be adopted as a vector point.

On the other hand, as shown in FIG. 27, when the straight line of “4” continues after the straight line of the chain code “5”, that is, k, k, k,..., K, k−1 , k−1,. , k−1, the first k−1 pixel b can be used as a vector point, as described with reference to FIG. The above is summarized as follows.

i) In a chain code string composed of different chain codes of k ₁ , k ₂ and k ₃ , k ₂ can be adopted as a vector point if k ₂ ≠ k ₁ -1. If k ₂ = k−1, k ₃ can be adopted as a vector point.

ii) k ₁ , k ₁ , k ₁ ,…, k ₁ , k ₂ , k ₃ (k ₁ ≠ k ₂ and k ₂ ≠ k ₃ and k ₃ ≠
In the chain code train of k _1), it may be adopted k ₂ ≠ k ₁ -1 if k ₂ as a vector point. If k ₂ = k ₁ −1, k ₃ can be adopted as the vector point.

iii) k ₁ , k ₂ , k ₂ , k ₂ ,…, k ₃ (k ₁ ≠ k ₂ and k ₂ ≠ k ₃ and k ₃ ≠
In the chain code sequence of k ₁ ), if k ₂ ≠ k ₁ −1, the first k ₂ can be adopted as a vector point.
If k ₂ = k ₁ −1, k ₃ can be adopted as the vector point.

iv) A chain code sequence of k ₁ , k ₁ , k ₁ ,..., k ₁ , k ₂ , k ₂ , k ₂ , k ₃ (k ₁ ≠ k ₂ and k ₂ ≠ k ₃ and k ₃ ≠ k ₁ ) In, the first k ₂ may be adopted as the vector point.

In addition to such algorithms, as exceptions to iii) and iv), if the following algorithm is adopted, accurate graphic reproduction can be performed while reducing the number of vector points.

v) FIG. 28 shows a figure in which a chain code string of “445” is repeatedly generated. As described above, when a chained combination of k and (k + 1) or (k-1) repeatedly occurs, it means a step-like figure having a fixed period, and these are straight lines shown in FIG. It can be expressed by l. Therefore, if only the pixels a and b at the top of the first and last steps of the stairs are used as vector points, a figure can be accurately represented with a minimum amount of data.

FIG. 30 is a figure having the reverse inclination of the figure of FIG. 28, a chain code string of “443” is repeatedly generated, and FIG. 31 is a figure having the opposite inclination of FIG. A chain code string of “001” is repeatedly generated. These can be similarly expressed by one straight line l, and the leading pixels of the first and last stages can be adopted as vector points.

The above description relates to a step-shaped figure having a gentle slope, but a step-shaped figure having a steep slope is as shown in FIGS.

FIG. 32 is a stepped figure in which a chain code string of “665” is repeatedly generated, FIG. 33 is a stepped figure in which a chain code string of “667” is repeatedly generated, and FIG. 34 is “223”.
Is a step-like figure in which the chain code sequence of
FIG. 35 is a step-like figure in which a chain code string of “221” is repeatedly generated. In these figures, when the boundary of the figure is upward (diagonally right upward or diagonally left upward), the pixel at the upper end of each stage should be set as a vector point. At that time, the pixel at the lower end of each stage should be the vector point.

 The above is summarized as follows.

When a set of k,..., k, k−1 chain code strings repeatedly occurs, the first “k” pixel (indicated by underlining) in the first and last chain code string sets is represented by a vector point. When a set of k,..., K, k + 1 chain code strings occurs repeatedly, the pixel of “k + 1” in the first and last chain code string sets is shown (underlined). Should be taken as the vector point.

These generalized algorithms can be applied to the inner circumference of a hole in the same way, and can be applied to the inner circumference of a counterclockwise hole as well. The same processing can be performed by reversing the code increase / decrease determination, and it goes without saying that the processing itself is also equivalent when a code equivalent to the chain code is used.

As described above, if the bent state of the outline of the figure is determined from the chain code or a code equivalent thereto and the vector points are extracted, vector data can be generated without the need for complicated angle calculations and the like. High quality figures can be reproduced as appropriate.

〔The invention's effect〕

As described above, the graphic vectorization method according to the present invention focuses on the fact that Freeman's chain code or a code equivalent thereto reflects the bent state of the outline of the graphic, and directly uses only such a code. Since the bent state is determined and a vector point is selected from the boundary pixel or a pixel in the vicinity thereof based on the determination, an excellent effect that vector data capable of reproducing a high-quality figure can be generated in a substantial processing time. Having.

[Brief description of the drawings]

FIG. 1 is a conceptual diagram showing a Freeman chain code, FIG. 2 is a conceptual diagram showing a state where a counterclockwise chain code is added to a specific figure, and FIG. 3 is a diagram in which two chain codes correspond to one pixel. FIG. 4 is a conceptual diagram showing an example, FIG. 4 is a conceptual diagram showing a convex portion, FIG.
FIG. 6 is a conceptual diagram showing a processing mode of a convex right angle portion, and FIGS.
FIG. 18 shows the processing of the right-angled part in more detail,
FIGS. 7 (a), 8 (a), 9 (a) and 10 (a) are conceptual diagrams showing a state in which a chain cord is attached to a concave right-angled portion in the first embodiment. FIGS. 7 (b), 8 (b), 9 (b), and 10 (b) are conceptual diagrams showing a chain cord processed according to the embodiment, and FIG. 11 shows an inclined right angle portion. FIG. 12 (a) is a conceptual diagram showing a state where a chain code is added to an inner boundary pixel according to the embodiment, and FIG. 12 (b) is a chain code of an inner boundary pixel processed according to the embodiment. FIG. 13 to FIG. 16 are conceptual diagrams showing the same graphic processing as in FIG. 7 to FIG. 10 according to the second embodiment, and FIG. 17 is an example of processing of inner boundary pixels according to the same embodiment. FIG. 18 is a conceptual diagram showing a fine stepwise boundary, FIG. 19 is a conceptual diagram showing a method of generating a chain code of outer boundary pixels, and FIG. 20 is an inner diagram. 21 to 28 show a more generalized processing method, and FIG. 21 is a conceptual diagram showing a graphic in which different chain codes exist one after another. , 22nd
FIG. 23 is a conceptual diagram showing a figure in which a certain chain code is followed by a chain code smaller by “1”, FIG. 23 is a conceptual diagram showing a straight portion having a deviation of 1 pixel or less at the start end, and FIG. FIG. 25 is a conceptual diagram showing a corner portion composed of a straight line, FIG. 25 is a conceptual diagram showing a concave portion of one pixel, FIG. 26 is a conceptual diagram showing a linear portion having a deviation of one pixel or less at the end, and FIG. FIG. 28 to FIG. 35 are conceptual diagrams showing a step portion having a constant period. a, b, b ₁ , b ₂ , b ₃ , c, c ₁ , c ₂ , c ₃ , c ₄ , c ₅ , d, e, a ₁ , a ₂ , a ₃ , a ₄ ……
Boundary pixel F ... Figure l, l '... Line.

Claims (1)

(57) [Claims] 1. A chain code of boundary pixels is generated in the order of tracing the boundary pixels of a figure, and k, (k
-1), (k-2) (k = 0 to 7; k is modulo 8), and if there is a continuation of three codes, this chain code is represented by k, k, (k-2), ( k-2), and a vectorization method of a figure using the first (k-2) as a vector point.